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Standard gravity
Standard gravity
Standard gravity
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The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity, is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as 9.80665 m/s2 (about 32.17405 ft/s2), denoted typically by ɡ0 (sometimes also ɡn, ɡe,[a] or simply ɡ). This value was established by the third General Conference on Weights and Measures (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration.[2][3] The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from the rotation of the Earth (but the latter is small enough to be negligible for most purposes); the total (the apparent gravity) is about 0.5% greater at the poles than at the Equator.[4][5]

Although the symbol ɡ is sometimes used for standard gravity, ɡ (without a suffix) can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on one's position on Earth (see Earth's gravity). The symbol ɡ should not be confused with G, the gravitational constant, or g, the symbol for gram. The ɡ is also used as a unit for any form of acceleration, with the value defined as above (see also: g-force).

The value of ɡ0 defined above is a nominal midrange value on Earth, originally based on the acceleration of a body in free fall at sea level at a geodetic latitude of 45°. Although the actual acceleration of free fall on Earth varies according to location, the above standard figure is always used for metrological purposes. In particular, since it is the ratio of the kilogram-force and the kilogram, its numeric value when expressed in coherent SI units is the ratio of the kilogram-force and the newton, two units of force.

History

[edit]

Already in the early days of its existence, the International Committee for Weights and Measures (CIPM) proceeded to define a standard thermometric scale, using the boiling point of water. Since the boiling point varies with the atmospheric pressure, the CIPM needed to define a standard atmospheric pressure. The definition they chose was based on the weight of a column of mercury of 760 mm. But since that weight depends on the local gravity, they now also needed a standard gravity. The 1887 CIPM meeting decided as follows:

The value of this standard acceleration due to gravity is equal to the acceleration due to gravity at the International Bureau (alongside the Pavillon de Breteuil) divided by 1.0003322, the theoretical coefficient required to convert to a latitude of 45° at sea level.[6]

All that was needed to obtain a numerical value for standard gravity was now to measure the gravitational strength at the International Bureau. This task was given to Gilbert Étienne Defforges of the Geographic Service of the French Army. The value he found, based on measurements taken in March and April 1888, was 9.80991(5) m⋅s−2.[7]

This result formed the basis for determining the value still used today for standard gravity. The third General Conference on Weights and Measures, held in 1901, adopted a resolution declaring as follows:

The value adopted in the International Service of Weights and Measures for the standard acceleration due to Earth's gravity is 980.665 cm/s2, value already stated in the laws of some countries.[8]

The numeric value adopted for ɡ0 was, in accordance with the 1887 CIPM declaration, obtained by dividing Defforges's result – 980.991 cm⋅s−2 in the cgs system then en vogue – by 1.0003322 while not taking more digits than are warranted considering the uncertainty in the result.

Conversions

[edit]
Conversions between common units of acceleration
Base value (Gal, or cm/s2) (ft/s2) (m/s2) (Standard gravity, g0)
1 Gal, or cm/s2 1 0.0328084 0.01 1.01972×10−3
1 ft/s2 30.4800 1 0.304800 0.0310810
1 m/s2 100 3.28084 1 0.101972
1 g0 980.665 32.1740 9.80665 1

See also

[edit]

Notes

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Standard gravity

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Standard gravity, also known as the standard acceleration due to gravity and denoted as gng_n or g0g_0, is a precisely defined representing the nominal magnitude of at Earth's surface under standard conditions, fixed at exactly 9.80665 m/s². This value provides a universal reference point in and , approximating the average experienced by objects in near while accounting for variations due to , altitude, and local . The adoption of this standard value traces back to the 3rd General Conference on Weights and Measures (CGPM) in 1901, where it was established as 980.665 cm/s² to resolve inconsistencies in international metrology and clarify the relationship between and . This decision built on prior agreements from the International Committee for Weights and Measures in 1887 and 1889, ensuring a consistent basis for defining force units like the in the at the time. Although the SI unit of force, the newton, is now defined independently as 1 kg·m/s² without direct reliance on gng_n, the standard gravity value remains foundational in legacy systems and conversions. In practical applications, standard gravity is essential for engineering calculations involving weight, buoyancy, and structural loads, where it standardizes assumptions about gravitational effects. It forms a core component of the (ISA) model, used in to define atmospheric pressure, temperature, and density profiles at . In meteorology, gng_n is applied in deriving heights, which adjust altitude measurements for gravitational variations to improve accuracy in and atmospheric modeling. These uses highlight its role in ensuring interoperability across scientific disciplines and global standards.

Definition and Value

Standard Value

The standard value of the acceleration due to gravity, often denoted as g0g_0 or gng_n, is defined as exactly 9.80665 m/s². This numerical value was adopted by the 3rd General Conference on Weights and Measures (CGPM) in to provide a universal reference for metrological purposes, particularly in defining as the product of and . The defining equation is: g0=9.80665 m/s2g_0 = 9.80665 \, \mathrm{m/s^2} This constant represents the conventional effective acceleration due to gravity at and a latitude of approximately 45°, where it serves as a practical benchmark incorporating Earth's rotational effects. It originates from measurements of , which is rounded to this precise figure for consistent use in , scientific computations, and standards like those from CODATA.

Physical Interpretation

Standard gravity, denoted as g0g_0 or gng_n, represents the nominal acceleration that a body would experience during free fall near the Earth's surface in a vacuum, under idealized conditions free from air resistance or other external forces. This value serves as a conventional reference for gravitational effects in metrology and physics, approximating the local acceleration due to gravity at sea level and 45° latitude. Physically, standard gravity relates directly to the concept of , defined as the acting on a . The WW of a body is given by the equation W=m⋅g0,W = m \cdot g_0, where mm is the in kilograms and g0=9.80665g_0 = 9.80665 m/s² exactly. This formulation distinguishes as a (measured in newtons) from as an intrinsic property (measured in kilograms), emphasizing that varies with while remains constant. Standard gravity specifically underpins the definition of the (kgf), a non-SI unit equal to the exerted by a 1 kg under g0g_0, which is precisely 9.80665 N. In practical terms, this interpretation has key implications for measurement devices like scales and balances, which detect the force of rather than directly. These instruments are often calibrated using standard gravity to convert observed forces back to equivalents, ensuring consistency in applications such as and scientific weighing. For instance, under standard gravity, a of 1 kg experiences a weight of exactly 9.80665 , providing a benchmark for verifying the accuracy of such devices and highlighting the need to account for the mass-weight distinction in everyday phenomena like object support or effects.

Historical Development

Early Concepts

In ancient times, Greek philosophers developed foundational ideas about what would later be understood as . (384–322 BCE) proposed that objects fall toward the Earth's center because it represents their natural place in a geocentric , with heavier bodies descending faster in proportion to their weight when falling through a medium like air. This view dominated for centuries, attributing motion to elemental tendencies rather than a universal force. (c. 287–212 BCE) advanced the concept by calculating centers of for geometric shapes, such as triangles and parabolas, treating it as a point of balance for stability without explaining the underlying attraction. During the , thinkers began challenging Aristotelian notions through observation and experiment. (1452–1519) explored as an accelerative force, recognizing through visualizations—such as the equivalence between a falling object and material pouring from a moving vase—that motion under accelerates uniformly, predating formal mechanics by a century. These ideas influenced (1564–1642), who around 1589–1592 reportedly dropped unequal lead weights from the , demonstrating that they struck the ground simultaneously regardless of , thus refuting Aristotle's speed-proportionality claim and establishing gravitational acceleration's independence from body weight. Galileo's inclined-plane experiments further quantified fall rates, laying groundwork for uniform acceleration under . In the 17th and 18th centuries, pendulum observations provided quantitative estimates of gravitational acceleration, denoted as g. Christiaan Huygens (1629–1695) in his 1673 work Horologium Oscillatorium analyzed pendulum periods to derive g at Paris, using the relation between swing length and oscillation time to yield a value near 9.81 m/s², while accounting for cycloidal paths to minimize errors. Subsequent measurements by figures like Jean Richer (1630–1696) in Cayenne and Giovanni Battista Riccioli (1598–1671) refined local g variations, often via seconds pendulums (those with 2-second periods). By the 18th century, national efforts, such as those by the Paris Academy, produced consistent estimates around 9.8 m/s² through air-swing pendulums corrected for buoyancy and temperature. The 19th century saw systematic surveys integrating latitude-dependent variations into mean g calculations. Friedrich Wilhelm Bessel (1784–1846), following Prussia's triangulation in the 1830s, computed Earth's ellipsoidal figure from pendulum data across latitudes, deriving a global mean g approximating 9.81 m/s² by modeling centrifugal and oblateness effects. National surveys, including British (Kater's 1818 value of ~980.9 cm/s²) and Prussian efforts, yielded site-specific figures near 9.8 m/s² but lacked unification, as discrepancies arose from instrumental and environmental factors without an agreed international reference—contrasting with the modern standard of 9.80665 m/s².

Modern Standardization

Building on decisions by the International Committee for Weights and Measures (CIPM) in 1887, which defined the kilogram as a unit of mass, and the 1st General Conference on Weights and Measures (CGPM) in 1889, which sanctioned the international prototypes of the metre and kilogram to distinguish mass from weight, efforts culminated in 1901 when the 3rd CGPM adopted the standard acceleration due to gravity as 980.665 cm/s², equivalent to 9.80665 m/s², to serve as a conventional reference for metrological purposes from pendulum measurements and geodetic observations. This value was selected to represent the nominal gravity at sea level under standard conditions, facilitating consistent calculations of weight and force in international standards. The adoption aimed to unify disparate national values that had varied slightly due to local gravitational anomalies, establishing a fixed benchmark independent of specific locations. Within the (SI), standard gravity plays a key role in defining derived units such as the newton, where the force of 1 N accelerates 1 kg at 1 m/s², but it also underpins the concept of standard weight as the product of mass and 9.80665 m/s². This integration ties standard gravity to the base units of the meter and second, ensuring coherence in mechanical measurements; for instance, it allows the (kgf) to be expressed exactly as 9.80665 N. The value's status as an exact conventional constant supports precise reductions of local gravity measurements to standard conditions in and . The 1983 CGPM redefinition of the meter as the distance light travels in vacuum in 1/299792458 of a second fixed the numerical value of standard gravity in SI units, as the became exact, thereby stabilizing its relation to the evolving definitions of length and time without altering the adopted figure. To enhance precision in global gravity networks, the International Committee for Weights and Measures (CIPM) issued recommendations addressing standardization efforts. In 1972, the CIPM endorsed the International Gravity Standardization Net 1971 (IGSN71), a worldwide reference system comprising over 1,800 stations with adjusted gravity values tied to absolute measurements, to minimize inconsistencies in relative gravimetry and ensure traceability to the SI. This network refined the application of the 1901 value by providing a datum for reducing observed accelerations to standard gravity, improving accuracy in international comparisons. Although the core value of 9.80665 m/s² has remained unchanged since 1901 as a conventional standard, it continues to be verified through modern geodetic surveys, such as the U.S. Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project, which collects airborne data to align local measurements with the global reference.

Physical Basis

Gravitational Acceleration

The gravitational acceleration experienced by objects near Earth's surface arises from , which posits that every particle of matter in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers./Book%3A_University_Physics_I_-Mechanics_Sound_Oscillations_and_Waves(OpenStax)/13%3A_Gravitation/13.03%3A_Gravitation_Near_Earth%27s_Surface) For an object of mass mm near Earth's surface, this force FF is given by F=GMmr2F = G \frac{M m}{r^2}, where GG is the (6.67430×10−116.67430 \times 10^{-11} m3^3 kg−1^{-1} s−2^{-2}), MM is Earth's mass (5.972×10245.972 \times 10^{24} kg), and rr is the distance from Earth's center (approximately the mean radius of 6.371×1066.371 \times 10^6 m)./Book%3A_University_Physics_I_-Mechanics_Sound_Oscillations_and_Waves(OpenStax)/13%3A_Gravitation/13.03%3A_Gravitation_Near_Earth%27s_Surface) By Newton's second law, this force equals mgm g, yielding the acceleration due to gravity as g = \frac{G M}{r^2}. $$/Book%3A_University_Physics_I_-_Mechanics_Sound_Oscillations_and_Waves_(OpenStax)/13%3A_Gravitation/13.03%3A_Gravitation_Near_Earth%27s_Surface) This expression describes the ideal free-fall [acceleration](/page/Acceleration) for an object in [vacuum](/page/Vacuum), neglecting air resistance and [Earth's rotation](/page/Earth's_rotation), assuming a spherically symmetric [Earth](/page/Earth). Substituting the measured geocentric gravitational parameter $GM = 3.986004418 \times 10^{14}$ m$^3$ s$^{-2}$ and mean radius into the formula gives a baseline value of approximately 9.82 m/s$^2$.[](https://ssd.jpl.nasa.gov/astro_par.html) In reality, Earth's [gravitational acceleration](/page/Gravitational_acceleration) deviates from this simple model due to its oblateness—an [equatorial bulge](/page/Equatorial_bulge) resulting from rotational forces—and its internal composition, which creates a heterogeneous [mass](/page/Mass) distribution with a dense iron-nickel core comprising about 32% of the planet's [mass](/page/Mass).[](https://www.britannica.com/place/Earth/The-interior) The oblateness increases the equatorial radius by about 21 km relative to the polar radius, reducing $g$ at the [equator](/page/Equator) to approximately 9.780 m/s$^2$ while increasing it at the poles to about 9.832 m/s$^2$, as poles are closer to the center of [mass](/page/Mass). These structural factors, combined with the overall [mass](/page/Mass) determined by Earth's silicate mantle and metallic core, result in a conventional global average [gravitational acceleration](/page/Gravitational_acceleration) of approximately 9.80665 m/s$^2$.[](https://physics.nist.gov/cgi-bin/cuu/Value?gn) ### Variations and Standard Conditions Gravity on Earth's surface varies primarily with latitude due to the planet's oblate [spheroid](/page/Spheroid) shape and rotational effects. At the [equator](/page/Equator), the effective [gravitational acceleration](/page/Gravitational_acceleration) is approximately 9.780 m/s², lower because of the greater distance from Earth's center and the maximum [centrifugal force](/page/Centrifugal_force) from rotation. At the poles, it reaches about 9.832 m/s², higher due to the closer proximity to the center of mass and absence of centrifugal reduction.[](https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=2036&context=istj) These latitude-dependent variations are approximated by the International Gravity Formula (IGF) of 1967: g(\phi) = 9.780327 \left(1 + 0.0053024 \sin^2 \phi - 0.0000058 \sin^2 2\phi \right) , \text{m/s}^2 where $\phi$ is the [latitude](/page/Latitude) in degrees. The $\sin^2 \phi$ term primarily accounts for the increase in [gravity](/page/Gravity) toward the poles from Earth's [flattening](/page/Flattening), while the smaller $\sin^2 2\phi$ term corrects for higher-order rotational and ellipsoidal effects.[](https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=2036&context=istj)[](https://ocw.mit.edu/courses/12-201-essentials-of-geophysics-fall-2004/7fa24d336366b74c52adb48ae6c8cf6f_ch2.pdf) Gravity also decreases with altitude above [sea level](/page/Sea_level), at a rate of approximately 0.003 m/s² per kilometer, as the distance from Earth's center increases. Local geological features further perturb this value; for instance, mountains can locally enhance gravity due to [added mass](/page/Added_mass), while subsurface [density](/page/Density) anomalies, such as those from varying crustal compositions, cause deviations up to several milligals.[](https://ocw.mit.edu/courses/12-201-essentials-of-geophysics-fall-2004/7fa24d336366b74c52adb48ae6c8cf6f_ch2.pdf) The standard value of gravity applies under idealized conditions: at 45° latitude on the reference ellipsoid, at [sea level](/page/Sea_level), with no topographic elevation or local density perturbations, and incorporating the effects of [Earth's rotation](/page/Earth's_rotation) as modeled in the IGF. These conditions ensure a consistent baseline for measurements and comparisons, isolating the reference from real-world variations.[](https://ocw.mit.edu/courses/12-201-essentials-of-geophysics-fall-2004/7fa24d336366b74c52adb48ae6c8cf6f_ch2.pdf)[](https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=2036&context=istj) ## Applications ### Engineering and Design In engineering and design, standard gravity $ g_0 = 9.80665 \, \mathrm{m/s^2} $ serves as the nominal acceleration due to gravity for calculating dead loads in structural systems, where the weight of materials and permanent fixtures is determined as $ W = m g_0 $ to ensure consistent [force](/page/Force) assessments across building codes.[](https://law.resource.org/pub/us/cfr/ibr/003/asce.7.2002.pdf) The [American Society of Civil Engineers](/page/American_Society_of_Civil_Engineers) (ASCE) 7 standard specifies dead loads for components like [concrete](/page/Concrete) decks and [steel](/page/Steel) girders using unit weights that embed this value, such as 150 lb/ft³ for [reinforced concrete](/page/Reinforced_concrete), preventing variations from local gravity differences that could lead to inconsistent designs.[](https://law.resource.org/pub/us/cfr/ibr/003/asce.7.2002.pdf) For instance, in multi-story buildings, these loads form the basis for vertical [force](/page/Force) combinations, with factors like 1.0 for serviceability and up to 1.25 for strength limit states, ensuring structural integrity under expected gravity-induced stresses.[](https://law.resource.org/pub/us/cfr/ibr/003/asce.7.2002.pdf) In [transportation engineering](/page/Transportation_engineering), standard gravity defines g-forces as multiples of $ g_0 $, guiding the design of vehicles to withstand [acceleration](/page/Acceleration) loads during operation.[](https://www.faa.gov/pilots/safety/pilotsafetybrochures/media/acceleration.pdf) [Aircraft](/page/Aircraft) structures, for example, are engineered for load factors up to 9g in high-performance fighters, where the [airframe](/page/Airframe) must resist forces equivalent to nine times the standard gravitational pull to maintain [safety](/page/Safety) during maneuvers like steep turns.[](https://www.faa.gov/pilots/safety/pilotsafetybrochures/media/acceleration.pdf) Similarly, [elevator](/page/Elevator) specifications limit [acceleration](/page/Acceleration) to 0.5g or less to protect passengers from discomfort or injury, with cab and shaft designs incorporating these multiples to balance speed and stability.[](https://www.faa.gov/pilots/safety/pilotsafetybrochures/media/acceleration.pdf) In [hydraulics](/page/Hydraulics) and [fluid mechanics](/page/Fluid_mechanics), standard gravity is integral to [hydrostatic pressure](/page/Pressure) calculations via the [formula](/page/Formula) $ p = \rho g_0 h $, where $ \rho $ is [fluid](/page/Fluid) [density](/page/Density) and $ h $ is depth, allowing engineers to scale pressure heads reliably for systems like [dams](/page/DAMS) and pipelines.[](https://www.engineeringtoolbox.com/hydrostatic-pressure-water-d_1632.html) This approach ensures that designs for [water](/page/Water) retention or [fluid](/page/Fluid) conveyance account for the consistent downward force of [gravity](/page/Gravity) at $ g_0 = 9.81 \, \mathrm{m/s^2} $, avoiding overestimation in low-gravity simulations or underestimation in variable conditions.[](https://www.engineeringtoolbox.com/hydrostatic-pressure-water-d_1632.html) A practical example is bridge design, where standard gravity assumptions underpin dead load evaluations to optimize material use and prevent over- or under-engineering.[](https://www.fhwa.dot.gov/bridge/pubs/nhi15047.pdf) Under AASHTO LRFD specifications, unit weights for elements like [concrete](/page/Concrete) decks (150 pcf) and [steel](/page/Steel) girders (490 pcf) are derived from $ g_0 $, enabling accurate computation of total vertical loads—such as 2.272 k/ft for non-composite sections—that inform [girder](/page/Girder) sizing and span configurations for long-term durability.[](https://www.fhwa.dot.gov/bridge/pubs/nhi15047.pdf) Safety factors in engineering incorporate standard gravity to mitigate risks from dynamic events, particularly in fall protection and seismic analysis. In fall arrest systems, designs limit deceleration to forces below [5g](/page/5G) (using $ g_0 $ as the baseline) with energy-absorbing lanyards rated for maximum arresting forces of 900 lb, ensuring the human body withstands impacts without exceeding tolerance thresholds of [5g](/page/5G) upward or -3g downward.[](https://www.rigidlifelines.com/blog/how-does-gravity-and-acceleration-impact-fall-protection/) For seismic applications, safety factors like the response modification coefficient (R = 1 to 8) and overstrength factor ($ \Omega_0 = 2 $ to 3) scale earthquake accelerations expressed as fractions of $ g_0 $ (e.g., peak ground acceleration of 0.3g), integrating gravity loads into combinations such as 1.2D + 1.0E to achieve life safety by preventing collapse under rare events.[](https://www.fema.gov/sites/default/files/documents/fema_p-749-earthquake-resistant-design-concepts_112022.pdf) ### Scientific Measurements Gravitational acceleration is measured using two primary categories of instruments: absolute gravimeters and relative gravimeters. Absolute gravimeters determine the acceleration due to gravity directly by tracking the free fall of a test [mass](/page/Mass), typically a corner cube retro-reflector, within a [vacuum chamber](/page/Vacuum_chamber) using [laser](/page/Laser) [interferometry](/page/Interferometry).[](https://pmc.ncbi.nlm.nih.gov/articles/PMC6098009/) The position of the falling corner cube is recorded at multiple points during its descent, allowing the [gravitational acceleration](/page/Gravitational_acceleration) to be fitted from the trajectory data with high precision.[](https://arxiv.org/pdf/1008.2884) In contrast, relative gravimeters measure differences in [gravity](/page/Gravity) between locations rather than absolute values; spring-based models, such as those using a [mass](/page/Mass) suspended on a zero-length spring, detect deflections caused by gravitational variations, while pendulum-based systems compare periods of [oscillation](/page/Oscillation) at different sites.[](https://www.sciencedirect.com/science/article/pii/S0422989408711553) These relative instruments require [calibration](/page/Calibration) against absolute measurements to tie local readings to the standard value.[](https://www.eolss.net/sample-chapters/c01/E6-16-06-02.pdf) In [geodesy](/page/Geodesy), measurements of [gravitational acceleration](/page/Gravitational_acceleration) play a crucial role in identifying local [gravity](/page/Gravity) anomalies, which are deviations from the [expected value](/page/Expected_value) based on Earth's theoretical model. These anomalies arise from subsurface [density](/page/Density) variations and topographic effects, enabling scientists to map irregularities in Earth's shape, such as the [geoid](/page/Geoid), and infer crustal [density](/page/Density) distributions.[](https://academic.oup.com/gji/article/154/1/35/604237) For instance, positive anomalies often indicate denser rocks or uplifted mantle material, while negative ones suggest sedimentary basins or low-density intrusions, contributing to global models of Earth's interior structure.[](https://pubs.usgs.gov/of/2002/0353/method.html) In laboratory physics, measurements of [gravitational acceleration](/page/Gravitational_acceleration) are essential for calibrating precision balances, where local [gravitational acceleration](/page/Gravitational_acceleration) must be accounted for to ensure accurate [mass](/page/Mass) determinations, particularly in air [buoyancy](/page/Buoyancy) corrections.[](https://www.coleparmer.com/tech-article/balance-calibration) Additionally, they support tests of the [equivalence principle](/page/Equivalence_principle), the foundational idea that gravitational and inertial [mass](/page/Mass)es are identical; experiments like atom interferometry use precise [gravity](/page/Gravity) data to verify this by comparing free-fall accelerations of different materials to sensitivities approaching $10^{-15}$. Modern gravimeters achieve precision on the order of $10^{-9} g$, equivalent to about 1 µGal, which underpins global networks such as the International Gravity Standardization Net 1971 (IGSN71), a [reference](/page/Reference) system of over 1,000 stations for consistent worldwide [gravity](/page/Gravity) data.[](https://www.researchgate.net/figure/Absolute-gravimeter-FG-5-capable-of-10-9-accuracy-during-a-1-2-day-measurement_fig1_228804734)[](https://link.springer.com/article/10.1007/s00190-020-01438-9) ## Conversions and Equivalents ### Unit Conversions Standard gravity, denoted as $ g_0 $, is defined as exactly 9.80665 m/s² in the [International System of Units](/page/International_System_of_Units) (SI).[](https://physics.nist.gov/cgi-bin/cuu/Value?gn) This value serves as the reference for converting acceleration due to gravity across unit systems. To convert from SI units to [imperial units](/page/Imperial_units), multiply the value in meters per second squared by the exact factor 3.280839895, derived from the definition of the foot as exactly 0.3048 meters.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9) Thus, $ g_0 = 9.80665 $ m/s² equals approximately 32.1740 ft/s². The precise conversion equation is: a_{\text{ft/s²}} = a_{\text{m/s²}} \times 3.280839895 where $ a $ represents acceleration.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9) In other units, standard gravity equates to 980.665 cm/s².[](https://physics.nist.gov/cgi-bin/cuu/Value?gn) The galileo (Gal), a unit accepted for use with the SI in geodesy and geophysics, is defined as exactly 1 cm/s² or 0.01 m/s².[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) Therefore, $ g_0 = 980.665 $ Gal. Derived units involving standard gravity include the pound-force (lbf), defined as the force exerted by $ g_0 $ on one avoirdupois pound (0.45359237 kg exactly).[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9) This yields exactly 4.4482216152605 N for 1 lbf.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9) The following table summarizes equivalents of standard gravity in selected units: | Unit | Symbol | Value for $ g_0 $ | |-------------------|--------|------------------------| | Meter per second squared | m/s² | 9.80665 (exact) | | Foot per second squared | ft/s² | 32.1740 | | Galileo | Gal | 980.665 | | [Dyne per gram](/page/Dyne) | dyn/g | 980.665 | The [dyne](/page/Dyne) per gram is equivalent to the galileo, as 1 [dyne](/page/Dyne) = 1 g·cm/s², making acceleration in dyn/g numerically equal to cm/s².[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) ### Related Standards The [kilogram-force](/page/Kilogram-force) (kgf), a unit of [force](/page/Force) in the [gravitational metric system](/page/Gravitational_metric_system), is defined as the gravitational [force](/page/Force) exerted on a [mass](/page/Mass) of one [kilogram](/page/Kilogram) at standard gravity, equivalent to exactly 9.80665 newtons.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) This definition ensures compatibility with SI units while accommodating engineering contexts where gravitational effects are prominent.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) The gal (Gal), a unit of [acceleration](/page/Acceleration) in the centimeter-gram-second (CGS) [system](/page/System), equals 1 centimeter per second squared (0.01 m/s²) and is primarily used in [geophysics](/page/Geophysics) and [geodesy](/page/Geodesy) to measure gravitational variations.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) Standard gravity corresponds to 980.665 Gal, providing a benchmark for calibrating instruments that detect subtle differences in Earth's [gravitational field](/page/Gravitational_field).[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si) In atmospheric models, standard gravity indirectly influences pressure standards through [hydrostatic equilibrium](/page/Hydrostatic_equilibrium), where the [pressure gradient](/page/Pressure_gradient) is given by dp/dz = -ρ g₀, with g₀ = 9.80665 m/s² serving as the reference acceleration in the U.S. Standard Atmosphere 1976.[](https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf) This relation ties the standard atmosphere's density and pressure profiles to gravitational effects, enabling consistent calculations for [aviation](/page/Aviation) and [space](/page/Space) applications.[](https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf) Historically, the foot-pound-second (FPS) system, particularly its gravitational variant (also known as the English Engineering system), relies on standard gravity to define the pound-force (lbf) as the weight of one avoirdupois pound-mass under g = 32.17405 ft/s².[](https://www.engineeringtoolbox.com/mass-weight-d_589.html) In contrast, the absolute FPS variant uses the poundal (pdl) as the force unit, defined as the force accelerating one pound-mass at 1 ft/s² without direct reference to gravity, though conversions between systems incorporate standard gravity for consistency.[](https://www.engineeringtoolbox.com/mass-weight-d_589.html) These standards, built upon standard gravity, promote interoperability between SI and non-SI systems in [engineering](/page/Engineering) disciplines, facilitating precise [force](/page/Force) and [acceleration](/page/Acceleration) computations across diverse applications.[](https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-5-units-outside-si)
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