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Physics

Ideal Gas Law

PV = nRT. Free online Ideal Gas Law. Calculate ideal gas law online — fast, accurate, mobile-friendly, no signup needed.

P·V = n·R·T.
Moles n
1.015606

Derivation

  1. ├── 01GivenP = 101325, V = 0.025, T = 300
  2. ├── 02Formulae.P × e.V / (8.314 × e.T)
  3. ├── 03Substitutee.101325 × e.0.025 / (8.314 × e.300)
  4. └── 04Compute Moles n1.015606
Did you know?

Robert Boyle (1662) discovered that for a fixed gas at constant T, P·V is constant — arguably the first scientific law expressed as an equation.

§01What is

Understanding the Ideal Gas Law

The Ideal Gas Law computes Moles n from 3 inputs: pressure (pa), volume (m³), temperature (k). PV = nRT.

Physics is the toolkit for turning a real-world observation into a prediction. Whether it’s a falling object, a moving car, or a stressed beam, the equations here are the same ones every engineer relies on. The Ideal Gas Law sits in that toolkit — it PV = nRT. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.P × e.V / (8.314 × e.T)

Where

P
Pressure (Pa)
V
Volume (m³)
T
Temperature (K)
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Pressure (Pa) = 101325, Volume (m³) = 0.025, Temperature (K) = 300.

  1. 01Start by noting the input — Pressure (Pa): 101325.
  2. 02Start by noting the input — Volume (m³): 0.025.
  3. 03Start by noting the input — Temperature (K): 300.
  4. 04Substitute these values into the formula: e.P × e.V / (8.314 × e.T)
  5. 05Compute Moles n: the calculator returns 1.01561.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Ideal Gas Law Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Pressure (Pa) halved

P = 50662.5 (from 101325)

Keep every other input at its default and halve the pressure (pa). See how moles n responds.

  1. 01New Pressure (Pa): 50662.5
  2. 02Baseline Moles n: 1.01561
  3. 03New Moles n: 0.507803
  4. 04Moles n decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Pressure (Pa) doubled

P = 202650 (from 101325)

Keep every other input at its default and double the pressure (pa). See how moles n responds.

  1. 01New Pressure (Pa): 202650
  2. 02Baseline Moles n: 1.01561
  3. 03New Moles n: 2.03121
  4. 04Moles n increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Volume (m³) halved

V = 0.0125 (from 0.025)

Keep every other input at its default and halve the volume (m³). See how moles n responds.

  1. 01New Volume (m³): 0.0125
  2. 02Baseline Moles n: 1.01561
  3. 03New Moles n: 0.507803
  4. 04Moles n decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Volume (m³) doubled

V = 0.05 (from 0.025)

Keep every other input at its default and double the volume (m³). See how moles n responds.

  1. 01New Volume (m³): 0.05
  2. 02Baseline Moles n: 1.01561
  3. 03New Moles n: 2.03121
  4. 04Moles n increases by 100% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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