The partial pressure calculator above applies Dalton's law of partial pressures to a mixture of up to four gases. You give it the total pressure and the relative amount of each component, and it returns the pressure each gas contributes on its own. The amounts can be moles, mole percent, volume percent or mole fractions, because all four describe the same ratio and the tool normalises them before it does anything else. It also handles the case that catches most students out: a gas collected by displacement of water, where part of the measured pressure belongs to water vapour and not to the gas you were trying to make.
Arb Digital publishes free calculators that answer one question properly instead of half-answering ten. This page exists because partial pressure is arithmetically trivial and conceptually slippery. The multiplication takes two seconds; deciding what counts as the total pressure, whether volume percent may be used as mole percent, and whether the water correction applies is where the marks and the measurements are actually lost. Everything below explains those decisions rather than just restating the equation.
What This Partial Pressure Calculator Does
Dalton's law says that in a mixture of gases that do not react with one another, each gas exerts the pressure it would exert if it occupied the whole container by itself, and the total pressure is the sum of those individual pressures. The practical form used here is pi = xi × Ptotal, where xi is the mole fraction of component i.
The tool computes every mole fraction by dividing each amount by the sum of all the amounts, multiplies each fraction by the total pressure, and displays the result in whichever pressure unit you selected. Nothing is converted internally except for the water-vapour correction, which is calculated in bar and then converted to your working unit, so the number you read is in the unit you asked for.
The bar chart shows each gas's share of the total pressure, which is its mole fraction as a percentage. The fourth grid item re-adds every partial pressure as a deliberate check: it should match the total pressure you typed.
One boundary worth stating. Our pressure converter changes an existing pressure value from one unit to another and knows nothing about mixtures. This page splits one pressure among several gases. They are complementary, not overlapping, and if you need mole fractions on their own without touching pressure, the mole fraction calculator is the more direct route.
How to Use It
- Enter the total pressure and pick its unit. Every partial pressure comes back in that same unit, so choose the one your data is already in rather than converting by hand first.
- Choose how you are giving the amounts. Moles if you weighed or counted the gases, mole or volume percent if you have a composition analysis, mole fraction if you already have decimals.
- Fill in the gas rows. Name each gas so the bars are readable. A row with a blank amount, or an amount of zero, is skipped entirely rather than counted as a component.
- Set the water correction if the gas was collected over water. Choose the yes option and enter the water temperature. The tool removes the water vapour pressure from the total before dividing the rest among your named gases.
- Read the check line. The summed partial pressures in the fourth tile confirm the arithmetic closed. A mismatch means a stray value somewhere in the inputs.
The Formula and How It Is Calculated
Start from the ideal gas law applied to one component in a shared volume: piV = niRT. Apply it to the whole mixture: PV = ntotalRT. Divide the first by the second and V, R and T all cancel, leaving pi/P = ni/ntotal. That ratio is the mole fraction xi, so pi = xiP. The cancellation is the whole proof, and it is also the reason the law only holds while the gases behave ideally.
Work the default example. Dry air is close to 78.0 percent nitrogen, 21.0 percent oxygen, 0.9 percent argon and about 0.04 percent carbon dioxide by amount of substance. At a total pressure of 101.325 kPa, the partial pressure of nitrogen is 0.780 × 101.325 = 79.03 kPa, oxygen is 0.210 × 101.325 = 21.28 kPa, argon is 0.900 kPa and carbon dioxide is 0.041 kPa. Adding those four back gives 101.25 kPa, slightly under the total only because the four fractions supplied sum to 0.9994 rather than exactly 1. The tool normalises, so it reports fractions that do sum to 1 and partial pressures that do sum to the total.
Pressure itself is force per unit area, and the SI unit is the pascal, defined as one newton per square metre in the NIST guide to the SI units. The standard atmosphere is defined as exactly 101,325 Pa, which is why the default above is not a rounded figure. NASA's Glenn Research Center has a clear account of what gas pressure physically is at the level of molecules striking a wall, which is the picture that makes Dalton's law feel obvious rather than arbitrary.
Why Volume Percent and Mole Percent Are the Same Number
Gas compositions are quoted in volume percent far more often than in mole percent — cylinder labels, flue gas analyses, breathing mixtures and atmospheric data almost all use volume. Students are then told to use mole fractions and reasonably wonder whether a conversion is needed. For an ideal gas mixture it is not, and the reason is worth understanding rather than memorising.
Avogadro's principle says equal volumes of ideal gases at the same temperature and pressure contain equal numbers of particles. Amagat's law of partial volumes extends that to a mixture: the volume a component would occupy alone at the mixture's temperature and pressure is proportional to its amount. So the ratio of volumes is the ratio of moles, and volume percent equals mole percent exactly for an ideal mixture. This is a property of gases alone. It emphatically does not carry over to liquids, where volumes are not additive at all and mixing ethanol with water actually shrinks the total.
The place this breaks is mass percent. A composition given by mass is a different quantity, and converting it needs the molar mass of each component. If you have masses rather than volumes, divide each mass by that gas's molar mass first — the molar mass calculator will give you the figures — and enter the resulting moles here. Feeding mass percentages straight into a mole-fraction slot overstates the light gases and understates the heavy ones, sometimes badly. In air, oxygen is 21 percent by volume but about 23 percent by mass.
Gas Collected Over Water, and the Correction Everyone Forgets
When a gas is generated in the lab and collected by displacing water from an inverted vessel, the gas that arrives is not dry. It picks up water vapour until the space above the water is saturated. The pressure you read on a barometer, once the water levels are equalised, is the total pressure of that wet mixture. Dalton's law then says the pressure due to your gas is the barometric pressure minus the vapour pressure of water at the temperature of the water.
The size of the error is not small. At 25 °C the vapour pressure of water is about 3.17 kPa, or roughly 3.1 percent of an atmosphere. At 40 °C it is about 7.4 kPa, over 7 percent. Skip the correction and every mole calculation downstream is inflated by that percentage, which is more than enough to fail a yield check. The calculator uses Antoine coefficients for water taken from the phase-change data in the NIST Chemistry WebBook entry for water, which reproduces the standard vapour-pressure table to well within a tenth of a kilopascal across ordinary room temperatures.
Two details decide whether the correction is right. The temperature that matters is the temperature of the water in the trough, not the room air and not the reaction flask. And the water levels inside and outside the collecting vessel must be level before the barometric reading is taken, otherwise a hydrostatic head is being added or subtracted on top of everything else. Our hydrostatic pressure calculator converts a residual level difference into the pressure it represents if you need to allow for one.
Where the Ideal Assumption Stops Being Safe
Dalton's law is exact for an ideal gas mixture and approximate for a real one. The approximation is excellent near ambient conditions and degrades in two directions: high pressure and low temperature. Near a few hundred atmospheres, molecules occupy a meaningful share of the container and attract one another strongly enough that the pressures do not simply add. Industrial high-pressure work uses fugacity, an effective pressure corrected by a fugacity coefficient, in place of partial pressure for exactly this reason.
The other failure mode is chemical rather than physical. Dalton's law assumes the components do not react and do not condense. Mix nitrogen dioxide and it dimerises to dinitrogen tetroxide, changing the number of particles and therefore the pressure. Cool a mixture until one component reaches its dew point and that component stops behaving as a gas at all. If you need the general behaviour of one gas as pressure, volume, temperature and amount change together, the ideal gas law calculator is the tool for that, and it carries the same ideal-behaviour caveat.
Partial Pressure Drives Diffusion, Not Concentration
A point that repays attention: gases move down a partial pressure gradient, not a total pressure gradient. A gas at high partial pressure on one side of a permeable barrier moves to the low-partial-pressure side even when the total pressure on the two sides is identical. That is why carbon dioxide leaves a fizzy drink into ordinary air which already contains far more gas overall.
It is also the basis of Henry's law, which states that the amount of a gas dissolved in a liquid at equilibrium is proportional to that gas's partial pressure above the liquid — not to the total pressure. Doubling the total pressure by adding an inert gas that does not dissolve barely changes how much oxygen goes into solution; doubling the oxygen partial pressure roughly doubles it. Anyone reasoning about dissolved gas from a cylinder pressure gauge needs the composition as well as the gauge reading, which is precisely what this calculator supplies.
Choosing a Unit Without Creating an Error
Pressure has more units in common use than almost any other quantity, and mixing them is the most frequent source of a wrong answer. The tool applies your chosen unit consistently to the total and to every partial pressure it reports, so nothing needs converting first.
One trap deserves naming: gauge pressure and absolute pressure are not interchangeable. A tyre gauge or a regulator reads the amount by which the contents exceed atmospheric pressure. Dalton's law needs absolute pressure, so a gauge reading must have roughly 101 kPa added to it first. Feeding a gauge reading in unchanged understates every partial pressure by a whole atmosphere.
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Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Using a gauge pressure as the total — gauges read above atmospheric. Add about 101 kPa to get the absolute pressure Dalton's law requires.
- Treating mass percent as mole percent — volume percent equals mole percent for gases, mass percent does not. Divide each mass by its molar mass first.
- Forgetting the water vapour term — a gas collected over water at 25 °C is about 3 percent water vapour by pressure, and ignoring it inflates every mole figure downstream.
- Using room temperature for the water correction — the vapour pressure follows the temperature of the water in the trough, which is often a degree or two off the air.
- Forcing percentages to add to exactly 100 by hand — the tool normalises for you, and rounding a component to make the total look tidy quietly changes its partial pressure.
Related Free Tools From Arb Digital
Work out composition ratios on their own with the mole fraction calculator, relate pressure, volume, temperature and amount for a single gas with the ideal gas law calculator, and change a pressure between units with the pressure converter. For liquid mixtures the equivalent job belongs to the Raoult's law calculator, and for a single pure liquid against temperature use the vapour pressure calculator. The full free online tools hub lists everything else Arb Digital has built.
Frequently Asked Questions
Partial pressure is the pressure one gas in a mixture would exert if it alone occupied the whole container at the same temperature. Dalton's law says the total pressure of a non-reacting mixture is the sum of the partial pressures of its components.
Divide the moles of that gas by the total moles of all gases to get its mole fraction, then multiply the mole fraction by the total pressure. The calculator does the normalising step for you, so the amounts do not have to add to any particular number.
Yes, for gases. Avogadro's principle makes equal volumes contain equal amounts at the same temperature and pressure, so volume percent and mole percent are the same number for an ideal mixture. This does not hold for liquids or for mass percent.
The collected mixture is saturated with water vapour, so part of the measured pressure belongs to water rather than to your gas. Subtracting the vapour pressure of water at the trough temperature leaves the pressure of the dry gas, which is about 3 percent of an atmosphere at 25 degrees Celsius.
It is exact for ideal gases and a good approximation near ambient conditions. It degrades at high pressure and low temperature, where molecular volume and intermolecular attraction matter, and high-pressure work uses fugacity instead of partial pressure.
Dry air is close to 21.0 percent oxygen by amount of substance, so at a total pressure of 101.325 kilopascals the partial pressure of oxygen is about 21.3 kilopascals, which is roughly 0.21 atmospheres or 159 millimetres of mercury.
For a dry ideal mixture, yes, and the fourth result tile shows that sum as a check. When the water correction is switched on they add to the total minus the water vapour pressure, because the water is accounted for separately.
No, but they are proportional at fixed temperature. Partial pressure divided by RT gives the amount concentration in moles per unit volume, which is why an equilibrium constant can be written either way for a gas-phase reaction.
This calculator is provided for education and general reference. It describes how partial pressures are computed and is not laboratory, safety, diving or medical guidance; follow the procedures and risk assessments issued by your own institution.
