Dalton’s Law of Partial Pressures is one of the most widely used relationships in chemistry, chemical engineering, atmospheric science and respiratory physiology. This calculator lets you analyse any ideal gas mixture in three flexible modes — whether you are starting from molar compositions, known partial pressures, or a single mole fraction — and shows you every step of the working so you can follow the derivation and check your own calculations.
What is Dalton’s Law?
John Dalton published his law of partial pressures in 1801. It states that the total pressure of a mixture of non-reacting ideal gases equals the arithmetic sum of the pressures each gas would exert if it occupied the container alone:
P_total = P_1 + P_2 + … + P_n
This is a direct consequence of the ideal gas law PV = nRT. Because the molecules of each
gas are assumed to occupy negligible volume and to exert no forces on one another, each
species contributes its own fraction of the total pressure independently.
Key relationships
The three equations the calculator uses are:
- Total pressure:
P_total = P_1 + P_2 + ... + P_n - Mole fraction:
x_i = n_i / n_total - Partial pressure from mole fraction:
P_i = x_i * P_total
Combining (2) and (3) gives the bridge between composition and pressure: the mole fraction
of any gas in an ideal mixture equals the ratio of its partial pressure to the total pressure
(x_i = P_i / P_total). This identity makes Dalton’s Law consistent with the ideal gas law
and is used throughout the calculator’s working steps.
How it works
Gas mixture mode — enter up to eight gases with their amounts (moles) or partial
pressures. When you use moles, the calculator first computes each mole fraction
(x_i = n_i / n_total), then multiplies by the supplied total pressure to get each partial
pressure. When you enter partial pressures directly, it sums them for P_total and divides
back to yield mole fractions. You can even mix both input types for scenarios where some
partial pressures are measured and others are known only by composition.
Find partial pressure mode — the simplest use case: enter one mole fraction and the
total pressure to get a single component’s partial pressure (P_i = x_i * P_total).
Sum partial pressures mode — enter the known partial pressure of every gas and the
calculator sums them to P_total and derives all mole fractions from the ratio
x_i = P_i / P_total.
All three modes display the step-by-step working so you can trace every arithmetic operation.
Worked example — dry air at 1 atm
Standard dry air is approximately 78.09 % N₂, 20.95 % O₂, 0.93 % Ar and 0.04 % CO₂ by mole. At a total pressure of 101.325 kPa (1 atm):
| Gas | Mole % | Mole fraction x | Partial pressure (kPa) |
|---|---|---|---|
| N₂ | 78.09 | 0.7809 | 79.12 |
| O₂ | 20.95 | 0.2095 | 21.22 |
| Ar | 0.93 | 0.0093 | 0.94 |
| CO₂ | 0.04 | 0.0004 | 0.04 |
| Total | 100.01 | 1.0001 | 101.32 |
The tiny rounding discrepancy arises from truncating the percentage figures. The calculator works with full floating-point precision, so rounding errors in the sum are negligible.
The partial pressure of oxygen in this example is about 21.22 kPa — the figure used in physiology when discussing the oxygen content of inhaled air at sea level.
Formula note
The formula P_i = x_i * P_total is strictly valid for ideal gases only. At pressures
well above ambient (roughly above 10 atm) or close to condensation conditions, interactions
between molecules become significant. For such conditions you would use the virial equation
or van der Waals equation, but for most laboratory, engineering and atmospheric calculations
at moderate pressures Dalton’s Law gives excellent accuracy.
The gas constant used throughout the related ideal gas calculations is R = 8.314 J mol⁻¹ K⁻¹ (CODATA 2018 recommended value).