The van der Waals equation is a corrected form of the ideal gas law for real gases: (P + a·n²/V²)(V − n·b) = nRT. Solving it for pressure gives P = nRT/(V − n·b) − a·n²/V². The term n·b shrinks the available volume because the molecules themselves take up space, and the term a·n²/V² lowers the pressure because molecules attract one another. With R = 0.0820573 L·atm·mol⁻¹·K⁻¹, volume in litres, and temperature in kelvin, the pressure comes out in atmospheres.

The constant a (in L²·atm·mol⁻²) measures the strength of the attraction between molecules — larger for polar or easily liquefied gases such as water vapour or ammonia, and small for the noble gases. The constant b (in L·mol⁻¹) is the excluded volume, roughly the space one mole of molecules physically occupies, so it grows with molecular size. Both are determined experimentally and tabulated per gas; for nitrogen a = 1.370 and b = 0.0387. They are entered here as plain numbers in those units.

The ideal gas law, P = nRT/V, assumes molecules are point particles with no attraction. The van der Waals equation adds two corrections that pull in opposite directions: the excluded volume n·b raises the pressure (the gas is squeezed into less free space), while the attraction term a·n²/V² lowers it. At low pressure and high temperature the two corrections are tiny and the two results agree closely. As the gas is compressed or cooled toward condensation, the attraction term usually dominates and the real pressure falls below the ideal value.

Deviations grow at high pressure and low temperature — conditions that crowd the molecules together so their finite size and mutual attraction can no longer be ignored. Near the point where a gas is about to liquefy, the van der Waals correction can be substantial. Gases with strong intermolecular forces, such as ammonia, carbon dioxide, and water vapour, deviate more than light, weakly interacting gases like helium and hydrogen. At ordinary room conditions most common gases are close to ideal, and the two pressures in this calculator differ by only a small amount.