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Orders of magnitude (energy)
Orders of magnitude (energy)
Orders of magnitude (energy)
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This list compares various energies in joules (J), organized by order of magnitude.

Below 1 J

[edit]
List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
10−35 1×10−35 J Optical dipole potential measured in a tune-out experiment with ultracold metastable helium[1].
10−34 6.626×10−34 J Energy of a photon with a frequency of 1 hertz.[2][3], equivalent to 4.14×10−15 eV or, alternatively stated, One two-hundred-fifty-trillionth of one eV.)
8×10−34 J Average kinetic energy of translational motion of a molecule at the lowest temperature reached (38 picokelvin[4] as of 2021[5])
10−30 quecto- (qJ)
10−28 6.6×10−28 J Energy of a typical AM radio photon (1 MHz) (4×10−9 eV)[6]
10−27 ronto- (rJ)
10−24 yocto- (yJ) 1.6×10−24 J Energy of a typical microwave oven photon (2.45 GHz) (1×10−5 eV)[7][8]
10−23 2×10−23 J Average kinetic energy of translational motion of a molecule in the Boomerang Nebula, the coldest place known outside of a laboratory, at a temperature of 1 kelvin[9][10]
10−22 2–3000×10−22 J Energy of infrared light photons[11]
10−21 zepto- (zJ) 1.7×10−21 J 1 kJ/mol, converted to energy per molecule[12]
2.1×10−21 J Thermal energy in each degree of freedom of a molecule at 25 °C (kT/2) (0.01 eV)[13]
2.856×10−21 J By Landauer's principle, the minimum amount of energy required at 25 °C to change one bit of information
3–7×10−21 J Energy of a van der Waals interaction between atoms (0.02–0.04 eV)[14][15]
4.1×10−21 J The "kT" constant at 25 °C, a common rough approximation for the total thermal energy of each molecule in a system (0.03 eV)[16]
7–22×10−21 J Energy of a hydrogen bond (0.04 to 0.13 eV)[14][17]
10−20 4.5×10−20 J Upper bound of the mass–energy of a neutrino in particle physics (0.28 eV)[18][19]
10−19 1.602176634×10−19 J 1 electronvolt (eV) by definition. This value is exact as a result of the 2019 revision of SI units.[20]
3–5×10−19 J Energy range of photons in visible light (≈1.6–3.1 eV)[21][22]
3–14×10−19 J Energy of a covalent bond (2–9 eV)[14][23]
5–200×10−19 J Energy of ultraviolet light photons[11]
10−18 atto- (aJ) 1.78×10−18 J Bond dissociation energy for the carbon monoxide (CO) triple bond, alternatively stated: 1072 kJ/mol; 11.11eV per molecule.[24]

This is the strongest chemical bond known.

2.18×10−18 J Ground state ionization energy of hydrogen (13.6 eV)
10−17 2–2000×10−17 J Energy range of X-ray photons[11]
10−16
10−15 femto- (fJ) 3 × 10−15 J Average kinetic energy of one human red blood cell.[25][26][27]
10−14 1×10−14 J Sound energy (vibration) transmitted to the eardrums by listening to a whisper for one second.[28][29][30]
> 2×10−14 J Energy of gamma ray photons[11]
2.7×10−14 J Upper bound of the mass–energy of a muon neutrino[31][32]
8.2×10−14 J Rest mass–energy of an electron[33] (0.511 MeV)[34]
10−13 1.6×10−13 J 1 megaelectronvolt (MeV)[35]
2.3×10−13 J Energy released by a single event of two protons fusing into deuterium (1.44 megaelectronvolt MeV)[36]
10−12 pico- (pJ) 2.3×10−12 J Kinetic energy of neutrons produced by DT fusion, used to trigger fission (14.1 MeV)[37][38]
10−11 3.4×10−11 J Average total energy released in the nuclear fission of one uranium-235 atom (215 MeV)[39][40]
10−10 1.492×10−10 J Mass-energy equivalent of 1 Da[41] (931.5 MeV)[42]
1.503×10−10 J Rest mass–energy of a proton[43] (938.3 MeV)[44]
1.505×10−10 J Rest mass–energy of a neutron[45] (939.6 MeV)[46]
1.6×10−10 J 1 gigaelectronvolt (GeV)[47]
3×10−10 J Rest mass–energy of a deuteron[48]
6×10−10 J Rest mass–energy of an alpha particle[49]
7×10−10 J Energy required to raise a grain of sand by 0.1mm (the thickness of a piece of paper).[50]
10−9 nano- (nJ) 1.6×10−9 J 10 GeV[51]
8×10−9 J Initial operating energy per beam of the CERN Large Electron Positron Collider in 1989 (50 GeV)[52][53]
10−8 1.3×10−8 J Mass–energy of a W boson (80.4 GeV)[54][55]
1.5×10−8 J Mass–energy of a Z boson (91.2 GeV)[56][57]
1.6×10−8 J 100 GeV[58]
2×10−8 J Mass–energy of the Higgs Boson (125.1 GeV)[59]
6.4×10−8 J Operating energy per proton of the CERN Super Proton Synchrotron accelerator in 1976[60][61]
10−7 1×10−7 J ≡ 1 erg[62]
1.6×10−7 J 1 TeV (teraelectronvolt),[63] about the kinetic energy of a flying mosquito[64]
10−6 micro- (μJ) 1.04×10−6 J Energy per proton in the CERN Large Hadron Collider in 2015 (6.5 TeV)[65][66]
10−5
10−4 1.0×10−4 J Energy released by a typical radioluminescent wristwatch in 1 hour[67][68] (1 μCi × 4.871 MeV × 1 hr)
10−3 milli- (mJ) 3.0×10−3 J Energy released by a P100 atomic battery in 1 hour[69] (2.4 V × 350 nA × 1 hr)
10−2 centi- (cJ) 4.0×10−2 J Use of a typical LED for 1 second[70] (2.0 V × 20 mA × 1 s)
10−1 deci- (dJ) 1.1×10−1 J Energy of an American half-dollar falling 1 metre[71][72]

1 to 105 J

[edit]
List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
100 J 1 J ≡ 1 N·m (newton–metre)
1 J ≡ 1 W·s (watt-second)
1 J Kinetic energy produced as an extra small apple (~100 grams[73]) falls 1 meter against Earth's gravity[74]
1 J Energy required to heat 1 gram of dry, cool air by 1 degree Celsius[75]
1.4 J ≈ 1 ft·lbf (foot-pound force)[62]
4.184 J ≡ 1 thermochemical calorie (small calorie)[62]
4.1868 J ≡ 1 International (Steam) Table calorie[76]
8 J Greisen-Zatsepin-Kuzmin theoretical upper limit for the energy of a cosmic ray coming from a distant source[77][78]
101 deca- (daJ) 1×101 J Flash energy of a typical pocket camera electronic flash capacitor (100–400 μF @ 330 V)[79][80]
5×101 J The most energetic cosmic ray ever detected.[81] Most likely a single proton traveling only very slightly slower than the speed of light.[82]
102 hecto- (hJ) 1.25×102 J Kinetic energy of a regulation (standard) baseball (5.1 oz / 145 g)[83] thrown at 93 mph / 150 km/h (MLB average pitch speed).[84]
1.5×102 - 3.6×102 J Energy delivered by a biphasic external electric shock (defibrillation), usually during adult cardiopulmonary resuscitation for cardiac arrest.
3×102 J Energy of a lethal dose of X-rays[85]
3×102 J Kinetic energy of an average person jumping as high as they can[86][87][88]
3.3×102 J Energy to melt 1 g of ice[89]
> 3.6×102 J Kinetic energy of 800 gram[90] standard men's javelin thrown at > 30 m/s[91] by elite javelin throwers[92]
5–20×102 J Energy output of a typical photography studio strobe light in a single flash[93]
6×102 J Use of a 10-watt flashlight for 1 minute
7.5×102 J A power of 1 horsepower applied for 1 second[62]
7.8×102 J Kinetic energy of 7.26 kg[94] standard men's shot thrown at 14.7 m/s[citation needed] by the world record holder Randy Barnes[95]
8.01×102 J Amount of work needed to lift a man with an average weight (81.7 kg) one meter above Earth (or any planet with Earth gravity)
103 kilo- (kJ) 1.1×103 J ≈ 1 British thermal unit (BTU), depending on the temperature[62]
1.4×103 J Total solar radiation received from the Sun by 1 square meter at the altitude of Earth's orbit per second (solar constant)[96]
2.3×103 J Energy to vaporize 1 g of water into steam[97]
3×103 J Lorentz force can crusher pinch[98]
3.4×103 J Kinetic energy of world-record men's hammer throw (7.26 kg[99] thrown at 30.7 m/s[100] in 1986)[101]
3.6×103 J ≡ 1 W·h (watt-hour)[62]
4.2×103 J Energy released by explosion of 1 gram of TNT[62][102]
4.2×103 J ≈ 1 food Calorie (large calorie)
~7×103 J Muzzle energy of an elephant gun, e.g. firing a .458 Winchester Magnum[103]
8.5×103 J Kinetic energy of a regulation baseball thrown at the speed of sound (343 m/s = 767 mph = 1,235 km/h. Air, 20°C).[104]
9×103 J Energy in an alkaline AA battery[105]
104 1.7×104 J Energy released by the metabolism of 1 gram of carbohydrates[106] or protein[107]
3.8×104 J Energy released by the metabolism of 1 gram of fat[108]
4–5×104 J Energy released by the combustion of 1 gram of gasoline[109]
5×104 J Kinetic energy of 1 gram of matter moving at 10 km/s[110]
105 3×105 – 15×105 J Kinetic energy of an automobile at highway speeds (1 to 5 tons[111] at 89 km/h or 55 mph)[112]

106 to 1011 J

[edit]
List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
106 mega- (MJ) 1×106 J Kinetic energy of a 2 tonne[111] vehicle at 32 metres per second (115 km/h or 72 mph)[113]
1.2×106 J Approximate food energy of a snack such as a Snickers bar (280 food calories)[114]
3.6×106 J = 1 kWh (kilowatt-hour) (used for electricity)[62]
4.2×106 J Energy released by explosion of 1 kilogram of TNT[62][102]
6.1×106 J Kinetic energy of the 4 kg tungsten APFSDS penetrator after being fired from a 120mm KE-W A1 cartridge with a nominal muzzle velocity of 1740 m/s.[115][116]
8.4×106 J Recommended food energy intake per day for a moderately active woman (2000 food calories)[117][118]
9.1×106 J Kinetic energy of a regulation baseball thrown at Earth's escape velocity (First cosmic velocity ≈ 11.186 km/s = 25,020 mph = 40,270 km/h).[119]
107 1×107 J Kinetic energy of the armor-piercing round fired by the ISU-152 assault gun[120][citation needed]
1.1×107 J Recommended food energy intake per day for a moderately active man (2600 food calories)[117][121]
3.3×107 J Kinetic energy of a 23 lb projectile fired by the Navy's mach 8 railgun.[122]
3.7×107 J $1 of electricity at a cost of $0.10/kWh (the US average retail cost in 2009)[123][124][125]
4×107 J Energy from the combustion of 1 cubic meter of natural gas[126]
4.2×107 J Caloric energy consumed by Olympian Michael Phelps on a daily basis during Olympic training[127]
6.3×107 J Theoretical minimum energy required to accelerate 1 kg of matter to escape velocity from Earth's surface (ignoring atmosphere)[128]
9×107 J Total mass-energy of 1 microgram of matter (25 kWh)
108 1×108 J Kinetic energy of a 55 tonne aircraft at typical landing speed (59 m/s or 115 knots)[citation needed]
1.1×108 J ≈ 1 therm, depending on the temperature[62]
1.1×108 J ≈ 1 Tour de France, or ~90 hours[129] ridden at 5 W/kg[130] by a 65 kg rider[131]
7.3×108 J ≈ Energy from burning 16 kilograms of oil (using 135 kg per barrel of light crude)[citation needed]
109 giga- (GJ) 1×109 J Energy in an average lightning bolt[132] (thunder)
1.1×109 J Magnetic stored energy in the world's largest toroidal superconducting magnet for the ATLAS experiment at CERN, Geneva[133]
1.2×109 J Inflight 100-ton Boeing 757-200 at 300 knots (154 m/s)
1.4×109 J Theoretical minimum amount of energy required to melt a tonne of steel (380 kWh)[134][135]
2×109 J Energy of an ordinary 61 liter gasoline tank of a car.[109][136][137]
2×109 J Unit of energy in Planck units,[138] roughly the diesel tank energy of a mid-sized truck.
2.49×109 J Approximate kinetic energy carried by American Airlines Flight 11 at the moment of impact with WTC 1 on September 11, 2001.[139][140]
3×109 J Inflight 125-ton Boeing 767-200 flying at 373 knots (192 m/s)
3.3×109 J Approximate average amount of energy expended by a human heart muscle over an 80-year lifetime[141][142]
3.6×109 J = 1 MW·h (megawatt-hour)
4.2×109 J Energy released by explosion of 1 ton of TNT.
4.5×109 J Average annual energy usage of a standard refrigerator[143][144]
6.1×109 J ≈ 1 bboe (barrel of oil equivalent)[145]
1010 1.9×1010 J Kinetic energy of an Airbus A380 at cruising speed (560 tonnes at 511 knots or 263 m/s)
4.2×1010 J ≈ 1 toe (ton of oil equivalent)[145]
4.6×1010 J Yield energy of a Massive Ordnance Air Blast bomb, the second most powerful non-nuclear weapon ever designed[146][147]
7.3×1010 J Energy consumed by the average U.S. automobile in the year 2000[148][149][150]
8.6×1010 J ≈ 1 MW·d (megawatt-day), used in the context of power plants (24 MW·h)[151]
8.8×1010 J Total energy released in the nuclear fission of one gram of uranium-235[39][40][152]
9×1010 J Total mass-energy of 1 milligram of matter (25 MW·h)
1011 1.1×1011 J Kinetic energy of a regulation baseball thrown at lightning speed (120 km/s = 270,000 mph = 435,000 km/h).[153]
2.4×1011 J Approximate food energy consumed by an average human in an 80-year lifetime.[154]

1012 to 1017 J

[edit]
List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
1012 tera- (TJ) 1.85×1012 J Gravitational potential energy of the Twin Towers, combined, accumulated throughout their construction and released during the collapse of the complex.[155][156][157]
3.4×1012 J Maximum fuel energy of an Airbus A330-300 (97,530 liters[158] of Jet A-1[159])[160]
3.6×1012 J 1 GW·h (gigawatt-hour)[161]
4×1012 J Electricity generated by one 20-kg CANDU fuel bundle assuming ~29%[162] thermal efficiency of reactor[163][164]
4.2×1012 J Chemical energy released by the detonation of 1 kiloton of TNT[62][165]
6.4×1012 J Energy contained in jet fuel in a Boeing 747-100B aircraft at max fuel capacity (183,380 liters[166] of Jet A-1[159])[167]
1013 1.1×1013 J Energy of the maximum fuel an Airbus A380 can carry (320,000 liters[168] of Jet A-1[159])[169]
1.2×1013 J Orbital kinetic energy of the International Space Station (417 tonnes[170] at 7.7 km/s[171])[172]
1.20×1013 J Orbital kinetic energy of the Parker Solar Probe as it dives deep into the Sun's gravity well in December 2024, reaching a peak velocity of 430,000 mph.[173][174][175]
6.3×1013 J Yield of the Little Boy atomic bomb dropped on Hiroshima in World War II (15 kilotons)[176][177]
9×1013 J Theoretical total mass–energy of 1 gram of matter (25 GW·h) [178]
1014 1.8×1014 J Energy released by annihilation of 1 gram of antimatter and matter (50 GW·h)
3.75×1014 J Total energy released by the Chelyabinsk meteor.[179]
6×1014 J Energy released by an average hurricane per day[180]
1015 peta- (PJ) > 1015 J Energy released by a severe thunderstorm[181]
1×1015 J Yearly electricity consumption in Greenland as of 2008[182][183]
4.2×1015 J Energy released by explosion of 1 megaton of TNT[62][184]
1016 1×1016 J Estimated impact energy released in forming Meteor Crater[citation needed]
1.1×1016 J Yearly electricity consumption in Mongolia as of 2010[182][185]
6.3×1016 J Yield of Castle Bravo, the most powerful nuclear weapon tested by the United States[186]
7.9×1016 J Kinetic energy of a regulation baseball thrown at 99% the speed of light (KE = mc^2 × [γ-1], where the Lorentz factor γ ≈ 7.09).[187]
9×1016 J Mass–energy of 1 kilogram of matter[188]
1017 1.4×1017 J Seismic energy released by the 2004 Indian Ocean earthquake[189]
1.7×1017 J Total energy from the Sun that strikes the face of the Earth each second[190]
2.1×1017 J Yield of the Tsar Bomba, the most powerful nuclear weapon ever tested (50 megatons)[191][192]
2.552×1017 J Total energy of the 2022 Hunga Tonga–Hunga Haʻapai eruption[193][194]
4.2×1017 J Yearly electricity consumption of Norway as of 2008[182][195]
4.516×1017 J Energy needed to accelerate one ton of mass to 0.1c (~30,000 km/s)[196]
8.4x1017 J Estimated energy released by the eruption of the Indonesian volcano, Krakatoa, in 1883[197][198][199]

1018 to 1023 J

[edit]
List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
1018 exa- (EJ) 9.4×1018 J Worldwide nuclear-powered electricity output in 2023.[200][201]
1019 1×1019 J Thermal energy released by the 1991 Pinatubo eruption[202]
1.1×1019 J Seismic energy released by the 1960 Valdivia Earthquake[202]
1.2×1019 J Explosive yield of global nuclear arsenal[203] (2.86 Gigatons)
1.4×1019 J Yearly electricity consumption in the U.S. as of 2009[182][204]
1.4×1019J Yearly electricity production in the U.S. as of 2009[205][206]
5×1019 J Energy released in 1 day by an average hurricane in producing rain (400 times greater than the wind energy)[180]
6.4×1019 J Yearly electricity consumption of the world as of 2008[207][208]
6.8×1019 J Yearly electricity generation of the world as of 2008[207][209]
1020 1.4×1020 J Total energy released in the 1815 Mount Tambora eruption[210]
2.33×1020 J Kinetic energy of a carbonaceous chondrite meteor 1 km in diameter striking Earth's surface at 20 km/s.[211] Such an impact occurs every ~500,000 years.[212]
2.4×1020 J Total latent heat energy released by Hurricane Katrina[213]
5×1020 J Total world annual energy consumption in 2010[214][215]
6.2×1020 J World primary energy generation in 2023 (620 EJ).[216][217]
8×1020 J Estimated global uranium resources for generating electricity 2005[218][219][220][221]
1021 zetta- (ZJ) 6.9×1021 J Estimated energy contained in the world's natural gas reserves as of 2010[214][222]
7.0×1021 J Thermal energy released by the Toba eruption[202]
7.9×1021 J Estimated energy contained in the world's petroleum reserves as of 2010[214][223]
9.3×1021 J Annual net uptake of thermal energy by the global ocean during 2003-2018[224]
1022 1.2×1022J Seismic energy of a magnitude 11 earthquake on Earth (M 11)[225]
1.5×1022J Total energy from the Sun that strikes the face of the Earth each day[190][226]
1.94×1022J Impact event that formed the Siljan Ring, the largest impact structure in Europe[227]
2.4×1022 J Estimated energy contained in the world's coal reserves as of 2010[214][228]
2.9×1022 J Identified global uranium-238 resources using fast reactor technology[218]
3.9×1022 J Estimated energy contained in the world's fossil fuel reserves as of 2010[214][229]
4.0×1022 J Mass-energy equivalent of the International Space Station (ISS), weighing around 450 tons.[230][231]
8.03×1022 J Total energy of the 2004 Indian Ocean earthquake[232]
1023 1.5×1023 J Total energy of the 1960 Valdivia earthquake[233]
2.2×1023 J Total global uranium-238 resources using fast reactor technology[218]
3×1023 J The energy released in the formation of the Chicxulub Crater in the Yucatán Peninsula[234]

Over 1024 J

[edit]

List of orders of magnitude for energy
Factor (joules) SI prefix Value Item
1024 yotta- (YJ) 2.31×1024 J Total energy of the Sudbury impact event[235]
2.69×1024 J Rotational energy of Venus, which has a sidereal period of (-)243 Earth days.[236][237][238] This incredibly anomalous value derives its origin from the deceleration of rotation by atmospheric tides from the Sun.[239]
3.8×1024 J Radiative heat energy released from the Earth's surface each year[202]
5.5×1024 J Total energy from the Sun that strikes the face of the Earth each year[190][240]
1025 4×1025 J Total energy of the Carrington Event in 1859[241]
1026 >1026J Estimated energy of early Archean asteroid impacts[242]
3.2×1026 J Bolometric energy of Proxima Centauri's superflare in March 2016 (10^33.5 erg). In one year, potentially five similar superflares erupts from the surface of the red dwarf.[243]
3.828×1026 J Total radiative energy output of the Sun per second[244], as defined by the IAU.[245]
1027 ronna- (RJ) 1×1027 J Estimated energy released by the impact that created the Caloris basin on Mercury.[246]
1×1027 J Upper limit of the most energetic solar flares possible (X1000)[247]
5.19×1027 J Thermal input necessary to evaporate all surface water on Earth.[248][249][250] Note that the evaporated water still remains on Earth, merely in vapor form.
4.2×1027 J Kinetic energy of a regulation baseball thrown at the speed of the Oh-My-God particle, itself a cosmic ray proton with the kinetic energy of a baseball thrown at 60 mph (~50 J).[251]
1028 3.8×1028 J Kinetic energy of the Moon in its orbit around the Earth (counting only its velocity relative to the Earth)[252][253]
7×1028 J Total energy of the stellar superflare from V1355 Orionis[254][255]
1029 2.1×1029 J Rotational energy of the Earth[256][257][258]
1030 quetta-(QJ) 1.79×1030 J Rough estimate of the gravitational binding energy of Mercury.[259]
1031 2×1031 J The Theia Impact, the most energetic event ever in Earth's history[260][261]
3.3×1031J Total energy output of the Sun each day[244][262]
1032 1.71×1032 J Gravitational binding energy of the Earth[263]
3.10×1032 J Yearly energy output of Sirius B, the ultra-dense and Earth-sized white dwarf companion of Sirius, the Dog Star. It has a surface temperature of about 25,200 K.[264]
1033 2.7×1033 J Earth's kinetic energy at perihelion in its orbit around the Sun[265][266]
1034 1.2×1034 J Total energy output of the Sun each year[244][267]
1035 3.5×1035 J The most energetic stellar superflare to date (V2487 Ophiuchi)[268]
1038 7.53×1038 J Baryonic (ordinary) mass-energy contained in a volume of one cubic light-year, on average.[269][270]
1039   2–5×1039 J Energy of the giant flare (starquake) released by SGR 1806-20[271][272][273]
6.60×1039 J  Theoretical total mass–energy of the Moon[274][275]
1040   1.61×1040 J Baryonic mass-energy contained in a volume of one cubic parsec, on average.[270][276]
1041 2.28×1041 J Gravitational binding energy of the Sun[277]
5.37×1041 J Mass–energy equivalent of the Earth[278][279]
1043 5×1043 J Total energy of all gamma rays in a typical gamma-ray burst if collimated[280][281]
>1043 J Total energy in a typical fast blue optical transient (FBOT)[282]
1044 ~1044 J Average value of a Tidal Disruption Event (TDE) in optical/UV bands[283]
~1044 J Estimated kinetic energy released by FBOT CSS161010[284]
~1044 J Total energy released in a typical supernova,[285][286] sometimes referred to as a foe.
1.23×1044 J Approximate lifetime energy output of the Sun.[287][288]
3×1044 J Total energy of a typical gamma-ray burst if collimated[285]
5.8 × 1044 J Kinetic energy of the star S2 as it made its closest approach to Sagittarius A*, the galactic center SMBH, at 7,650 km/s on May 2018.[289][290]
1045 ~1045 J Estimated energy released in a hypernova and pair instability supernova[291]
1045 J Energy released by the energetic supernova, SN 2016aps[292][293]
1.7-1.9×1045J Energy released by hypernova ASASSN-15lh[294]
2.3×1045 J Energy released by the energetic supernova PS1-10adi[295][296]
>1045 J Estimated energy of a magnetorotational hypernova[297]
>1045 J Total energy (energy in gamma rays+relativistic kinetic energy) of hyper-energetic gamma-ray burst if collimated[298][299][300][301][302]
1046 >1046 J Estimated energy in theoretical quark-novae[303]
~1046 J Upper limit of the total energy of a supernova[304][305]
1.5×1046 J Total energy of the most energetic optical non-quasar transient, AT2021lwx[306]
1047 1045-47 J Estimated energy of stellar mass rotational black holes by vacuum polarization in an electromagnetic field[307][308]
1047 J Total energy of a very energetic and relativistic jetted Tidal Disruption Event (TDE)[309]
~1047 J Upper limit of collimated- corrected total energy of a gamma-ray burst[310][311][312]
1.8×1047 J Theoretical total mass–energy of the Sun[313][314]
5.4×1047 J Mass–energy emitted as gravitational waves during the merger of two black holes, originally about 30 Solar masses each, as observed by LIGO (GW150914)[315]
8.6×1047 J Mass–energy emitted as gravitational waves during the most energetic black hole merger observed until 2020 (GW170729)[316]
8.8×1047 J GRB 080916C – formerly the most powerful gamma-ray burst (GRB) ever recorded – total/true[317] isotropic energy output estimated at 8.8 × 1047 joules (8.8 × 1054 erg), or 4.9 times the Sun's mass turned to energy[318]
1048 1048 J Estimated energy of a supermassive Population III star supernova, denominated "General Relativistic Instability Supernova."[319][320]
~1.2×1048 J Approximate energy released in the most energetic black hole merging to date (GW190521), which originated the first intermediate-mass black hole ever detected[321][322][323][324][325]
1.2–3×1048 J GRB 221009A – the most powerful gamma-ray burst (GRB) ever recorded – total/true[317][326] isotropic energy output estimated at 1.2–3 × 1048 joules (1.2–3 × 1055 erg)[327][328][329]
1050 ≳1050 J Upper limit of isotropic energy (Eiso) of Population III stars Gamma-Ray Bursts (GRBs).[330]
1053 >1053 J Mechanical energy of very energetic so-called "quasar tsunamis"[331][332]
6×1053 J Total mechanical energy or enthalpy in the powerful AGN outburst in the RBS 797[333]
7.65×1053 J Mass-energy of Sagittarius A*, Milky Way's central supermassive black hole[334][335]
1054 3×1054 J Total mechanical energy or enthalpy in the powerful AGN outburst in the Hercules A (3C 348)[336]
1055 >1055 J Total mechanical energy or enthalpy in the powerful AGN outburst in the MS 0735.6+7421,[337] Ophiucus Supercluster Explosion[338] and supermassive black holes mergings[339][340]
1057 ~1057 J Estimated rotational energy of M87 SMBH and total energy of the most luminous quasars over Gyr time-scales[341][342]
~2×1057 J Estimated thermal energy of the Bullet Cluster of galaxies[343]
7.3×1057 J Mass-energy equivalent of the ultramassive black hole TON 618, an extremely luminous quasar / active galactic nucleus (AGN).[344][345]
1058 ~1058 J Estimated total energy (in shockwaves, turbulence, gases heating up, gravitational force) of galaxy clusters mergings[346]
4×1058 J Visible mass–energy in our galaxy, the Milky Way[347][348]
1059 1×1059 J Total mass–energy of our galaxy, the Milky Way, including dark matter and dark energy[349][350]
1.4×1059 J Mass-energy of the Andromeda galaxy (M31), ~0.8 trillion solar masses.[351][352]
1062 1–2×1062 J Total mass–energy of the Virgo Supercluster including dark matter, the Supercluster which contains the Milky Way[353]
1066 1.207×1066 J Average mass-energy of ordinary matter contained within one cubic gigaparsec in the observable universe.[354]
1070 1.462×1070 J Rough estimate of total mass–energy of ordinary matter (atoms; baryons) present in the observable universe.[355][356][270]
1071 3.177×1071 J Rough estimate of total mass-energy within our observable universe, accounting for all forms of matter and energy.[357][270]

SI multiples

[edit]
SI multiples of joule (J)
Submultiples Multiples
Value SI symbol Name Value SI symbol Name
10−1 J dJ decijoule 101 J daJ decajoule
10−2 J cJ centijoule 102 J hJ hectojoule
10−3 J mJ millijoule 103 J kJ kilojoule
10−6 J μJ microjoule 106 J MJ megajoule
10−9 J nJ nanojoule 109 J GJ gigajoule
10−12 J pJ picojoule 1012 J TJ terajoule
10−15 J fJ femtojoule 1015 J PJ petajoule
10−18 J aJ attojoule 1018 J EJ exajoule
10−21 J zJ zeptojoule 1021 J ZJ zettajoule
10−24 J yJ yoctojoule 1024 J YJ yottajoule
10−27 J rJ rontojoule 1027 J RJ ronnajoule
10−30 J qJ quectojoule 1030 J QJ quettajoule

The joule is named after James Prescott Joule. As with every SI unit named after a person, its symbol starts with an upper case letter (J), but when written in full, it follows the rules for capitalisation of a common noun; i.e., joule becomes capitalised at the beginning of a sentence and in titles but is otherwise in lower case.

See also

[edit]

Notes

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Orders of magnitude (energy)

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Orders of magnitude (energy) classify quantities on a , where each successive order represents a tenfold increase or decrease, typically measured in joules (J), the () derived unit for equivalent to one meter squared per second squared. This framework enables concise comparisons across vast disparities, from the minuscule energies of atomic bonds (~10^{-19} J for a ) to the immense outputs of astrophysical phenomena (~10^{45} J for a explosion). Such scales are fundamental in physics for contextualizing natural and human-induced processes, spanning quantum to cosmological domains. At the lowest orders, energies like the ionization of (~10^{-18} J or 13.6 eV) govern molecular stability, while human-scale activities involve ~10^4 J per or ~10^7 J in daily caloric intake. Larger magnitudes encompass geophysical events, such as a magnitude 6.5 earthquake releasing ~10^{14} J, or global , with the U.S. annual use at ~10^{20} J (as of 2023). Extreme scales highlight cosmic scales, including Earth's total reserves (~10^{23} J) and comet impacts (~10^{23} J), underscoring the utility of orders of magnitude in estimating and approximating without precise values.

Fundamentals

Units of Energy

Energy in physics is defined as a physical quantity that represents the capacity of a system to perform work, where work is the transfer of energy resulting from a force acting over a distance. This concept emerged prominently in the 19th century through experiments by James Prescott Joule, who demonstrated the equivalence between mechanical work and thermal energy, laying the groundwork for the law of conservation of energy. Joule's paddle-wheel experiments in the 1840s showed that a fixed amount of mechanical energy could produce a predictable quantity of heat, establishing energy as a conserved quantity transferable between forms such as mechanical, thermal, and electrical. The (SI) designates the joule (J) as the base unit for energy, defined as the work done by a force of one newton acting over a distance of one meter, or equivalently expressed in base SI units as 1 J=1 kg⋅m2/s21 \, \mathrm{J} = 1 \, \mathrm{kg \cdot m^2 / s^2}. This derived unit also equals one watt-second, since power in watts (joules per second) integrated over one second yields one joule, making it suitable for both mechanical and electrical contexts. For everyday mechanical applications, such as lifting an object or accelerating a vehicle, the joule provides a convenient scale; for instance, the of a 1 kg moving at 1 m/s is 0.5 J. Other units are preferred for specific domains due to scale or tradition. The measures energy at microscopic levels, defined as the kinetic energy gained by an accelerating through a potential difference of one volt, with 1 eV=1.602×10−19 J1 \, \mathrm{eV} = 1.602 \times 10^{-19} \, \mathrm{J}; conversion follows E(eV)=E(J)/1.602×10−19E(\mathrm{eV}) = E(\mathrm{J}) / 1.602 \times 10^{-19}. It is commonly used in atomic and , like describing electron transitions in atoms. In thermal contexts, the thermochemical quantifies heat as the to raise 1 gram of water by 1°C, exactly 1 cal=4.184 J1 \, \mathrm{cal} = 4.184 \, \mathrm{J}. Engineering applications often employ the , the heat to raise 1 pound of water by 1°F, where the International Table BTU equals approximately 1055 J. For mechanical work in imperial systems, the foot-pound force (ft·lbf) represents the work of one pound-force over one foot, equivalent to about 1.356 J. Unit selection depends on context: electronvolts for subatomic processes, joules for macroscopic , calories or BTUs for , and foot-pounds for traditional mechanical calculations.

SI Prefixes and Multiples

The SI prefixes form a standardized decimal system for denoting multiples and submultiples of SI units by powers of 10, allowing concise representation of quantities spanning over 48 orders of magnitude from the subatomic to the cosmic scale. These prefixes are affixed to base units such as the joule (J), the SI unit of , to create derived units like millijoule (mJ) or petajoule (PJ). The system ensures uniformity in scientific communication by avoiding cumbersome in many cases, though both approaches coexist for very large or small values. The original set of SI prefixes was adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960 as part of the establishment of the (SI). Subsequent expansions addressed growing needs in fields like and ; notably, the prefixes zetta- and yotta- for multiples, along with zepto- and yocto- for submultiples, were added by the 19th CGPM in 1991 to extend the range to 10^{24} and 10^{-24}, respectively. Further extensions were approved by the 27th CGPM in 2022, adding ronna- and quetta- for 10^{27} and 10^{30}, and ronto- and quecto- for 10^{-27} and 10^{-30}, to accommodate even larger and measurement scales in modern . This development reflected advances in measurement precision and the handling of extreme scales in physics. The full list of SI prefixes relevant to energy scaling, from the smallest to the largest, is presented below:
FactorPrefixSymbolPower of 10
10^{-30}quecto-q-30
10^{-27}ronto-r-27
10^{-24}yocto-y-24
10^{-21}zepto-z-21
10^{-18}atto-a-18
10^{-15}femto-f-15
10^{-12}pico-p-12
10^{-9}nano-n-9
10^{-6}micro-µ-6
10^{-3}milli-m-3
10^{-2}centi-c-2
10^{-1}deci-d-1
10^{1}deca-da1
10^{2}hecto-h2
10^{3}kilo-k3
10^{6}mega-M6
10^{9}giga-G9
10^{12}tera-T12
10^{15}peta-P15
10^{18}exa-E18
10^{21}zetta-Z21
10^{24}yotta-Y24
10^{27}ronna-R27
10^{30}quetta-Q30
In energy contexts, these prefixes enable the description of phenomena from quantum to astronomical scales. For instance, 1 zeptojoule (zJ) = 10−2110^{-21} J represents energies detectable in quantum microwave experiments, where limits are set by vacuum fluctuations in superconducting circuits. At the opposite extreme, 1 yottajoule (YJ) = 102410^{24} J corresponds to scales in planetary gravitational binding energies; for example, the binding energy of Earth is approximately 2.49×10322.49 \times 10^{32} J, or 2.49×1082.49 \times 10^{8} YJ, illustrating how prefixes handle such vast multiples. Rules for using SI prefixes with energy units emphasize clarity and consistency: prefixes are attached directly to the unit (e.g., kJ for kilojoule), but compound prefixes (e.g., millimicro-) are prohibited, and only one prefix per unit is allowed. They should not be combined with non-SI units like the or , though conversions are standard; instead, serves as an alternative for extremes, such as 101810^{18} J versus 1 EJ (exajoule). These conventions, outlined in official SI guides, prevent errors in interdisciplinary work. A common pitfall in large-scale energy discussions, particularly in , is the occasional use of non-SI units like the "foe" (short for 10^{51} ergs), which equals approximately 104410^{44} J and quantifies energy releases; such terms should be converted to SI prefixes (e.g., 1 foe = 10^{20} YJ) to maintain standardization and avoid ambiguity.

Low-Energy Scales

Below 1 J

The sub-joule regime encompasses energies from approximately 10−3410^{-34} J, corresponding to the fundamental quantum of action given by Planck's constant for frequencies around 1 Hz (E=hνE = h \nu, where h≈6.626×10−34h \approx 6.626 \times 10^{-34} J s), up to just below 1 J. This scale is dominated by quantum mechanical phenomena, where energies are expressed using SI prefixes such as atto- (10−1810^{-18}), femto- (10−1510^{-15}), pico- (10−1210^{-12}), nano- (10−910^{-9}), and micro- (10−610^{-6}) joules. These levels are far below macroscopic perception and govern atomic, molecular, and subatomic processes, with the (1 eV ≈1.602×10−19\approx 1.602 \times 10^{-19} J) serving as a convenient subunit for many such measurements. At the thermal scale, the average per degree of freedom for particles at (300 K) is given by kTkT, where [k](/page/K)=1.381×10−23[k](/page/K) = 1.381 \times 10^{-23} J/K is the , yielding kT≈4.14×10−21kT \approx 4.14 \times 10^{-21} J. This energy sets the benchmark for molecular vibrations, , and in gases and liquids, influencing reaction rates and phase transitions in chemical systems. In biological contexts, it represents the scale for random that drive processes like and enzyme activity. Chemical bond energies fall in the range of 10−2010^{-20} to 10−1810^{-18} J per molecule. For instance, a typical hydrogen bond, such as those in water, has an energy of about 20 kJ/mol, or roughly 3.3×10−203.3 \times 10^{-20} J per bond when divided by Avogadro's number (NA≈6.022×1023N_A \approx 6.022 \times 10^{23} mol−1^{-1}). These weak intermolecular forces, about 1/20th the strength of covalent bonds, enable structures like DNA base pairing and liquid water's cohesion. In energy transduction, the hydrolysis of one adenosine triphosphate (ATP) molecule releases approximately 30 kJ/mol under cellular conditions, equating to about 5×10−205 \times 10^{-20} J per event, powering molecular motors and ion pumps in living cells. Quantum-specific examples highlight even finer scales. A visible (wavelength ≈500\approx 500 nm) carries energy E=hc/λ≈4×10−19E = hc / \lambda \approx 4 \times 10^{-19} J, where hh is Planck's constant, cc is the , and λ\lambda is the ; this spans 2.5×10−192.5 \times 10^{-19} J for [to 5](/page/TO−5)×10−195](/page/TO-5) \times 10^{-19} J for violet. In quantum systems like the model for molecular vibrations, the —the ground-state minimum—is 12ℏω\frac{1}{2} \hbar \omega, where ℏ=h/2π\hbar = h / 2\pi and ω\omega is the ; for a like HCl, this is approximately 3×10−203 \times 10^{-20} J, preventing absolute rest even at . At ultralow energies, superconducting qubits operate near 10−2410^{-24} J, corresponding to transition frequencies of 3–10 GHz (E=hfE = h f), enabling quantum coherence for computing applications. Neutrino detection experiments, such as those in , register interaction energies around 10−1310^{-13} J (a few MeV recoils from solar or atmospheric neutrinos), probing weak nuclear forces despite the particles' high total energies. These examples underscore how sub-joule scales reveal the probabilistic of quantum phenomena, from fluctuations to coherent superpositions.

1 J to 10⁵ J

The range of 1 J to 10⁵ J encompasses energies encountered in everyday human activities, simple mechanical tasks, and small-scale electrical or thermal processes. For instance, the gravitational potential energy required to lift a 100 g apple approximately 1 m against Earth's is about 1 J. Similarly, the imparted to a small object, such as an apple of 10 g dropping from a height of 10 m, reaches roughly 1 J just before impact, illustrating basic gravitational conversion in daily scenarios. Mechanical examples in this scale include the of a thrown , which is approximately 100 J when pitched at typical speeds around 40 m/s with a of 0.145 kg. A solid punch delivers kinetic energy on the order of 100 J, depending on the force and velocity involved in the motion of the arm and fist. Biologically, a single in the , such as flexing a bicep, involves about 100 J of mechanical work, derived from to enable movement. Electrical and thermal energies at this magnitude appear in common devices; a typical AA alkaline battery stores around 10⁴ J of chemical energy, convertible to electrical output for powering small gadgets. Charging a battery, with a capacity of about 3000 mAh at 3.7 V, requires roughly 4 × 10⁴ J. An LED camera flash on a consumes approximately 1 J per burst to produce a brief illumination. Wearable fitness trackers, with batteries holding 3000–6000 J, operate within this range to monitor activities over hours. Thermally, operating a 100 W incandescent bulb for 10 minutes dissipates about 6 × 10⁴ J as heat and light. In biological contexts, a segment of the human —such as the energy expended in one hour of rest for an —totals around 3 × 10⁵ J, supporting vital functions like circulation and respiration, though portions align with lower values in this scale for specific processes. , like a small 10 g serving of (providing about 200 kcal total for a full bar scaled down), yields roughly 10⁵ J when metabolized, fueling short bursts of activity. A 100 Wh rechargeable battery, common in portable tools, stores up to 3.6 × 10⁵ J, bridging personal-scale applications. These examples highlight how such energies underpin perceptible actions without entering larger industrial domains.

Medium-Energy Scales

10⁶ J to 10¹¹ J

This energy range, spanning 10⁶ J (1 MJ) to 10¹¹ J (100 GJ), represents scales relevant to engineered human activities, including moderate explosives, vehicle propulsion, and industrial operations that power modern infrastructure. Explosive events in this range provide a benchmark for destructive potential in and applications. The detonation of 1 kg of trinitrotoluene (TNT) releases 4.184 × 10⁶ J, serving as the standard unit for measuring explosive yields. A typical fragmentation hand , such as the U.S. M67 containing 180 g of (a mix of and TNT with approximately 1.35 times that of TNT), yields about 10⁶ J upon explosion, sufficient to fragment the casing and injure personnel within a 5-meter radius. In transportation, these energies correspond to or electrical inputs for accelerating and propelling vehicles. A standard automobile holding 30 L of stores roughly 9.6 × 10⁸ J, based on gasoline's of 32 MJ/L, enabling hundreds of kilometers of travel depending on . For , the from consumed during the takeoff phase of a (approximately 200-300 kg at 43 MJ/kg) totals around 10¹⁰ J, accounting for the high needed to overcome drag and lift a 50-ton to cruising altitude. Electric rail systems operate at lower scales per event; accelerating a 100-ton commuter from rest to 100 km/h requires about 4 × 10⁷ J of , though total electrical input including inefficiencies reaches 10⁸ J. Industrial processes in this band highlight energy-intensive manufacturing and emerging technologies. Producing one ton of steel in an electric arc furnace minimill consumes approximately 2 × 10⁹ J, primarily from electricity (around 500-700 kWh/ton) to melt scrap metal, contrasting with higher inputs for traditional blast furnaces. Renewable energy generation, such as a 2 MW onshore wind turbine operating at 30% capacity factor, yields about 5 × 10¹⁰ J daily, equivalent to powering several hundred households. Large data centers, like those supporting cloud computing, use around 9 × 10¹¹ J per day for a facility with 10 MW average demand, driven by servers and cooling systems. In experimental fusion research, the National Ignition Facility (NIF) delivers about 3.5 × 10⁸ J of electrical energy to its lasers for a pre-ignition test shot, compressing fuel pellets to initiate fusion reactions (with post-2022 ignition experiments achieving up to 2 MJ fusion yield as of 2023).

10¹² J to 10¹⁷ J

This energy range, spanning terajoules (TJ) to hundreds of petajoules (PJ), represents scales where human-engineered systems intersect with natural geophysical processes, including substantial infrastructural outputs, controlled nuclear reactions, and catastrophic events like earthquakes and eruptions. These magnitudes highlight the transition from everyday cumulative consumption to planet-altering releases, often involving mechanisms that store or convert vast amounts of into kinetic, thermal, or electrical forms. Understanding this band underscores the fragility of Earth's systems and the engineered controls needed for harnessing such power safely. At the lower end, around 10¹² J, the annual total consumption of an average —encompassing , heating, transportation fuels, and other uses—totals approximately 7.4 × 10¹¹ J as of 2023, placing it firmly in this when considering typical family sizes of 2.5 persons. Similarly, a magnitude 5 on the unleashes roughly 2.8 × 10¹² J of seismic energy, equivalent to the kinetic release from fault slippage over kilometers, sufficient to cause localized structural damage but rarely widespread devastation. This energy is calculated using the empirical relation log₁₀ E = 5.24 + 1.44 M_w, where E is in joules and M_w is the magnitude, emphasizing how logarithmic scales capture the in geophysical impacts. Nuclear fission processes dominate mid-range examples, with the complete fission of 1 kg of liberating about 8 × 10¹³ J through the release of approximately 200 MeV per fission event across roughly 2.56 × 10²⁴ atoms. This value assumes ideal conditions, where each fission converts a of the nucleus's to energy via E = mc², yielding a density orders of magnitude higher than chemical fuels. At larger scales, the 1986 Chernobyl accident involved a reactor core with fuel equivalent to roughly 4 tons of , whose total release approached 10¹⁷ J, though only a was realized in the uncontrolled power excursion and subsequent meltdown, leading to widespread thermal and radioactive dispersal. Geophysical events extend this scale, as a small volcanic eruption—classified under (VEI) 2–3—involves the explosive release of about 10¹² J, primarily from and conversion during ejection of and lava volumes on the order of 0.01–0.1 km³. Such events, like those at Strombolian vents, propel material to heights of hundreds of meters, with energy partitioned into kinetic blasts (often referenced briefly in TNT equivalents of 0.1–1 kt for scaling) and heat, influencing regional climates through injection. Large-scale infrastructure exemplifies harnessed energies in this range. The , a seminal hydroelectric facility, generates an average of 4.2 billion kWh annually as of recent records, equating to 1.5 × 10¹⁶ J of derived from in the Colorado River's flow. This output powers over 1.3 million homes, demonstrating efficient conversion via turbines where efficiency exceeds 90%, though it depends on variable water inflows affected by climate patterns. Comparably, the energy content of a very large crude carrier (VLCC) tanker's cargo—typically 250,000 metric tons of crude oil at 42 MJ/kg—totals around 10¹⁶ J, stored as for global transport and refining, underscoring the dependency in . Emerging climate mitigation efforts introduce additional contexts, particularly in models projecting net-zero pathways. For instance, capturing 10 Gt of CO₂ annually—a scale aligned with IPCC scenarios for mid-century decarbonization—requires roughly 10^{20} J of energy using advanced direct air capture technologies at 10 GJ per ton, factoring in thermal and electrical inputs for sorbent regeneration and compression. This estimate draws from process efficiencies improving toward 1–2 GJ/ton but currently higher due to thermodynamic minima and parasitic loads, highlighting the trade-offs in scaling carbon dioxide removal (CDR) without exacerbating energy demands. Recent extraterrestrial events provide bounded examples of uncontrolled impacts within this range. The 2013 , a 20-meter entering Earth's atmosphere at ~19 km/s, dissipated about 2 × 10¹⁵ J in an airburst explosion, equivalent to 500 kilotons of TNT and generating a shockwave that injured over 1,000 people and damaged structures across 200 km². Updated orbital analyses and data confirm this as one of the most energetic impacts since the , informing planetary defense models for near-Earth objects.

High-Energy Scales

10¹⁸ J to 10²³ J

The range of 10¹⁸ J to 10²³ J encompasses exajoules (EJ) to zettajoules (ZJ), representing immense scales typically associated with large-scale astronomical events and global geophysical phenomena, far exceeding terrestrial human activities but below the total outputs of stellar explosions. These energies highlight the transition from planetary to stellar influences, where kinetic impacts, radiative fluxes, and eruptive releases dominate natural processes. For context, this order surpasses the world's annual consumption of approximately 6.34 × 10²⁰ J in , equivalent to about 634 EJ, underscoring the vast disparity between human utilization and cosmic scales. In astronomical contexts, meteoroid impacts provide key examples at the lower end of this range. A 1-km-diameter meteor striking Earth's atmosphere at 20 km/s carries on the order of 2 × 10²⁰ J, calculated from its of roughly 10¹² kg and velocity, sufficient to form craters tens of kilometers wide and cause regional devastation. Such events occur approximately every 500,000 years, releasing comparable to millions of nuclear bombs but localized to the impact site. Larger impacts, like the Chicxulub event 66 million years ago, involved an about 10-15 km in diameter, liberating approximately 3 × 10²³ J of upon collision, triggering mega-earthquakes, tsunamis, and global climate disruption that contributed to the Cretaceous-Paleogene extinction. This , equivalent to billions of times the annual global use, vaporized rock and ejected material into the , blocking sunlight for years. Solar phenomena also fall within this scale, particularly the energy intercepted by Earth from the Sun. The planet receives about 1.5 × 10²² J of solar energy daily, derived from the total solar power intercepted by Earth of 1.74 × 10¹⁷ W (from the solar constant of approximately 1366 W/m² averaged over Earth's cross-sectional area of about 1.275 × 10¹⁴ m²) and a 24-hour period, powering weather patterns, ocean currents, and the biosphere. Annually, this totals around 5.5 × 10²⁴ J incident, with about 70% absorbed, but daily portions align with the upper end of this range. Solar flares, explosive magnetic reconnections in the Sun's corona, release energies from 10²⁰ J for minor C-class events to 10²⁵ J for extreme X-class flares, with typical large flares around 10²⁴-10²⁵ J in electromagnetic radiation and particles, potentially disrupting Earth's ionosphere and satellites when directed planetward. These events convert stored magnetic energy into heat, light, and accelerated particles, illustrating the Sun's role in delivering portioned high-energy bursts to the heliosphere. Gravitational interactions offer additional examples, though rarer. The formation of exoplanets involves accretion processes where protoplanetary disks dissipate gravitational potential energy as and , with total binding energies for Earth-like worlds around 10³² J but incremental accretion phases releasing subsets in the 10²⁰-10²³ J range per significant collision or merger event during assembly. Observations from missions like Kepler suggest such energies drive the thermal evolution of young exoplanets, influencing atmospheres and . Meanwhile, precursor activities to stellar events, such as mass ejections from unstable stars, can involve 10²¹-10²³ J, bridging to larger explosions without reaching full scales. These phenomena emphasize how gravitational and radiative processes at this magnitude shape planetary systems and interstellar media.

Above 10²⁴ J

Energies exceeding 10²⁴ joules represent the most extreme scales in the , encompassing cataclysmic stellar events, galactic structures, and the total content of the itself. These magnitudes dwarf human-engineered energies and even planetary-scale phenomena, illustrating the vast power inherent in , over cosmic timescales, and the fundamental mass- equivalence described by Einstein's equation E=mc2E = mc^2, where mm is in kilograms, cc is the (3×1083 \times 10^8 m/s), and EE is in joules. At these levels, energies are often estimated through astronomical observations and theoretical models, revealing processes that shape the universe's evolution. Supernova explosions, the explosive deaths of massive stars, release kinetic energies on the order of 10⁴⁴ joules, primarily from the rebound of shock waves against infalling material in a core-collapse event. This output, equivalent to the Sun's integrated over billions of years, propels at fractions of the and synthesizes heavy elements essential for planetary formation. Gamma-ray bursts (GRBs), brief and intense flashes from collapsing massive stars or merging compact objects, can unleash isotropic-equivalent energies up to approximately 10⁴⁷ joules, making them the most luminous events in the over short durations. The Sun's total energy output over its approximately 10-billion-year main-sequence lifetime amounts to about 10⁴⁴ joules, calculated from its average of 3.8 × 10²⁶ watts sustained for roughly 3 × 10¹⁷ seconds. On galactic scales, the of the , which holds its approximately 10¹² solar masses together against dispersion, is estimated at around 10⁵⁴ joules, derived from E≈GM2RE \approx \frac{GM^2}{R}, where GG is the , MM is the galaxy's total mass (including ), and RR is its characteristic radius of about 15 kiloparsecs. Recent (JWST) observations of early universe galaxies at redshifts greater than 10 reveal unexpectedly massive structures forming within 500 million years after the , with stellar masses up to 10¹⁰ solar masses implying rest-mass energies via E=mc2E = mc^2 on the order of 10⁵⁸ joules per galaxy, challenging models of rapid baryonic assembly and suggesting enhanced efficiencies. The observable universe's total rest-mass energy, encompassing baryonic matter, dark matter, and radiation, reaches approximately 10⁷¹ joules, computed from its estimated total mass of about 10⁵⁴ kilograms using E=mc2E = mc^2, with c2=9×1016c^2 = 9 \times 10^{16} m²/s². This mass includes roughly 1.5 × 10⁵³ kilograms of ordinary matter distributed across 10²³ and galaxies, augmented by contributions. , which drives the universe's accelerated expansion and constitutes about 68% of its energy budget, has a density of roughly 6 × 10^{-10} joules per cubic meter; integrated over the observable universe's volume of approximately 4 × 10^{80} cubic meters (a sphere of radius 46.5 billion light-years), its total is on the order of 10⁷¹ joules. , often associated with the and quantum field fluctuations, contributes similarly at this density, though theoretical predictions from vastly overestimate it compared to observations. Theoretical models of the singularity posit that the initial energy content within the observable 's comoving volume was equivalent to its current total , approximately 10⁷¹ joules, conserved through expansion in a flat universe dominated by and . This scale underscores the 's origin as a hot, dense state where all subsequent structures and energies trace back to this primordial release.

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