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Chemistry

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂. Free online Combined Gas Law. Calculate combined gas law online — fast, accurate, mobile-friendly, no signup needed.

P₁V₁/T₁ = P₂V₂/T₂.
V₂
5.494505

Derivation

  1. ├── 01GivenP1 = 1, V1 = 10, T1 = 273, P2 = 2, T2 = 300
  2. ├── 02Formulat × a × e.T2 / (n × r)
  3. ├── 03Substitutet × a × e.300 / (n × r)
  4. └── 04Compute V₂5.494505
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 Combined Gas Law

The Combined Gas Law computes V₂ from 5 inputs: p₁, v₁, t₁, p₂, t₂. P₁V₁/T₁ = P₂V₂/T₂.

Chemistry turns grams and moles into reactions. Getting the stoichiometry, dilutions, or concentrations right is the difference between a lab result you can trust and one you can’t reproduce. The Combined Gas Law sits in that toolkit — it P₁V₁/T₁ = P₂V₂/T₂. 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

t × a × e.T2 / (n × r)

Where

P1
P₁
V1
V₁
T1
T₁
P2
P₂
T2
T₂
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: P₁ = 1, V₁ = 10, T₁ = 273, P₂ = 2, T₂ = 300.

  1. 01Start by noting the input — P₁: 1.
  2. 02Start by noting the input — V₁: 10.
  3. 03Start by noting the input — T₁: 273.
  4. 04Start by noting the input — P₂: 2.
  5. 05Start by noting the input — T₂: 300.
  6. 06Substitute these values into the formula: t × a × e.T2 / (n × r)
  7. 07Compute V₂: the calculator returns 5.49451.
  8. 08Cross-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 Combined 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

P₁ halved

P1 = 0.5 (from 1)

Keep every other input at its default and halve the p₁. See how v₂ responds.

  1. 01New P₁: 0.5
  2. 02Baseline V₂: 5.49451
  3. 03New V₂: 2.74725
  4. 04V₂ decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

P₁ doubled

P1 = 2 (from 1)

Keep every other input at its default and double the p₁. See how v₂ responds.

  1. 01New P₁: 2
  2. 02Baseline V₂: 5.49451
  3. 03New V₂: 10.989
  4. 04V₂ increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

V₁ halved

V1 = 5 (from 10)

Keep every other input at its default and halve the v₁. See how v₂ responds.

  1. 01New V₁: 5
  2. 02Baseline V₂: 5.49451
  3. 03New V₂: 2.74725
  4. 04V₂ decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

V₁ doubled

V1 = 20 (from 10)

Keep every other input at its default and double the v₁. See how v₂ responds.

  1. 01New V₁: 20
  2. 02Baseline V₂: 5.49451
  3. 03New V₂: 10.989
  4. 04V₂ 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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