Pressure, Mass, and Volume Formula Explained

The pressure–mass–volume formula for an ideal gas is pV = mRT, where pressure times volume equals mass times the specific gas constant times absolute temperature. This calculator uses gas mass, volume, temperature, and gas-specific constant to find pressure, with the result in kilopascals.

Formula

The ideal-gas relationship is pV = mRT. Rearranged to calculate pressure:

p = mRT / V

• p is absolute pressure, in pascals (Pa) or kilopascals (kPa).
• m is gas mass, in kilograms (kg).
• V is gas volume, in cubic metres (m³).
• R is the specific gas constant for the gas, in joules per kilogram per kelvin (J/(kg·K)).
• T is absolute temperature, in kelvins (K).

The calculator reports pressure in kPa and also gives the equivalent value in Pa. Since 1 kPa = 1,000 Pa, it divides the pressure in pascals by 1,000 for the main result. The equation calculates absolute pressure, not gauge pressure relative to the surrounding atmosphere.

Worked Example

Using the calculator’s default values—mass 1 kg, volume 1 m³, temperature 300 K, and specific gas constant 287 J/(kg·K)—substitute into the equation:

p = (1 kg × 287 J/(kg·K) × 300 K) ÷ 1 m³

The kelvin and kilogram units cancel appropriately, leaving pressure in pascals. The numerator is 86,100, so:

• Pressure = 86,100 Pa.
• Convert to kilopascals: 86,100 ÷ 1,000 = 86.10 kPa.

The displayed result is 86.10 kPa, with the helper output showing 86,100 Pa.

What the Formula Describes

The equation comes from the ideal gas law, commonly written as pV = nRᵤT, where n is the amount of gas in moles and Rᵤ is the universal gas constant. Replacing the amount in moles with mass divided by molar mass gives the mass-based form pV = mRT. In that form, R is specific to the gas: it equals the universal gas constant divided by the gas’s molar mass.

The model captures a useful relationship among a gas’s pressure, volume, temperature, and quantity. If the gas mass and volume stay fixed, raising its absolute temperature raises its pressure in direct proportion. If mass and temperature stay fixed, reducing the volume raises pressure. Doubling the gas mass at the same volume and temperature also doubles the calculated pressure.

These proportional relationships assume the gas behaves ideally. Real gases can depart from that approximation, especially at high pressure or near condensation, when interactions between molecules and their finite size matter more.

Choosing Inputs and Units

Use consistent units throughout. The calculator’s inputs follow SI units: kilograms, cubic metres, kelvins, and J/(kg·K). For air, a commonly used approximate specific gas constant is 287 J/(kg·K); other gases have different values. For a precise calculation, use a value appropriate to the gas composition and conditions rather than assuming air.

Convert measurements before entering them. For example, 1 litre is 0.001 m³, and 1 gram is 0.001 kg. Temperature must be absolute: convert Celsius to kelvins by adding 273.15, or Fahrenheit to kelvins using (°F − 32) × 5/9 + 273.15. Do not enter a Celsius or Fahrenheit number as though it were kelvins.

In US customary work, pressure may be expressed in pounds per square inch (psi), mass in pounds mass, volume in cubic feet, and temperature in degrees Rankine. Those units require a compatible gas constant and careful treatment of force and mass units. A reliable approach is to convert all inputs to SI, calculate, then convert the pressure if needed: 1 kPa is approximately 0.1450 psi. Do not combine an SI value of R with unconverted US customary inputs.

When It Applies—and Its Limits

Use the formula for a gas when its mass, volume, temperature, and specific gas constant are known and an ideal-gas estimate is suitable. It can help with basic classroom problems, approximate gas-state calculations, and checking how pressure changes when one condition varies. The result presumes the listed gas occupies the stated volume at a uniform temperature and pressure.

The equation is not a general formula for liquids or solids. It also does not by itself account for a mixture’s detailed composition, changing temperature across a container, chemical reactions, leakage, or non-ideal behavior. For a gas mixture, an appropriate mixture-specific gas constant can be used for an ideal-mixture calculation, but the composition must be known.

For high-accuracy work with a dense or strongly non-ideal gas, a real-gas equation of state or measured property data may be needed. The ideal-gas result should then be treated as an estimate, not as a guaranteed physical measurement.

Common Mistakes

• Using gauge pressure as absolute pressure: The equation yields absolute pressure. Gauge pressure is measured above local atmospheric pressure, so convert it to absolute pressure before using it; approximately, absolute pressure equals gauge pressure plus atmospheric pressure.
• Entering the wrong temperature scale: The formula requires kelvins. A temperature of 27°C is about 300.15 K, not 27 K.
• Mixing units: A volume in litres or a mass in grams must be converted to cubic metres or kilograms for the calculator’s inputs.
• Using the wrong gas constant: R depends on the gas. The approximate air value is not valid for every gas.
• Rounding too early: Keep extra digits through the calculation and round the final pressure to a sensible precision. A calculator’s decimal display does not make uncertain input data more precise.

Frequently Asked Questions

What is the formula for pressure when mass and volume are known?
For an ideal gas, use p = mRT/V. You also need absolute temperature and the specific gas constant for the gas.

Can pressure be calculated from mass and volume alone?
No. Mass and volume alone do not determine gas pressure. Temperature and the gas’s specific gas constant are also required.

What is the pressure–volume formula?
The ideal gas law is pV = nRᵤT, or pV = mRT in mass-based form. If the amount and temperature are fixed, pressure and volume vary inversely in this model.

Does this formula give gauge pressure?
No. It gives absolute pressure. To obtain gauge pressure, subtract the surrounding atmospheric pressure from the calculated absolute pressure, using matching units.

Which value of R should I use?
Use the specific gas constant for the gas and units in your calculation. For air, about 287 J/(kg·K) is a common approximation; other gases require their own value.

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in m | Gas mass | kg | 1 | 0
in v | Volume | m^3 | 1 | 0
in t | Temperature | K | 300 | 0
in r | Specific gas constant | J/(kg·K) | 287 | 0
out p | Pressure | kPa | m * r * t / v / 1000 | 2
out pd | Pressure | Pa | m * r * t / v | 0