Van der Waals Equation Calculator
Van der Waals equation calculator for real gases: solve for pressure, volume, temperature, moles or the a and b constants.
(P + an²V²)(V − n·b) = n · R · T
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
The van der Waals equation corrects the ideal gas law for real gases: the term a·n²/V² accounts for attraction between molecules and n·b for their own volume.
Enter a and b for your gas (CO₂: a = 3.640 L²·bar/mol², b = 0.04267 L/mol). Pressure, temperature, a and b are solved exactly; volume and amount need the cubic equation, which is solved numerically and returns the gas-phase root.
Formula
(P + an²V²)(V − n·b) = n · R · T
| Symbol | Quantity | Units |
|---|---|---|
| n | Amount of gas | mol, mmol, µmol, nmol, kmol |
| T | Temperature | K, °C, °F, °R |
| a | Attraction parameter a | L²·bar/mol², L²·atm/mol², Pa·m⁶/mol² |
| b | Excluded volume b | L/mol, cm³/mol, m³/mol |
| V | Volume | L, mL, µL, m³, dm³, cm³, gal, gal (UK), qt, pt, cup, fl oz, ft³, in³ |
| P | Pressure | Pa, kPa, MPa, hPa, bar, mbar, atm, Torr, mmHg, psi, inHg |
Constants used: R = 8.314462618 J·mol⁻¹·K⁻¹
Worked example
Given: n = 1 mol · T = 26.85 °C · a = 3.64 L²·bar/mol² · b = 0.04267 L/mol · V = 24.5 L
P = n · R · TV − n·b − a · n²V²
Result: P = 1.01381 bar
Frequently asked questions
What do the constants a and b mean?
a measures intermolecular attraction (larger for easily liquefied gases); b is the volume excluded by one mole of molecules.
When should I use it instead of PV = nRT?
At high pressures (above about 10 bar) or low temperatures, where the ideal gas law error exceeds a few percent.