Quick answer: specific volume is v = V ÷ m = 1 ÷ ρ — the space one unit of mass occupies, in m³/kg. Water is 0.001002 m³/kg, air is 0.83 m³/kg, steam at 100 °C is 1.67 m³/kg. It is density turned upside down, and thermodynamics prefers it because it appears directly in the work term of the first law.
The formula, three ways in
R = 8.314 J/(mol·K) · T in kelvin · P in pascals · M in kg/mol
The first two are the same statement. If you know density, specific volume takes one keystroke — it is the reciprocal, nothing more. Water at 998.2 kg/m³ gives 1 ÷ 998.2 = 0.001002 m³/kg.
The third is where the concept earns its keep. For a gas, density changes with pressure and temperature, so quoting a fixed number is meaningless. The ideal gas form lets you compute it from conditions:
Worked example — air at 1 atm and 20 °C. P = 101,325 Pa, T = 293.15 K, M = 0.028964 kg/mol for dry air.
- Numerator: 8.314 × 293.15 = 2,437.3
- Denominator: 101,325 × 0.028964 = 2,934.8
- v = 2,437.3 ÷ 2,934.8 = 0.8305 m³/kg
Check it back: 1 ÷ 0.8305 = 1.204 kg/m³, which is the standard density of air at 20 °C. The two routes agree.
Specific volume versus density
They carry identical information, so the choice between them is about convenience — and about which one appears in the equation you are solving.
| Density (ρ) | Specific volume (v) | |
|---|---|---|
| Question it answers | How much mass fits in this space? | How much space does this mass need? |
| SI unit | kg/m³ | m³/kg |
| US unit | lb/ft³ | ft³/lb |
| Relationship | ρ = 1/v | v = 1/ρ |
| Property type | Intensive | Intensive |
| Preferred in | Liquids, solids, civil and materials work | Thermodynamics, steam tables, gas work |
| Denser substance | Higher number | Lower number |
That last row catches people. Lead has a high density and a tiny specific volume; steam has a low density and a large specific volume. The intuition inverts, which is exactly why mixing the two up produces answers wrong by orders of magnitude rather than by a little.
If density is what you actually want, the density–mass–volume calculator solves ρ = m/V in any direction.
Specific volume reference table
At 20 °C and 1 atm unless stated. Note the range: nearly five orders of magnitude between mercury and steam.
| Substance | Density (kg/m³) | v (m³/kg) | v (ft³/lb) |
|---|---|---|---|
| Mercury | 13,534 | 0.0000739 | 0.00118 |
| Lead | 11,340 | 0.0000882 | 0.00141 |
| Steel | 7,850 | 0.000127 | 0.00204 |
| Aluminium | 2,700 | 0.000370 | 0.00593 |
| Concrete | 2,400 | 0.000417 | 0.00667 |
| Water (20 °C) | 998.2 | 0.001002 | 0.01605 |
| Ice (0 °C) | 917 | 0.001090 | 0.01747 |
| Diesel | 850 | 0.001176 | 0.01885 |
| Petrol | 750 | 0.001333 | 0.02136 |
| Carbon dioxide (gas) | 1.842 | 0.543 | 8.70 |
| Air (dry) | 1.204 | 0.8305 | 13.30 |
| Steam (100 °C, saturated) | 0.598 | 1.672 | 26.78 |
| Helium | 0.1664 | 6.010 | 96.28 |
| Hydrogen | 0.0838 | 11.93 | 191.1 |
The water and steam rows sit next to each other and differ by a factor of 1,670. That single comparison is the whole reason boilers and steam plant are designed the way they are: boiling one litre of water produces about 1.67 cubic metres of steam at atmospheric pressure, and the pressure vessel exists to contain that expansion.
Why thermodynamics uses it
Specific volume is not an alternative notation for density chosen by preference. It shows up in the equations directly.
Work done by a closed system as it expands is W = ∫P dV. Divide through by the mass of the system and you get w = ∫P dv — work per unit mass, in terms of specific volume. Every property diagram in thermodynamics is built on that: the P–v diagram, the T–v diagram, and every steam table you will ever read.
The second reason is practical range. Following water from liquid through to superheated vapour, density falls from 1,000 to under 1 kg/m³. Expressed as specific volume the same journey runs from 0.001 to over 1 m³/kg — numbers that sit comfortably on a linear axis and in a printed table, which is why steam tables have been written that way for over a century.
Common mistakes & pro tips
- Confusing it with specific gravity. Completely different quantities. Specific gravity is a dimensionless ratio of a density to water's; specific volume has units of m³/kg.
- Confusing it with molar volume. Molar volume is per mole (m³/mol), specific volume is per kilogram. They differ by the molar mass.
- Using gauge pressure in the gas equation. The ideal gas law needs absolute pressure. Add atmospheric pressure to a gauge reading before using it.
- Using Celsius in the gas equation. T must be in kelvin. Add 273.15.
- Quoting a fixed specific volume for a gas. It changes with pressure and temperature. There is no single value for "air" without stating the conditions.
- Pro tip — sanity-check by inverting. Take 1/v and see whether you get a density you recognise. It catches decimal-place errors instantly.
- Pro tip — near a phase change, stop using the ideal gas law. Saturated and wet steam depart from ideal behaviour substantially. Use steam tables or a real-gas equation of state instead.
How to use this calculator
- From mass & volume — the direct definition, for a sample you can weigh and measure.
- From density — one keystroke if you already have ρ, in kg/m³, g/cm³ or lb/ft³.
- Ideal gas — enter absolute pressure, temperature and molar mass, with presets for common gases.
- Read both unit systems — m³/kg and ft³/lb are shown together, along with the density it implies.
Frequently asked questions
What is specific volume?
Specific volume is the volume that one unit of mass of a substance occupies, written v and measured in cubic metres per kilogram. It answers the question "how much space does one kilogram of this take up". It is the exact reciprocal of density: where density says how much mass fits into a given space, specific volume says how much space a given mass needs.
What is the formula for specific volume?
v = V ÷ m, which is the same as 1 ÷ ρ. For a gas behaving ideally it can also be written v = RT ÷ (PM), where R is the universal gas constant of 8.314 J/(mol·K), T is absolute temperature in kelvin, P is absolute pressure in pascals and M is the molar mass in kg/mol.
What is the difference between specific volume and density?
They are reciprocals of each other and contain exactly the same information. Density is mass per unit volume; specific volume is volume per unit mass. Engineers working with liquids and solids normally use density, while thermodynamics and steam tables use specific volume, because for gases the numbers are more convenient — steam at atmospheric pressure has a specific volume of about 1.67 m³/kg, which is easier to work with than a density of 0.598.
What is the specific volume of water?
About 0.001002 m³/kg at 20 °C, or 0.01605 ft³/lb. That is simply 1 ÷ its density of 998.2 kg/m³. It is very nearly 0.001 exactly, which is a useful anchor: one kilogram of water occupies almost exactly one litre.
Why does thermodynamics use specific volume instead of density?
Because it appears directly in the work term of the first law. Work done by a closed system is pressure times the change in volume, and dividing through by mass gives pressure times the change in specific volume. Property diagrams and steam tables are therefore built around specific volume, and the numbers stay convenient across the enormous density range between a liquid and its vapour.
What are the units of specific volume?
The SI unit is cubic metres per kilogram. In US customary work it is cubic feet per pound, where 1 m³/kg = 16.0185 ft³/lb. Cubic centimetres per gram is also used and is numerically identical to the reciprocal of density in g/cm³; note that 1 cm³/g = 0.001 m³/kg.
References & further reading
- Çengel, Y. A. & Boles, M. A., Thermodynamics: An Engineering Approach — specific volume as the fundamental intensive property.
- IAPWS steam tables — specific volume of water and steam across the full range of conditions.
- NIST Chemistry WebBook — thermophysical property data for gases and liquids.
- CODATA value for the molar gas constant, R = 8.314462618 J/(mol·K).
Ideal gas results assume ideal behaviour and will depart from reality near condensation, at high pressure, or close to the critical point. Use steam tables or a real-gas equation of state for those conditions. See our accuracy policy.