Ideal Gas Law Calculator (PV = nRT)
Solve PV = nRT for any unknown. Enter three of pressure (Pa), volume (m³), moles and temperature (K) to find the fourth. Uses R = 8.314 J/mol·K.
How to use this tool
- Enter pressure (p), volume (v), amount (n) and temperature (t) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your pressure and the full breakdown beneath it.
The ideal gas law combines Boyle's, Charles's and Avogadro's laws: PV = nRT, where P is pressure (Pa), V is volume (m³), n is amount (mol), R = 8.314 J/mol·K, and T is temperature (K). Convert Celsius to Kelvin: T(K) = T(°C) + 273.15.
Formula
PV = nRT
Solve for any unknown: P = nRT ÷ V | V = nRT ÷ P | n = PV ÷ (RT) | T = PV ÷ (nR)
Where P = pressure (Pa), V = volume (m³), n = moles (mol), T = temperature (K), R = 8.31446 J/(mol·K).
How it works
This calculator applies the ideal gas law, which relates the pressure, volume, amount, and temperature of a gas through the universal gas constant R = 8.31446 J/(mol·K). Set one of the four variables to zero to designate it as the unknown; the calculator solves the appropriate rearrangement. The ideal gas law is accurate for most gases at moderate pressures and temperatures, but deviates for real gases at very high pressures or near condensation points.
Worked example
- Given: V = 0.022414 m³, n = 1 mol, T = 273.15 K (0 °C, STP). Pressure is unknown.
- Apply: P = nRT ÷ V = 1 × 8.31446 × 273.15 ÷ 0.022414.
- Calculate numerator: 8.31446 × 273.15 ≈ 2271.15; then 2271.15 ÷ 0.022414 ≈ 101324.83 Pa.
Pressure = 101,324.83 Pa (very close to 1 standard atmosphere = 101,325 Pa)
Common mistakes to avoid
- Entering temperature in Celsius instead of Kelvin -- 25 degrees C must be entered as 298.15 K; using 25 gives a wildly wrong result.
- Using pressure in atm or bar instead of Pascals without converting -- 1 atm = 101325 Pa, and R = 8.314 J/(mol K) only pairs correctly with Pa and m cubed.
- Entering volume in litres instead of cubic metres -- 1 L = 0.001 m cubed, so a 2-litre flask must be entered as 0.002.
Key terms
- Ideal gas
- A theoretical gas whose molecules occupy no volume and exert no intermolecular forces. Real gases approximate this behaviour at low pressure and high temperature.
- Universal gas constant (R)
- A physical constant equal to 8.31446 J/(mol·K), relating energy scale to temperature and amount in the ideal gas law.
- STP (Standard Temperature and Pressure)
- Defined as 273.15 K (0 °C) and 101,325 Pa (1 atm). One mole of an ideal gas occupies approximately 22.414 litres at STP.
- Mole (mol)
- The SI unit for amount of substance. One mole contains approximately 6.022 × 1023 particles (Avogadro's number).
- Temperature in Kelvin (K)
- The absolute temperature scale required by the ideal gas law. K = °C + 273.15. Zero Kelvin is absolute zero, the lowest possible temperature.
Frequently asked questions
- What is standard temperature and pressure (STP)?
- STP is 273.15 K (0 °C) and 101,325 Pa (1 atm). One mole of ideal gas occupies 22.414 litres at STP.
- When does the ideal gas law break down?
- At very high pressures or very low temperatures, intermolecular forces matter and you need the van der Waals equation or other corrections.