Dalton's Law (Partial Pressure) Calculator
Add up partial pressures with P_total = P1 + P2 + P3 + P4, or work the other way from mole fractions and total pressure. Static 3D diagrams and charts show how a gas mixture's total pressure comes from each gas contributing independently.
Reviewed by the ToolNestr Editorial Team — July 2026
Two ideas that trip students up
1. Mixed together, still independent
Four gas types (different colored spheres) share one container. Each still contributes its own partial pressure exactly as if it were alone — mixing does not reduce any gas's contribution.
2. Same gases, separated into containers
The same four gases, now split into separate containers of equal volume. Each container's pressure is that gas's partial pressure — summing them gives the same total as the mixture on the left.
Partial pressure graphs
How it works
The core idea in one line: in a mixture of gases, each gas exerts its own pressure independently, as if the others were not there — total pressure is simply the sum of the parts.
Ptotal = P₁ + P₂ + P₃ + P₄
sum of partial pressures of each gas
Pi = Xi × Ptotal
partial pressure from mole fraction, Xi = ni/ntotal
Rearranged with mole fractions, Pi = Xi × P_total lets you go the other way: if you know the composition of a mixture (as mole fractions) and its total pressure, you can find any individual gas's partial pressure directly, without needing to know moles or volume at all.
Worked example 1 — approximate composition of air
Given: A gas mixture approximating dry air: P(N₂) = 0.780 atm, P(O₂) = 0.210 atm, P(Ar) = 0.0093 atm, P(CO₂) = 0.0004 atm. Find the total pressure.
The four partial pressures sum to almost exactly 1.00 atm — consistent with dry air at roughly 1 atm total pressure.
Worked example 2 — partial pressure from mole fraction
Given: A cylinder holds a mixture of O₂ and N₂ at a total pressure of 5.00 atm. The mole fraction of O₂ is 0.30. Find the partial pressure of O₂.
The remaining mole fraction (0.70) belongs to N₂, giving P(N₂) = 0.70 × 5.00 = 3.50 atm, and 1.50 + 3.50 = 5.00 atm checks out.
Approximate composition of dry air at sea level
Partial pressures at a total pressure of 1 atm — the classic textbook example of Dalton's law.
| Gas | Mole fraction | Partial pressure (atm) |
|---|---|---|
| Nitrogen (N₂) | 0.780 | 0.780 |
| Oxygen (O₂) | 0.210 | 0.210 |
| Argon (Ar) | 0.0093 | 0.0093 |
| Carbon dioxide (CO₂) | 0.0004 | 0.0004 |
Mole fraction and partial pressure (in atm, at 1 atm total) are numerically identical — a handy shortcut for gas mixtures at 1 atm total pressure.
Where Dalton's law actually matters
🤿 Scuba diving gas mixtures
Divers breathe mixtures like nitrox or trimix where the partial pressure of oxygen and nitrogen must stay within safe limits. Dalton's law lets divers calculate each gas's partial pressure at depth, where ambient pressure — and therefore every partial pressure — rises.
🫁 Respiratory physiology
Oxygen moves from lungs to blood because its partial pressure in the alveoli is higher than in venous blood. Clinicians track arterial partial pressures of O₂ and CO₂ (PaO₂, PaCO₂) as core measures of lung function.
🧪 Collecting gas over water
When a gas is collected by water displacement in the lab, the container also holds water vapor. Subtracting water's known vapor pressure from the total measured pressure isolates the partial pressure of the actual gas produced.
🏭 Industrial gas blending
Manufacturers of specialty gas mixtures — welding gases, calibration standards, medical gas blends — rely on Dalton's law to blend components to an exact total pressure and composition.
Common misconceptions
"Each gas in a mixture exerts less pressure because it shares space with others."
A gas's partial pressure depends on how many of its own molecules are present, not on sharing space — each gas behaves as though it alone filled the container. Adding more of a different gas does not reduce the first gas's partial pressure at all.
"Mole fraction and partial pressure are always numerically the same."
They are only numerically equal (in atm) when the total pressure is exactly 1 atm, since Pi = Xi × P_total. At any other total pressure, you must multiply the mole fraction by that total to get the partial pressure.
"Dalton's law only works for exactly two gases."
It applies to any number of non-reacting gases in a mixture — the sum simply has more terms. The calculator here supports up to four gases, and the same additive logic extends to as many components as the mixture contains.
"Partial pressure means the gas is only partially present."
"Partial" refers to that gas's share of the total pressure, not an incomplete amount of the gas. The gas is fully present at its actual concentration — partial pressure is simply the pressure contribution attributable to it.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 9, Gases: Dalton's law of partial pressures (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 10, Gases.
- • Zumdahl & Zumdahl, Chemistry — partial pressures and gas mixtures.
P_total = ΣPi; Pi = Xi × P_total. Air composition figures are standard approximate reference values. Results are rounded for display.
How to use this calculator
Pick the mode
"Sum pressures" totals up to four partial pressures; "From mole fractions" finds each Pi from Xi and P_total.
Enter the values
Leave unused gas rows blank to work with 2, 3 or 4 gases.
Read the result
The total pressure (or each partial pressure) solves live, with the 3D diagrams and charts.
Related tools
Frequently asked questions
What is Dalton's law of partial pressures?
Dalton's law states that the total pressure of a mixture of non-reacting gases equals the sum of the partial pressures each gas would exert if it alone occupied the whole container: P_total = P1 + P2 + P3 + ... Each gas behaves as if the others were not there.
What is a partial pressure?
The partial pressure of a gas in a mixture is the pressure that gas alone would exert if it occupied the entire container at the same temperature. It depends only on how many molecules of that gas are present and the container volume and temperature — not on what other gases share the space.
How does mole fraction relate to partial pressure?
The partial pressure of a component equals its mole fraction times the total pressure: Pi = Xi × P_total, where Xi = ni / n_total. This is often the fastest way to find a partial pressure when you know the composition of a mixture and its total pressure.
Does Dalton's law apply to real (non-ideal) gases?
Dalton's law is exact for ideal gases and a very good approximation for most real gas mixtures at ordinary pressures and temperatures, where intermolecular interactions are small. At very high pressure or low temperature, real gases deviate and the simple additive rule becomes less accurate.
Why is Dalton's law used for collecting gas over water?
When a gas is collected by displacing water, the collected sample is actually a mixture of the target gas plus water vapor. Dalton's law lets you subtract the known vapor pressure of water at that temperature from the total measured pressure to isolate the partial pressure of the gas you actually collected.