Ideal Gas Law Calculator (PV = nRT)
Pick the quantity you want to find, enter the other three, and choose your units. The calculator uses R = 8.314462618 J/(mol K) and converts everything for you.
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Formula
P × V = n × R × T
- P is pressure, V is volume, n is the amount of gas in moles and T is absolute temperature in kelvin.
- R = 8.314462618 J/(mol K), the exact SI value.
- Rearranged:
P = nRT / V,V = nRT / P,n = PV / RT,T = PV / nR. - Units are converted to pascals, cubic metres and kelvin first: 1 atm = 101325 Pa, 1 bar = 100000 Pa, 1 mmHg = 101325 / 760 Pa, 1 L = 0.001 m³, K = °C + 273.15.
Worked example
What pressure do 2 mol of gas exert in a 10 L container at 25 °C?
- T = 25 + 273.15 = 298.15 K and V = 10 L = 0.010 m³.
- P = 2 × 8.314462618 × 298.15 ÷ 0.010 = 495 791 Pa.
- That is 495.79 kPa, or about 4.893 atm.
Frequently asked questions
What is the ideal gas law formula?
PV = nRT, where P is pressure, V is volume, n is the amount of gas in moles, T is the absolute temperature in kelvin and R = 8.314462618 J/(mol K). For 1 mol at 273.15 K and 101325 Pa, V = 8.314462618 × 273.15 ÷ 101325 = 0.022414 m³, or 22.414 L.
Why must temperature be in kelvin?
Gas volume and pressure fall towards zero at absolute zero, not at 0 °C, so the law needs a scale that starts there. If you enter Celsius, the calculator adds 273.15 for you: 25 °C becomes 298.15 K.
Which value of R should I use with atm and litres?
In atm and litres R is 0.082057 L atm/(mol K). This calculator converts every unit to pascals, cubic metres and kelvin first, so you never pick R yourself. 2 mol in 10 L at 25 °C gives 495.79 kPa, which is 4.893 atm.
When does the ideal gas law stop being accurate?
It works best for gases at low pressure and high temperature, where molecules are far apart and barely attract each other. Near condensation or above roughly 10 atm real gases deviate, and the van der Waals equation is a better model.
How many litres is one mole of gas?
It depends on conditions. At 0 °C and 1 atm it is 22.414 L, and at 25 °C and 1 atm it is 24.465 L. At 0 °C and 1 bar (the current IUPAC standard pressure) it is 22.711 L.