What this calculator does
Find out how much of a gas mixture's pressure comes from each gas. In a mixture, each gas pushes on the walls of its container as if the others weren't there. The pressure one gas would create on its own is its partial pressure. Dalton's law says the partial pressures add up to the total. So each gas's share of the pressure equals its share of the molecules. That share is called its mole fraction.
This calculator works Dalton's law both ways. You can find one gas's partial pressure from its mole fraction and the total pressure. (Instead of the mole fraction, you can give its moles and the total moles. A mole is a set count of molecules.) Or you can list the partial pressures of every gas, to get the total and each gas's share. Choose any common pressure unit. The main answer is also shown in kilopascals, atmospheres and millimeters of mercury.
Where it's used
Why this math matters outside the classroom:
- Diving gases. Divers find that air at 30 m depth, about 4 atm, carries an oxygen partial pressure of 0.21 × 4 = 0.84 atm.
- High altitude. Mountaineers learn that oxygen stays near 21% of the air at altitude, but its partial pressure falls as total pressure drops.
- Gas over water. Chemistry students subtract water's vapor pressure from the total to get the pressure of a gas collected over water.
- Air at sea level. At sea level, about 101.3 kPa, nitrogen's 78% share of air gives it a partial pressure near 79 kPa.
How to use it
- Choose whether you want one gas's partial pressure or the total pressure of a mixture.
- Pick the pressure unit you're working in. It applies to every pressure you enter and to the answer.
- For a partial pressure, enter the mole fraction and the total pressure. Or enter the moles of the gas and the total moles, instead of the mole fraction.
- For a total, list each gas's partial pressure. The table shows each gas's mole fraction and percent share.
What the inputs mean
- Pressure unit
- Used for every pressure you enter and for the answer.
- Mole fraction of the gas (χ)
- The gas's moles divided by the total moles, from 0 to 1. For ideal gases, it equals the share by volume. So 20.95% oxygen by volume is a mole fraction of 0.2095.
- Moles of this gas
- Moles of the gas you're interested in. It can't be more than the total.
- Total moles of all gases
- Moles of every gas in the mixture added together.
- Partial pressures of each gas
- One partial pressure per gas, all in the chosen unit.
Formula and method
Pᵢ = χᵢ × P_total χᵢ = nᵢ ÷ n_total P_total = P₁ + P₂ + … + Pₙ
Here Pᵢ is the partial pressure of one gas (gas number i). χᵢ (the Greek letter chi) is its mole fraction. nᵢ is its moles, and n_total is the moles of all the gases. P_total is the total pressure. For ideal gases at a fixed volume and temperature, pressure grows in step with the number of molecules. So a gas that makes up a fraction χ of the molecules supplies the same fraction χ of the pressure.
Adding every gas's partial pressure gives the total. Divide any one partial pressure by that total, and you get back its mole fraction. The mole fractions of all the gases add up to 1.
Unit changes use the exact definitions from the pressure converter: 1 atm = 101,325 Pa = 760 Torr, and 1 mmHg = 133.322387415 Pa.
Worked example
Dry air at sea level is at 1 atm and contains 20.95% oxygen by volume. What is the partial pressure of oxygen?
- Mole fraction of oxygen: χ = 0.2095.
- Partial pressure: 0.2095 × 1 atm = 0.2095 atm.
- In other units: 0.2095 atm = 21.2276 kPa = 159.22 mmHg.
Result: Oxygen's partial pressure in dry sea-level air is 0.2095 atm, about 21.23 kPa or 159.22 mmHg.
Understanding the result
Partial pressure, not percentage, controls how much of a gas dissolves in a liquid or passes through a thin barrier (a membrane). At high altitude, air is still about 21% oxygen. But the total pressure is lower, so the oxygen partial pressure is lower too.
When you add up a mixture, a gas with a large share of the total controls how the mixture behaves. The table makes those shares easy to compare.
Assumptions and limitations
- The gases behave as ideal gases, and they don't react with each other.
- All pressures are absolute pressures in the same unit. They aren't gauge pressures, which leave out the surrounding air pressure.
- Water vapor counts as one of the gases. For a gas collected over water, subtract the water vapor pressure from the total. That gives the dry gas's pressure.
- At high pressures or low temperatures, real gases stray from Dalton's law. The partial pressures then no longer add up exactly.
- The calculator doesn't find vapor pressures. It also doesn't use the ideal gas law to work with volumes and temperatures.
Frequently asked questions
What is Dalton's law of partial pressures?
It says that in a mixture of gases that don't react, the total pressure is the sum of each gas's own pressure. Each gas's own pressure is what it would create alone, at the same volume and temperature. John Dalton described it in the early 1800s.
How do I convert a percentage of a gas into a mole fraction?
Divide by 100. A gas that is 78% of a mixture, by volume or by moles, has a mole fraction of 0.78. Percent by mass (weight) is different. It needs each gas's molar mass (the weight of one mole) first.
Does the pressure unit matter?
Only for labeling. Mole fractions have no units. So the partial pressure comes out in whatever unit the total pressure uses. To save you a step, the calculator also shows the answer in kPa, atm and mmHg.
Why does my list of partial pressures not add to exactly 1 atm?
Rounded figures for what's in a mixture rarely add up to exactly 100%. Gases present in tiny amounts (trace gases) are often left out too. The calculator adds what you enter. So the total reflects your data, not an assumed 1 atm.
How this calculator is checked
Method: Dalton's law of partial pressures, P_i = χ_i·P_total and P_total = ΣP_i, for ideal gas mixtures. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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