Boyles Law Calculator
The piston’s bargain at constant temperature: pressure and volume trade exactly, P·V — blank the box, the squeeze prices itself.
Boyles Law Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Isothermal only — fast squeezes that heat break the bargain
- Absolute pressure; add 1 atm to gauge readings
In short: 2 L of gas at 1 atm squeezed to 1 L: P·V is the same either side — 1 × 2 = 2 × 1 — so the pressure reads 2.000000 atm. A 6 L breath taken to 5 m of depth (where ambient is 1.5–3 atm depending on the tables) shrinks to 1.200000 L at 5 atm: the same moles, half the room, twice the push. The isothermal fine print is doing real work here — temperature held, bargain honoured.
Formula
P₁V₁ = P₂V₂ · P·V constant at constant T · half the room, twice the push
Boyle’s law is the spring inside every gas: at fixed temperature, pressure times volume is a constant, so the two trade in exact inverse — double one, halve the other. It is compressed kinetics, not a new law: the same nRT from the ideal-gas equation with T pinned, wearing its seventeenth-century hat.
Worked Example
- Enter the before state: P₁ and V₁.
- Enter one of the after state’s boxes.
- Leave exactly one after-box blank to solve.
- Read the trade on the middle card.
Defaults: 1 atm × 2 L squeezed at 2 atm → 1.000000 L. The 6 L breath at 5 atm: 1.200000 L. Reverse: 1 atm × 2 L freed to 1 atm → 2.000000 L.
Strengths & Limits Of This Model
Where this engine is strong
- Exactly-one-blank solver on the after state
- The trade printed as the product’s equality
Where it stops
- No adiabatic branch
- No real-gas correction
Practical Use Cases
Syringes and pistons
the squeeze, priced
Gas transfer
what the receiving cylinder holds
Diving physics
volume changes with depth
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Boyles Law Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why must temperature stay constant for Boyle’s law?
Because the law is the ideal-gas equation with T pinned: P·V = nRT, and the right side is a constant only while T is. Compress a gas fast and it heats — the pump’s warm cap is the fine print made visible. Slow squeezes exchange heat with the room and keep the bargain; fast ones break it.
Why does doubling pressure halve the volume exactly?
Because the trade is inverse, not merely negative: the product P·V is the fixed thing, so every doubling on one side is a halving on the other. Tenth the volume, ten times the push — which is why compressed-gas cylinders hold enormous quantities in a small drum at enormous pressure.
Is the law still true for a sealed syringe half-plugged?
The arithmetic holds for the GAS; the plug changes the story — blocked outlets turn volume changes into pressure spikes with no give. Boyle describes what the gas must do; engineering describes what the container survives. The two meet at the pressure rating.
What does the law say about a diver’s lungs?
The famous warning: a breath taken at depth expands as the diver rises — 6 L at 5 atm would try to be far more volume at the surface, and lungs are not built to stretch. Exhale on ascent is the whole of the safety doctrine, and it is Boyle’s bargain read aloud. This page prices the arithmetic; training prices the habit.
Can I use gauge pressure in the boxes?
No — the law speaks ABSOLUTE pressure, and gauge reads the excess over atmosphere. A tyre at 0 gauge still holds 1 atm of gas. Add 1 atm to gauge readings before entry, or the inverse trade misfires at the very low pressures where it matters most.
How does this connect to the Charles page?
They are the two slices of the same state equation: Boyle holds TEMPERATURE and trades P against V; Charles holds PRESSURE and trades V against T. Together with Avogadro’s V–n slice they reassemble into PV = nRT — the seventeenth and eighteenth centuries discovering one equation one slice at a time.
Why does the page need exactly one blank?
Three of the four state numbers fix the fourth — that is what an equation of state means. Filling everything over-determines the state; blanking two under-determines it. The refusal messages are the grammar of equations, not fussiness.
Where did the constant go?
Into the product: P₁V₁ = P₂V₂ says the before and after products are the same number, so the page never needs the constant’s value — only its equality. If you want the constant with units and all, it is nRT wearing Boyle’s hat, and the ideal-gas page unwears it.