Partial Pressure Calculator — Dalton's Law

Background.

Air on a high mountain is the same mixture as air at the coast, about 20.95% oxygen, yet it leaves people breathless. What pushes oxygen into the blood is not its percentage but its partial pressure, its share of the total pressure. With the barometer at 101.325 kPa that share is 0.2095 × 101.325 = 21.23 kPa; where the barometer reads 60 kPa it is only 12.57 kPa.

That multiplication is Dalton's law. In a mixture of gases each component contributes a partial pressure equal to its mole fraction times the total, pᵢ = xᵢ × p, and the partial pressures of all the components add up to the total. Four modes cover the ways the question arrives: a mole fraction and a total pressure give the partial pressure; a partial pressure and a total give the fraction; a partial pressure and a fraction give the total; or mole amounts give the fraction first and the partial pressure from it. Every result is also shown in millimetres of mercury and standard atmospheres, beside the pressure left over for the rest of the mixture.

Temperature and volume never come into it. For ideal gases sharing one container, pᵢ = nᵢRT ⁄ V and p = nRT ⁄ V, so their ratio is nᵢ ⁄ n and R, T and V cancel. Heating a sealed cylinder raises every partial pressure and the total by the same factor and leaves the composition alone.

Three habits keep the numbers right: enter the composition as a fraction (0.2095, not 20.95), use absolute pressures rather than gauge readings, and keep both pressures in one unit. The fields are labelled in kilopascals, and because the law is a plain proportion, psi in gives psi out for the partial pressure, though the mmHg and atm conversions assume kilopascals.

What is partial pressure calculator (dalton's law)?

A component's partial pressure is the pressure it would exert if it alone filled the container at the same temperature. The IUPAC Gold Book defines it under its entry for pressure as pᵢ = xᵢp, where xᵢ is the amount fraction of the constituent and p the total pressure; the Green Book writes the same relation as p_B = y_B p, using y for a gas-phase fraction. The amount fraction is the component's moles divided by the total moles. For ideal gases it equals the volume fraction, since equal volumes of gases at the same temperature and pressure hold equal numbers of molecules, which is why cylinder labels quote percent by volume. It is not the mass fraction: oxygen makes up 20.95% of dry air's molecules but about 23.1% of its mass, because an O₂ molecule (32.00 g/mol) outweighs the average air molecule (28.96 g/mol).

How to use this calculator.

1. 01Choose the mode: partial pressure from a fraction, fraction from a partial pressure, total pressure from both, or partial pressure from mole amounts.
2. 02Enter the fraction as a decimal between 0 and 1, so a cylinder labelled 32% oxygen goes in as 0.32. A composition quoted by mass has to be turned into moles first.
3. 03Enter absolute pressures in kilopascals: 1 atm = 101.325 kPa, 1 bar = 100 kPa, 1 psi = 6.894757 kPa. Add atmospheric pressure to a gauge reading before entering it.
4. 04For mole amounts, give the moles of your component and the total moles of the whole mixture, that component included. Millimoles or molecule counts work equally well, since only the ratio is used.
5. 05Check the result with the balance output. Repeat for each component and the partial pressures should add back up to the total.

The formula.

Dalton's law follows from the ideal gas law. In one container at one temperature, component i obeys pᵢ = nᵢRT ⁄ V and the whole mixture obeys p = nRT ⁄ V. Dividing gives pᵢ ⁄ p = nᵢ ⁄ n = xᵢ, so pᵢ = xᵢ × p, and summing over every component gives p = Σpᵢ because the fractions add to 1. The four modes are rearrangements of that one line: pᵢ = xᵢp, xᵢ = pᵢ ⁄ p, p = pᵢ ⁄ xᵢ, and, from moles, xᵢ = nᵢ ⁄ n followed by pᵢ = xᵢp. The balance output is p − pᵢ.

The unit conversions use exact definitions: 1 atm = 101,325 Pa, and the conventional millimetre of mercury is 13,595.1 kg/m³ × 9.80665 m/s² × 0.001 m = 133.322387415 Pa exactly. The torr, defined as 101,325 ⁄ 760 Pa, is smaller by about 1.4 parts in ten million, so NIST lists the two with the same rounded factor.

The ideal model weakens where the ideal gas law does: at high pressure, near condensation, and with strongly interacting molecules, where real-gas equations of state with mixing rules take over. It also cannot set the pressure of a component in contact with its own liquid. Water vapour over liquid water is pinned at the saturation vapour pressure, about 3.17 kPa at 25 °C, whatever fraction you might choose. Because the fraction must lie between 0 and 1, a partial pressure above the total, or component moles above the total moles, is refused as a sign of mixed units or a gauge reading.

A worked example.

Frequently asked questions.

References& sources.

1. [1]International Union of Pure and Applied Chemistry. Compendium of Chemical Terminology (the 'Gold Book'), 5th edition, online version 5.0.0 (2025), entry 'pressure' (P04819), which also defines partial pressure: 'Normal force acting on a surface divided by the area of that surface. For a mixture of gases the contribution by each constituent is called the partial pressure pᵢ = xᵢ p, where xᵢ is the amount fraction of the ith constituent and p is the total pressure.' Source documents: Green Book, 2nd ed., p. 12; Pure Appl. Chem. 1996, 68, 957, p. 987. Independent standards body; open access; retrieved and quoted 2026-07-29.
2. [2]International Union of Pure and Applied Chemistry. Quantities, Units and Symbols in Physical Chemistry (the 'Green Book'), 3rd edition, 2nd printing 2012, §2.10 'Chemical thermodynamics', p. 48. Tabulates 'partial pressure pB pB = yB p Pa' alongside mole fraction (amount fraction) x, y and total pressure p. Used as the SECOND, independent statement of the same definition — it writes the gas-phase amount fraction as y rather than x, and it is the document the Gold Book entry cites as its own source. Agrees exactly. Open access PDF, text verified locally; retrieved 2026-07-29.
3. [3]Thompson, A. & Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811, 2008 edition, Appendix B.8 'Factors for units listed alphabetically': 'millimeter of mercury, conventional (mmHg) → pascal (Pa): 1.333 224 E+02' and 'torr (Torr) → pascal (Pa): 1.333 224 E+02'. The source of this page's pressure-unit conversions and of the statement that mmHg and Torr are indistinguishable at published precision. Independent national metrology institute; open access; retrieved and quoted 2026-07-29.
4. [4]Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA Recommended Values of the Fundamental Physical Constants: 2022. NIST Standard Reference Database 121, 'molar gas constant' R = 8.314 462 618… J mol⁻¹ K⁻¹, listed as exact. Cited for the derivation pᵢ/p = nᵢ/n, in which R cancels; no numerical use is made of R on this page. Open access; retrieved 2026-07-29.
5. [5]National Oceanic and Atmospheric Administration, National Aeronautics and Space Administration & United States Air Force (1976). U.S. Standard Atmosphere, 1976. NOAA-S/T 76-1562, Washington DC. The tabulation from which the illustrative dry-air oxygen fraction used as this page's default input is taken. SCANNED GOVERNMENT REPORT: the NASA NTRS and NOAA copies both load (HTTP 200) but carry an unusable OCR text layer, so the figure could not be machine-verified from the scan; it is used here only as a rounded illustrative default, and composition is a user input rather than a fixed constant precisely for this reason. Retrieved 2026-07-29.