Partial Pressure Calculator — Dalton's Law

Background.

This partial pressure calculator applies Dalton's law, pᵢ = xᵢ × p: the partial pressure of one component of a gas mixture is its mole fraction multiplied by the total pressure of the mixture. It answers the question in four directions — give it a fraction and a total to get a partial pressure, a partial and a total to get a fraction, a partial and a fraction to get a total, or the raw mole amounts of a component and of the whole mixture and it will work the fraction out itself.

The idea behind the law is that in an ideal gas mixture the components ignore one another. Each behaves as if the others were not there, so each contributes pressure in proportion to how many of its molecules are present, regardless of whether those molecules are helium atoms or sulphur hexafluoride. The partial pressure of a component is defined as the pressure it would exert alone in the same container at the same temperature, and the total pressure is the sum of all of them. That summation property is the other half of Dalton's law and the fastest way to check a mixture calculation: work out every component's partial pressure and they must add back up to the total.

Temperature does not appear anywhere on this page, and that is not an omission. Writing pᵢ = nᵢRT/V for the component and p = nRT/V for the mixture and dividing one by the other cancels R, T and V entirely, leaving pᵢ/p = nᵢ/n = xᵢ. Dalton's law is temperature-independent and volume-independent for an ideal mixture. Heat a cylinder of medical air and both the oxygen partial pressure and the total pressure rise by the same factor, so the fraction is unchanged — which is why gas cylinders are labelled by percent composition rather than by partial pressure.

Three conventions govern the numbers. **Mole fraction, not percentage, and not mass fraction.** The input is a dimensionless amount fraction strictly greater than 0 and at most 1; oxygen in dry air is about 20.95 percent by volume, so the input is 0.2095. Entering 20.95 is rejected rather than silently used. Mole fraction and mass fraction are different quantities: O₂ is 20.95 percent of dry air's molecules but about 23.1 percent of its mass, because an O₂ molecule is heavier than the N₂ average. **Absolute pressure, not gauge.** A gauge reads the excess over ambient, so a cylinder gauge showing zero is at about 101.325 kPa absolute. **The units only have to be consistent.** Because pᵢ = xᵢp is a straight proportionality, entering both pressures in psi returns an answer in psi. The fields are labelled kPa because that is the SI-coherent choice; the results panel also reports the answer in conventional mmHg (1 mmHg = 133.322387415 Pa exactly) and in standard atmospheres (1 atm = 101 325 Pa exactly).

The model is an ideal gas mixture, and it inherits every limitation of the ideal gas law plus one of its own. It assumes the molecules have no volume and exert no forces on each other, so it degrades at high pressure and near condensation — a 200 bar diving cylinder is well outside the regime, and the real partial pressures in it differ measurably from the ideal prediction. Beyond that, it assumes the components do not react with one another and are not in equilibrium with a condensed phase. If a mixture contains water vapour in contact with liquid water, the water's partial pressure is fixed by its saturation vapour pressure at that temperature, not by any fraction you choose. If two components react, the composition is not constant and the question is not well posed.

A note on composition figures generally: the composition of dry air is not a universal constant. Atmospheric CO₂ has risen by roughly a third since 1960 and continues to climb about 2 to 3 ppm a year, with O₂ falling correspondingly, and any real sample carries a variable amount of water vapour on top. This page therefore takes composition as an input you supply and never bakes a value in. The 0.2095 default for the oxygen fraction is a rounded illustrative figure drawn from the U.S. Standard Atmosphere 1976 tabulation of dry air; treat it as an example, not as an authority for your own sample. On significant figures, the solver carries every step at 30-digit precision and rounds once, at the end, to ten decimal places; round the answer yourself to the precision your own composition figure justifies, which for most real mixtures is three or four significant figures at best.

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

The partial pressure of a component in a gas mixture is the pressure that component would exert if it alone occupied the whole container at the same temperature. Dalton's law of partial pressures states two things about it. First, each component's partial pressure is its amount (mole) fraction times the total pressure: pᵢ = xᵢ × p. Second, the total pressure of the mixture is the sum of the partial pressures of all the components: p = Σ pᵢ. The IUPAC Compendium of Chemical Terminology states the first form directly under the entry for pressure: '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.' The IUPAC Green Book gives the same definition with the gas-phase symbol y for the amount fraction, pB = yB p, and lists its coherent SI unit as the pascal. The amount fraction xᵢ is moles of component i divided by total moles of all components. It is dimensionless, lies between 0 and 1, and for an ideal gas is numerically identical to the volume fraction and to the pressure fraction — which is why compressed-gas cylinders are labelled in 'percent by volume' and why a 21 percent oxygen mixture has an oxygen partial pressure of 0.21 atm when the total pressure is 1 atm. It is not the mass fraction. Dalton's law holds exactly for ideal gases and is an excellent approximation for real gas mixtures at moderate pressure, well away from condensation, provided the components neither react nor sit in equilibrium with a liquid phase. Where a liquid is present — water in a humidifier, a solvent in a headspace vial — that species' partial pressure is set by its saturation vapour pressure at the system temperature and is not free to be chosen; that is Raoult's law territory rather than Dalton's.

How to use this calculator.

1. 01Choose what you want to work out. The first three options rearrange pᵢ = xᵢ × p; the fourth lets you enter mole amounts instead of a fraction.
2. 02If you know the composition as a fraction, enter it as a decimal between 0 and 1 — 20.95 percent is 0.2095. Percentages are rejected, not silently converted.
3. 03Enter the total pressure of the mixture in kilopascals, absolute. 1 atm = 101.325 kPa; 1 bar = 100 kPa; 1 mmHg = 0.133322387415 kPa; 1 psi = 6.894757 kPa. Add local atmospheric pressure to any gauge reading first.
4. 04If you know mole amounts instead, pick 'from mole amounts' and enter the moles of your component and the total moles of the whole mixture. Any consistent amount unit works because only the ratio is used.
5. 05Read the partial pressure in kPa, and the same value converted to conventional mmHg and to standard atmospheres beneath it.
6. 06Check your work with the 'everything else in the mixture' output: it is the total minus your component, so repeating the calculation for every component should make all the partial pressures add back up to the total.
7. 07Round the answer yourself to the significant figures your composition figure justifies — usually three or four, rarely more.

The formula.

Write the ideal gas law for one component of a mixture and for the mixture as a whole, in the same container at the same temperature:

pᵢ = nᵢ R T / V p = n R T / V

Divide the first by the second. R, T and V all cancel, leaving pᵢ / p = nᵢ / n = xᵢ, or pᵢ = xᵢ p. That cancellation is why this page has no temperature field and no volume field: they are genuinely absent from the relation, not merely assumed. The four modes are the three rearrangements of that equation plus one change of input basis:

pᵢ = xᵢ × p solve for the partial pressure xᵢ = pᵢ / p solve for the mole fraction p = pᵢ / xᵢ solve for the total pressure xᵢ = nᵢ / n, then pᵢ = xᵢ × p enter mole amounts instead of a fraction

Rounding stage: FINAL ONLY. Every division and multiplication is carried out in Decimal.js at 30-digit working precision, and one rounding to ten decimal places is applied at the return boundary. Nothing is rounded in between. One consequence is worth knowing: a partial pressure below about 1 × 10⁻⁷ kPa is at the edge of what ten decimal places can represent, so trace-gas work should be done in pascals or in parts per million rather than in kilopascals.

Unit conversions in the output panel. The conventional millimetre of mercury is defined exactly as 0.001 m × 13 595.1 kg m⁻³ × 9.806 65 m s⁻² = 133.322387415 Pa, and that is the factor used here. The torr is a different definition — exactly 101 325/760 Pa = 133.322368421… Pa — and is smaller by 1.4 parts in ten million. NIST Special Publication 811 lists both as 1.333224 × 10² Pa, i.e. they are interchangeable at any precision anyone measures. The standard atmosphere is exactly 101 325 Pa.

Invalid domain and what the calculator does about it. A mole fraction must satisfy 0 < xᵢ ≤ 1; exactly 1 is allowed and means a pure gas, exactly 0 is rejected because a component that is not present has no partial pressure to compute. A value above 1 is rejected, which catches the common mistake of entering a percentage. Pressures must be strictly positive, because they are absolute; a negative value is usually a gauge reading. A partial pressure greater than the total pressure is rejected, because it implies a mole fraction above 1 — the usual cause is one of the two being a gauge reading or being in a different unit. Moles of a component greater than total moles is rejected for the same reason. In every case the calculator names the offending field rather than returning a NaN or an infinity.

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 hard-coded constant precisely for this reason. Retrieved 2026-07-29.