Van der Waals Equation Calculator
Solve the van der Waals equation for any real gas. Select a gas to pre-load its a and b constants, choose which variable to find, enter the remaining state variables, and compare the real-gas result with the ideal-gas prediction.
Gas
Solve for
m³
mol
K
From the van der Waals equation (P + an²/V²)(V − nb) = nRT
- 1
Excluded volume n×b
1 × 0.0000427 = 0.0000427 - 2
Thermal pressure nRT/(V−nb)
1 × 8.314 × 300 ÷ (0.001 − 0.0000427) = 2,605,516.16 - 3
Attraction correction an²/V²
0.36442 × 1² ÷ 0.001² = 364,420 - 4
Pressure P
2,605,516.16 − 364,420 = 2,241,096.1599Real-gas pressure equals ideal thermal pressure minus the intermolecular-attraction correction.
How does this calculator work?
The van der Waals equation (P + an²/V²)(V − nb) = nRT corrects ideal-gas law for molecular size (b) and attraction (a). Select a gas, enter any three of P, V, n, T, and the calculator solves for the fourth — using Newton-Raphson iteration for volume — then shows how far the result deviates from ideal gas behaviour.
Formula
How this is calculated
The ideal gas law PV = nRT treats molecules as point particles with no interactions. The van der Waals equation corrects for two real-gas effects: the constant a accounts for intermolecular attraction, which reduces the pressure a gas exerts (the a·n²/V² term adds back to the measured pressure P); and b is the excluded volume per mole — the physical space occupied by the molecules themselves — which reduces the space available for motion (replaced V with V − nb).
Solving for pressure and temperature requires simple rearrangement. Solving for volume is harder: the van der Waals equation is a cubic in V, which this calculator solves numerically using Newton-Raphson iteration starting from the ideal gas volume. Near the liquid–vapour coexistence region a cubic can have three real roots (representing liquid, unstable, and vapour phases); the solver tracks the largest physically meaningful (gas-phase) root.
All a and b constants are given in SI units (Pa·m⁶/mol² and m³/mol) and sourced from the CRC Handbook of Chemistry and Physics, 97th Edition. The deviation from ideal is computed as (P_vdW − P_ideal)/P_ideal × 100 %. Large deviations appear at high pressure or low temperature — exactly the conditions where the ideal-gas approximation breaks down.
Frequently asked questions
The constant a (Pa·m⁶/mol²) measures the strength of intermolecular attraction: larger a means stronger attractive forces, which pull molecules toward each other and reduce the pressure below the ideal value. The constant b (m³/mol) is the molar excluded volume — the hard-sphere space each mole of molecules occupies and prevents others from entering.
Near or below the gas critical point the cubic equation can have multiple roots (liquid/gas coexistence) or no physically valid real root at all. The Newton-Raphson method used here targets the gas-phase (largest) root and validates that V > nb. If conditions are too close to condensation, no result is returned.
Pressure: 1 Pa = 9.869×10⁻⁶ atm = 1×10⁻⁵ bar. Volume: 1 m³ = 1000 L. Temperature stays in kelvin; K = °C + 273.15. The a constants in the usual L²·atm/mol² can be converted to Pa·m⁶/mol² by multiplying by 0.101325.
Also known as
TG we-Calculate Editorial Team. (2026). Van der Waals Equation Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/van-der-waals-equation-calculator
TG we-Calculate Editorial Team. "Van der Waals Equation Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/van-der-waals-equation-calculator.
TG we-Calculate Editorial Team, "Van der Waals Equation Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/van-der-waals-equation-calculator
@misc{wecalculate_van_der_waals_equation_calculator, title = {Van der Waals Equation Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/van-der-waals-equation-calculator}}, year = {2026}, note = {TG we-Calculate} }
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