Van der Waals equation formulas and interpretation
The Van der Waals equation modifies the ideal-gas model for molecular attraction and finite molecular volume.
The interface retains gas presets and separate pressure, temperature, and numerical volume modes.
How to use the Van der Waals equation calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
The attraction parameter corrects pressure and the covolume parameter corrects available volume.
(P + an²/V²)(V − nb) = nRT- P — Pressure
- Real-gas pressure (atm)
- V — Volume
- Container volume (L)
- n — Amount
- Amount of gas (mol)
- T — Temperature
- Absolute temperature (K)
- a — Attraction constant
- Gas-specific attraction parameter (L²·atm/mol²)
- b — Covolume constant
- Gas-specific excluded-volume parameter (L/mol)
Nitrogen pressure example
Estimate pressure for 1 mol N₂ at 298.15 K in 24.47 L.
- a
- 1.370 L²·atm/mol²
- b
- 0.0387 L/mol
- Volume
- 24.47 L
- P = nRT/(V−nb) − a(n/V)²
Result: The pressure is approximately 1.00 atm.
At this low density, the real-gas correction is small.
Understanding your results
Interpreting the result
Results depend on the selected empirical constants and are least reliable near phase boundaries.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.