Ideal Gas Law
Solve ideal gas law problems for pressure using PV = nRT with clear substitutions, SI units, and step-by-step output.
Key formula
PV = nRT
How do you use the ideal gas law?
Use PV = nRT. Solve for the unknown: P = nRT/V, V = nRT/P, n = PV/RT, or T = PV/nR. Temperature must be in kelvin. Keep R matched to your pressure and volume units.
About this tool
The ideal gas law connects pressure, volume, temperature, and amount of gas in one equation: PV = nRT. This page keeps that model visible so you can solve for any one variable without losing the Kelvin and unit checks.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: find pressure
n = 1.0 mol, V = 0.024 m³, T = 300 K, R = 8.314. P = nRT/V = (1)(8.314)(300)/0.024 ≈ 1.04 × 10⁵ Pa ≈ 1.04 atm.
Example 2: convert °C first
P = 1.0 atm, V = 10 L, n = 0.40 mol, t = 27 °C. T = 300 K. With R = 0.0821, check V ≈ nRT/P = (0.40)(0.0821)(300)/1 ≈ 9.9 L — consistent.
Example 3: find moles
P = 2.0 atm, V = 5.0 L, T = 250 K, R = 0.0821. n = PV/RT = (2)(5)/(0.0821 × 250) ≈ 0.49 mol.
Frequently asked questions
What is the ideal gas law formula?
PV = nRT, where P is pressure, V volume, n moles, T absolute temperature in kelvin, and R the gas constant matched to your units.
Which value of R should I use?
Match R to P and V units. Common choices: 8.314 J/(mol·K) with Pa and m³, or 0.0821 L·atm/(mol·K) with liters and atmospheres. Mixing R with the wrong units breaks the answer.
Why must T be in kelvin?
Gas laws use absolute temperature. Convert °C with T(K) = t(°C) + 273 (or 273.15). Using Celsius directly in PV = nRT is wrong.
How is this different from the combined gas law?
PV = nRT includes amount of gas n and one state. The combined gas law P₁V₁/T₁ = P₂V₂/T₂ compares two states at fixed n. Use combined gas when n is constant and you have before/after data.
When does the ideal gas law fail?
It is a model. Real gases deviate at high pressure or low temperature near liquefaction. For school problems, use PV = nRT unless the paper says otherwise.