# Van der Waals Equation Calculator

URL: https://speedycalculator.com/calculators/physics/van-der-waals-equation/
Last updated: 2026-10-30

> The van der Waals equation calculator finds the pressure (or temperature) of a real gas from its amount, volume and temperature using the van der Waals constants a and b, and compares it with the ideal gas law.

## Inputs

- Gas
- a (Pa·m⁶/mol²)
- b (m³/mol)
- Find
- Amount n (mol)
- Volume V (L, m³, mL, ft³)
- Temperature T (K, °C, °F)
- Pressure p (kPa, Pa, bar, atm, psi, MPa)

## Results

- Pressure (van der Waals)
- Pressure (ideal gas)
- Temperature (van der Waals)
- Temperature (ideal gas)

## Formula

```
(p + a·n²/V²)·(V − n·b) = n·R·T
```

## Explanation

Real gas molecules attract each other and take up space. Johannes van der Waals added two corrections to the ideal gas law in 1873 – a for attraction and b for molecular volume – earning a Nobel Prize and explaining condensation.

### How to use the Van der Waals Equation Calculator

- **Gas**
- **a (Pa·m⁶/mol²)**
- **b (m³/mol)**
- **Find**
- **Amount n (mol)**
- **Volume V**
- **Temperature T**
- **Pressure p**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the gas (or enter a and b), what to find, and the amount, volume and temperature or pressure.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterGasChoose one: Helium, Neon, Hydrogen, Nitrogen …a (Pa·m⁶/mol²)A numberb (m³/mol)A numberFindChoose one: Pressure p, Temperature TAmount n (mol)A numberVolume VUnits: L, m³, mL, ft³Temperature TUnits: K, °C, °FPressure pUnits: kPa, Pa, bar, atm, psi, MPa

### What each result means

- **Pressure (van der Waals)** = [Amount n (mol)]×8.314462618×[Temperature T]÷([Volume V] - [Amount n (mol)]×[b]) - [a]×[Amount n (mol)]^2÷[Volume V]^2
- **Pressure (ideal gas)** = [Amount n (mol)]×8.314462618×[Temperature T]÷[Volume V]
- **Temperature (van der Waals)** = ([Pressure p] + [a]×[Amount n (mol)]^2÷[Volume V]^2)×([Volume V] - [Amount n (mol)]×[b])÷([Amount n (mol)]×8.314462618)
- **Temperature (ideal gas)** = [Pressure p]×[Volume V]÷([Amount n (mol)]×8.314462618)

### Example values

How the main result changes when **a** changes and everything else stays at the example values above:

a (Pa·m⁶/mol²)Pressure (van der Waals) (kPa)0.06852,241.51620.10282,241.51620.1372,241.51620.17132,241.51620.20552,241.51620.2742,241.5162

## Worked example

Inputs — Gas: Carbon dioxide; Find: Pressure p; Amount n (mol): 1; Volume V: 1 L; Temperature T: 300 K.

Results — **Pressure (van der Waals) = 2,241.51616 kPa**; Pressure (ideal gas) = 2,494.33879 kPa.

## Key terms

- **Real gas**: Gas with intermolecular forces and finite molecular size.

## FAQ

**What do a and b represent?**
a: intermolecular attraction; b: volume excluded by the molecules.

**When is the correction important?**
At high pressures and low temperatures.

**Can the equation predict condensation?**
Qualitatively, with the Maxwell construction.

**Is it the most accurate real-gas model?**
No – Peng–Robinson and others are better for engineering.


## Sources

- [OpenStax – Chemistry 2e](https://openstax.org/details/books/chemistry-2e)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)