How this Boyle’s Law Calculator Works
This tool applies the isothermal gas relationship P₁V₁ = P₂V₂, which holds for a fixed amount of gas at constant temperature.
Enter any three known values and select the unknown (P₂, V₂, P₁, or V₁). The calculator converts all inputs into consistent SI units behind the scenes, performs the algebra, and then displays the result in your chosen units.
Because pressure and volume are inversely related at constant temperature and moles, increasing pressure compresses the gas (smaller volume), while decreasing pressure allows expansion (larger volume).
Formula, Variables, and Units
Boyle’s Law is typically written as P₁V₁ = P₂V₂. Here, P represents pressure and V volume.
Common pressure units include Pa, kPa, MPa, bar, atm, Torr/mmHg, and psi. Volume units include m³, L, mL, ft³, and in³.
The calculator is unit-aware: it accepts any combination and ensures proper conversion before solving. You can optionally display results in scientific notation and control significant figures, including trailing zeros for lab-style reporting.
| Symbol | Quantity | Typical Units | Notes |
|---|
| P₁, P₂ | Pressure (initial/final) | atm, bar, kPa, Pa, psi, Torr | Use the unit selectors; conversions are automatic. |
| V₁, V₂ | Volume (initial/final) | L, mL, m³, ft³, in³ | Works with both metric and imperial units. |
| T | Temperature (context) | K, °C | Constant for Boyle’s Law; used if switching to the Combined Gas Law. |
| Z | Compressibility factor | — | First-order non-ideal correction when gases deviate from ideal behavior. |
Using the Interface Efficiently
Choose the unknown, type known values, and adjust the sliders for quick “what-if” exploration. The PV badge shows the product (or PV/(TZ) in Combined mode), helping you verify internal consistency.
The isotherm plot updates in real time and displays tooltips with the current P, V, and PV product at the cursor point.
Scenario presets (SCUBA, syringe, balloon, lung, piston) instantly populate realistic values. Uncertainty fields (±%) propagate a basic percentage estimate into the final answer for quick error awareness.
Worked Example
Suppose P₁ = 1.00 atm and V₁ = 2.00 L. If the gas is compressed to P₂ = 1.33 atm, Boyle’s Law predicts the new volume:
V₂ = (P₁V₁)/P₂ = (1.00 × 2.00)/1.33 ≈ 1.50 L. The calculator performs this with correct unit handling and lets you compare ratios P₂/P₁ and V₂/V₁.
| State | Pressure | Volume | PV Product | Ratios |
|---|
| Initial | 1.00 atm | 2.00 L | 2.00 atm·L | — |
| Final | 1.33 atm | 1.50 L | 2.00 atm·L | P₂/P₁ = 1.33, V₂/V₁ = 0.75 |
Beyond the Ideal Assumption
At high pressures or low temperatures, real gases deviate from ideal behavior. Use the Z toggle for a simple correction, or enable the van der Waals option (requires n and T) to compute P₂ or V₂ under isothermal conditions with the vdW equation.
If temperature changes are significant, switch to the Combined Gas Law mode to incorporate T₁ and T₂ properly.
Saving and Sharing Your Work
Use the export buttons to download input data, a batch CSV of results, and the PV plot image. Print to PDF for a clean report of inputs, steps, and outputs.
The permalink encodes your settings so the exact scenario can be reopened or shared with classmates or colleagues.