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Cubic metre
One cubic metre of concrete (representing the world annual production per capita) (on the left).
General information
Unit systemSI
Unit ofvolume
Symbolm3
Look up cubic metre in Wiktionary, the free dictionary.

The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI).[1] Its symbol is m3.[1] It is the volume of a cube with edges one metre in length. An alternative name, which allowed a different usage with metric prefixes, was the stère, still sometimes used for dry measure (for instance, in reference to wood). Another alternative name, no longer widely used, was the kilolitre.

Conversions

[edit]
Some SI units of volume to scale and approximate corresponding mass of water
Main article: Unit conversion
1 cubic metre = 1000 litres (exactly)[2][3]
≈ 35.3146667 cubic feet
≈ 1.3079506 cubic yards
≈ 6.2898108 oil barrels
≈ 219.96925 imperial gallons
≈ 264.17205 US fluid gallons

A cubic metre of pure water at the temperature of maximum density (3.983 °C) and standard atmospheric pressure (101.325 kPa) has a mass of 1000 kg, or one tonne. At 0 °C, the freezing point of water, a cubic metre of water has slightly less mass, 999.85 kilograms.[4]

A cubic metre is sometimes abbreviated to m^3, M3, m**3, cum, m3, CBM, cbm when superscript characters or markup cannot be used (e.g. in some typewritten documents and postings in Usenet newsgroups). The "cubic metre" symbol is encoded by Unicode at code point U+33A5 ㎥ SQUARE M CUBED.[5]

Multiples and submultiples

[edit]
Main articles: Metric prefix and Orders of magnitude (volume)

Multiples

[edit]
Cubic decametre
the volume of a cube of side length one decametre (10 m)
equal to a megalitre
1 dam3 = 1000 m3 = 1 ML
Cubic hectometre
the volume of a cube of side length one hectometre (100 m)
equal to a gigalitre
in civil engineering abbreviated MCM for million cubic metres
1 hm3 = 1000000 m3 = 1 GL
Cubic kilometre
the volume of a cube of side length one kilometre (1000 m)
equal to a teralitre
1 km3 = 1000000000 m3 = 1 TL (810713.19 acre-feet; 0.239913 cubic miles)

Submultiples

[edit]
Cubic decimetre
the volume of a cube of side length one decimetre (0.1 m)
equal to a litre
1 dm3 = 0.001 m3 = 1 L
(also known as DCM (=Deci Cubic Meter) in Rubber compound processing)
Cubic centimetre[6]
the volume of a cube of side length one centimetre (0.01 m)
equal to a millilitre
1 cm3 = 0.000001 m3 = 10−6 m3 = 1 mL
Cubic millimetre
the volume of a cube of side length one millimetre (0.001 m)
equal to a microlitre
1 mm3 = 0.000000001 m3 = 10−9 m3 = 1 μL

See also

[edit]

References

[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Cubic metre

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from Grokipedia
The cubic metre (symbol: m³) is the (SI) coherent derived , defined as the volume occupied by a with edges of exactly one in length. This unit measures the three-dimensional extent of space enclosed by an object or substance, applicable to solids, liquids, and gases alike. The , from which the cubic metre is derived, is the of length, fixed by defining the in as exactly 299 792 458 metres per second, such that one metre is the distance travels in during a time interval of 1/299 792 458 of a second. Consequently, the cubic metre equates to (1 m)³ and serves as the reference for expressing volumes in the SI system, with the m³ formed by superscripting the numeral 3 after the . It is equivalent to 1 000 cubic s (dm³), and since the (L) is a special name for the cubic , one cubic metre equals 1 000 s. For smaller volumes, the cubic centimetre (cm³) is commonly used, where 1 cm³ = 10⁻⁶ m³, while larger volumes may employ multiples like the cubic (km³ = 10⁹ m³). The cubic metre's foundations trace back to the late in , where scientists developed the during the to create universal, decimal-based units derived from natural phenomena. Initially, the was provisionally defined in 1793 as one ten-millionth of the distance from the equator to the along a meridian, and volume measurements were based on the cubic (then called the ) for practicality, as the cubic metre was deemed too large for everyday use. The modern SI, including the cubic metre as its volume unit, was formally established by the 11th General Conference on Weights and Measures (CGPM) in 1960, building on the metric system's evolution and redefinitions of base units over time. Today, the cubic metre is essential in scientific research, , trade, and , such as calculating water resources, fuel capacities, or atmospheric volumes.

Definition and Fundamentals

Definition

The cubic metre, symbol m³, is the SI coherent derived , representing the volume of a whose edges each measure exactly one in , or equivalently, the volume of a cubical measuring 1 m × 1 m × 1 m. Mathematically, this is expressed as the of the :
V=l3V = l^3
where l=1l = 1 m, yielding V=1V = 1 m³. As the standard unit for volume in the (SI), the cubic metre is derived from the , which serves as the base SI unit of length.

Physical Interpretation

The cubic metre represents the volume of a with each side measuring one , providing a tangible sense of scale in . To visualize this, imagine a roughly the size of a standard chair or armchair, which typically occupies about one cubic metre when accounting for its overall dimensions and shape. Alternatively, it equates to the space filled by approximately 1,000 standard one-litre cartons stacked together, as one cubic metre precisely holds 1,000 litres. In practical comparisons, one cubic metre can contain the volume of equivalent to a small backyard measuring one by one with a depth of one . It also holds approximately 1,057 U.S. liquid quarts, offering a sense of its capacity relative to common liquid measures in non-metric regions. These analogies highlight the cubic metre's substantial yet manageable size for everyday comprehension, bridging abstract to familiar objects and containers. For sensory perspective, particularly with liquids, one cubic metre of pure at standard conditions—specifically and 1 atmosphere —weighs exactly 1,000 kilograms, or one metric , underscoring the direct link between and for water due to its of 1,000 kg/m³ at that . This equivalence not only aids in intuitive grasp but also reflects the historical basis for defining the in terms of water .

Historical Development

Origins in the Metric System

The originated during the in the 1790s, as part of a broader effort to create a unified, decimal-based that would replace the inconsistent and regionally varied units of the , such as the cubic used for measuring volumes like grain or firewood. In response to a 1790 decree from the , the formed a commission to design rational standards grounded in natural phenomena, proposing the as the fundamental —initially defined provisionally in 1793 as one ten-millionth of a quarter meridian from the to the . The , as the volume of a cube with sides, was thus derived directly from this base unit, embodying the system's decimal logic where multiples and submultiples followed powers of ten. An early precursor to the cubic metre appeared in 1795 with the introduction of the stère, a provisional unit decreed by the Convention Nationale primarily for quantifying stacks, explicitly defined as equivalent to one cubic metre to facilitate trade and standardization amid wartime shortages. This name, derived from the Greek stereos meaning "solid," reflected its focus on bulk solid volumes, though it was not immediately tied to a finalized prototype. By , the Academy of Sciences formally defined the metric units through a enacted on 7 April (18 Germinal, Year III), establishing the mètre cube—later simply cubic metre—as the standard volume unit, derived from the provisional metre and intended for broader applications beyond firewood. Central to this development were key figures from the , including mathematician and naval officer Jean-Charles de Borda, who chaired the 1790 commission and championed decimal reforms while inventing precision instruments like the Borda circle for accurate angular measurements essential to defining the . Astronomer Pierre Méchain, alongside Jean-Baptiste Delambre, led the arduous survey from 1792 to 1798, braving revolutionary turmoil to gather data that refined the 's length and, by extension, enabled the precise derivation of the cubic metre. Their collaborative efforts culminated in 1799 with the platinum prototype, solidifying the cubic metre's foundational role in the nascent metric framework.

Standardization and Evolution

The cubic metre was formally integrated into the international framework of measurement through the , signed on 20 May 1875 in by representatives of 17 nations, which established the International Bureau of Weights and Measures (BIPM) to maintain and promote the globally. This convention facilitated the widespread adoption of the metre and its derived units, including the cubic metre, with mandatory implementation in signatory countries by the late , ensuring uniformity in scientific and commercial measurements. The cubic metre received definitive status as a derived unit of the (SI) during the 11th General Conference on Weights and Measures (CGPM) in 1960, where Resolution 12 codified the SI based on seven base units, with volume expressed as the cube of the . This establishment built upon the metre–kilogram–second (MKS) system, providing a coherent framework for the cubic metre's use in precise volumetric calculations. A significant refinement occurred in 1983 at the 17th CGPM, where the was redefined as the distance travels in in 1299 792 458\frac{1}{299\,792\,458} of a second, fixing the at exactly c=299 792 458 m/sc = 299\,792\,458 \, \mathrm{m/s}. This change indirectly enhanced the precision of the cubic metre by anchoring it to an invariant , reducing uncertainties in length-based volume determinations. The 26th CGPM in 2018 approved the 2019 revision of the SI, effective 20 May 2019, which redefined base units like the using the while preserving the metre's 1983 definition. Although the cubic metre underwent no direct alteration, this update improved overall traceability and stability across the SI system, supporting advanced metrological applications without disrupting established volume standards.

Equivalences and Conversions

Conversions to Imperial and US Customary Units

The cubic metre is converted to Imperial and customary units through factors established by international standards, primarily based on the exact definitions of the metre relative to the foot, yard, and in the NIST Guide to the SI. Key equivalences include 1 m³ = 35.3147 cubic feet, 1 m³ = 1.30795 cubic yards, 1 m³ = 264.172 gallons (), and 1 m³ = 219.969 imperial gallons. These values are approximate representations of the exact conversions derived from precise linear and base unit definitions.
UnitConversion (1 m³ ≈)Exact Basis (from NIST SP 811)
(ft³)35.3147 ft³1 ft³ = 0.028316846592 m³ (exact)
(yd³)1.30795 yd³1 yd³ = 0.764554857984 m³ (exact)
US (gal)264.172 gal1 US gal = 0.003785411784 m³ (exact)
Imperial 219.969 gal1 imp gal = 0.00454609 m³ (exact)
These conversion factors arise from the cubic scaling of linear measurements, as is the product of three dimensions. For instance, the is defined as exactly 3.280839895 international feet, so the cubic metre equates to (3.280839895)³ cubic feet, yielding approximately 35.3147 ft³. Similar derivations apply to yards (1 yd = 0.9144 m exactly) and gallons, which are tied to definitions convertible to cubic metres. In practical applications, such as estimating volumes for or HVAC, a space measuring 4 m long by 3 m wide by 2.5 m high totals 30 m³, equivalent to about 30 × 35.3147 = 1,059 ft³. This conversion aids in cross-system comparisons, like translating metric building plans to customary specifications.

Relation to Other SI Volume Units

The cubic metre (m³) serves as the base unit of volume in the (SI), from which all other SI volume units are derived through coherent decimal scaling. Other volume units in the SI system are expressed as multiples or submultiples of the cubic metre, ensuring a unified and decimal-based structure that facilitates precise measurements across scales. A key coherent unit related to the cubic metre is the litre (L), which is defined as exactly one cubic decimetre (dm³). Since one decimetre equals 0.1 metre, it follows that 1 dm3=(0.1 m)3=0.001 m31 \, \mathrm{dm}^3 = (0.1 \, \mathrm{m})^3 = 0.001 \, \mathrm{m}^3, making 1 L=0.001 m31 \, \mathrm{L} = 0.001 \, \mathrm{m}^3. This equivalence positions the litre as a practical unit for everyday volumes, with one cubic metre corresponding to exactly 1000 litres, a relation that aligns capacity measures with the SI framework. Among derived volume units, the cubic decimetre (dm³) directly equals the , reinforcing its role as 0.001 m30.001 \, \mathrm{m}^3. Similarly, the (cm³) is a submultiple, where 1 cm3=(0.01 m)3=10−6 m31 \, \mathrm{cm}^3 = (0.01 \, \mathrm{m})^3 = 10^{-6} \, \mathrm{m}^3, and it is commonly used in medical and laboratory contexts under the name millilitre (mL), since 1 mL=10−3 L=10−6 m31 \, \mathrm{mL} = 10^{-3} \, \mathrm{L} = 10^{-6} \, \mathrm{m}^3. The SI volume units embody a scaling principle based on powers of 10 relative to the cubic metre, promoting coherence throughout the ; for instance, larger volumes like those of reservoirs are expressed as 1 km3=(1000 m)3=109 m31 \, \mathrm{km}^3 = (1000 \, \mathrm{m})^3 = 10^9 \, \mathrm{m}^3. This structure, inherent to the metric system's design, allows seamless conversions without fractional factors, distinguishing it from non-decimal systems.

Prefixes and Derived Units

SI Prefixes for Multiples

The SI prefixes for multiples are applied to the metre to form larger volume units, resulting in powers of 10 that are cubes of the linear prefix factors, in accordance with the (SI) standards. These prefixes facilitate the expression of very large volumes without resorting exclusively to , though the latter is common for extreme scales. The notation adheres to rules specified in ISO 80000, where the prefix symbol precedes the unit symbol, and the exponentiation (cube) applies to the combined symbol, such as km³ rather than k(m³). Common multiples begin with the kilocubic metre (km³), which denotes a of 10910^9 m³—the of 1000 m. This unit corresponds to the volume of a measuring 1 km on each side and equals 101210^{12} litres, providing a scale for substantial bodies or earthworks. In , km³ is widely used to quantify lake volumes and watershed storage capacities; for example, holds about 12,100 km³ of , representing a significant portion of the world's freshwater reserves. Larger multiples include the megacubic metre (Mm³ = 101810^{18} m³), which is rare in practical applications due to its enormous magnitude, equivalent to a cube 1000 km on each side, and is occasionally invoked in geophysical modeling of massive deposits or hypothetical mega-reservoirs. The gigacubic metre (Gm³ = 102710^{27} m³) is even less common, as its scale exceeds most terrestrial needs, though SI standards permit it for consistency; planetary volumes, such as Earth's at approximately 1.083×10211.083 \times 10^{21} m³ (or 1.083×10121.083 \times 10^{12} km³), are typically reported using km³ multiples or direct rather than higher linear prefixes to avoid unwieldy powers.
PrefixSymbolLinear FactorVolume Multiple (m³)Typical Scale Example
kilo-k10310^310910^9Lake or reservoir volumes (e.g., 12,100 km³ for )
mega-M10610^6101810^{18}Rare; large-scale geological formations
giga-G10910^9102710^{27}Theoretical; far beyond planetary scales

Common Submultiples and Applications

The cubic decimetre (dm³), equivalent to 0.001 m³, corresponds exactly to one litre (L) and serves as a primary submultiple for everyday volume measurements, particularly in consumer contexts such as beverages and packaging. For instance, a typical 2 L soda bottle contains 0.002 m³ of liquid, facilitating standardized labeling and distribution in the food and beverage industry. The cubic centimetre (cm³), or 10^{-6} m³, is identical to one millilitre (mL) and is frequently employed in precise applications like pharmaceutical liquid dosing and automotive engine specifications. In engine displacement, volumes are commonly denoted in cm³, with a 1,000 cm³ engine equating to 1 L capacity, providing a metric for performance and efficiency comparisons. Further subdivided, the cubic millimetre (mm³), at 10^{-9} m³, supports micro-scale measurements in pharmaceuticals, such as micro-dosing where volumes like 250 mm³ (0.25 ) enable accurate administration of small quantities. Per SI recommendations, these submultiples are often notated using the accepted special names—litre for dm³ and millilitre for cm³—to enhance practicality, though the cubic forms remain valid alternatives. This aligns with the 's established role as a non-SI unit compatible with the cubic metre system.

Usage in Various Fields

Scientific and Engineering Applications

In physics and chemistry, the cubic metre serves as the fundamental SI unit for measuring gas volumes in thermodynamic equations, particularly the , which relates , , , and the . The equation is expressed as PV=nRTPV = nRT, where VV represents the volume in cubic metres (m³), PP is in pascals, nn is the number of moles, RR is the (8.314 J/mol· in SI units), and TT is in kelvins. This unit ensures consistency in calculations for gas behavior under standard conditions, such as determining the volume occupied by one mole of an at 0°C and 1 atm, which approximates 0.0224 m³. In fluid dynamics, a subfield of physics and engineering, the cubic metre is integral to quantifying flow rates, defined as the volume of fluid passing through a cross-section per unit time, typically in cubic metres per second (m³/s). This measure is essential for analyzing pipe flow, hydraulic systems, and aerodynamic simulations, where the volumetric flow rate QQ is calculated as Q=AvQ = A v, with AA as the cross-sectional area in square metres and vv as the average velocity in metres per second. For instance, in water supply networks, flow rates on the order of 0.1 to 10 m³/s help engineers design pumps and valves to minimize energy losses and ensure efficient transport. Within disciplines, the cubic metre quantifies material volumes critical to structural integrity and system design. In , concrete volumes for , beams, and slabs are specified in m³ to determine mix proportions and procurement; for example, a standard mix might require approximately 0.15 m³ of , 0.25 tonnes of , 0.7 tonnes of , and 1.2 tonnes of aggregates per m³ of . This unit facilitates precise cost estimation and , as deviations can compromise load-bearing capacity in buildings or bridges. In mechanical and HVAC , air volumes in systems are sized using m³ to achieve desired rates, often calculated as 1–3 based on room volume, ensuring and air quality. For a typical of 100 m³, this translates to supply rates of 0.03–0.08 m³/s to maintain indoor conditions. In precision for laboratory applications, the cubic metre underpins the of volume measurements to international standards maintained by the International Bureau of Weights and Measures (BIPM). Equipment such as and burettes is calibrated against primary volume artifacts, with uncertainties linked through key comparisons like CCM.FF-K4.2.2011, which verifies micropipette calibrations at 100 μL by comparing results across national metrology institutes to the SI cubic metre. This chain ensures that submultiples like the microlitre (10⁻⁶ m³) used in are accurate to within 0.1–0.5% relative standard , supporting reproducible experiments in fields like biochemistry and pharmaceuticals.

Environmental and Economic Contexts

In and , the cubic metre serves as a fundamental unit for quantifying volumes in reservoirs and patterns. For instance, the total storage capacity of reservoirs in the exceeds 600 billion cubic metres, enabling assessments of availability for , , and flood control. Annual rainfall is often expressed as cubic metres per to evaluate over large areas; a typical conversion from millimetres of multiplies the depth by 1,000 to yield the volume per , facilitating regional hydrological modeling. In air quality analysis, pollutant dispersion models calculate concentrations in micrograms per cubic metre (µg/m³) to predict the spread of emissions from sources like industrial stacks, informing regulatory standards for ambient air protection. Sustainability metrics further underscore the cubic metre's role in tracking environmental impacts. Forests globally remove approximately 14 gigatonnes of CO₂ annually from the atmosphere (2001-2024 average)—equivalent to about 7.1 trillion cubic metres at —through biomass growth and storage, mitigating atmospheric carbon accumulation. Waste management relies on cubic metre measurements for landfill capacities; under U.S. Environmental Protection Agency regulations (40 CFR Part 60 Subpart Cf), municipal solid waste landfills with a design capacity of at least 2.5 million megagrams by mass and 2.5 million cubic meters by volume must install methane emission controls if nonmethane emissions exceed 34 megagrams per year, to reduce releases. Economically, the cubic metre standardizes trading and , influencing global markets. is frequently priced and traded per cubic metre in international pipelines and regional markets, with spot prices varying by supply dynamics; for example, import pricing mechanisms in some Asian and European contexts use this unit to benchmark contracts against alternatives like . In maritime shipping, standard 40-foot s have an internal volume of approximately 67.7 cubic metres, serving as a baseline for freight equivalents (FEU) in trade valuations and , which supports around 80% of global merchandise by volume. These applications highlight how cubic metre-based metrics enable precise economic valuations in resource extraction, energy markets, and efficiency, often integrated with larger multiples like cubic kilometres for mega-scale reservoirs.

References

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