Partial Pressure Calculator

A partial pressure calculator finds the pressure that one gas contributes inside a mixture of gases. It uses Dalton's law: enter the total pressure and the mole fraction of each gas, and the tool returns each gas's share of that pressure.

What is partial pressure?

A gas mixture, such as air, contains several different gases sealed in the same space. Each gas pushes on the walls of its container just as if it were alone there. The push from one single gas is called its partial pressure.

John Dalton, an English chemist, described this behavior in 1801. His rule, now called Dalton's law of partial pressures, says the total pressure of a gas mixture equals the sum of the pressures each gas would exert on its own:

$P_{total} = P_1 + P_2 + P_3 + \dots + P_n$

This holds for an ideal gas, a simplified model where gas molecules do not attract or interact with each other. Air at everyday pressures behaves close enough to this model for the law to give accurate results.

Partial pressure formula

The partial pressure of one gas equals its mole fraction multiplied by the total pressure:

$P_i = X_i \times P_{total}$

$P_i$ is the partial pressure of gas $i$ .
$X_i$ is the mole fraction of gas $i$ , a number between 0 and 1.
$P_{total}$ is the total pressure of the mixture.

Mole fraction is the share of all the gas particles that belong to one gas:

$X_i = \frac{n_i}{n_{total}}$

Here $n_i$ is the number of moles of gas $i$ , and $n_{total}$ is the number of moles of every gas in the mixture combined. Because every gas particle belongs to some component, all the mole fractions in a mixture must add up to 1.

How to calculate partial pressure: example

Suppose a sealed tank holds a gas mixture at a total pressure of 2 atmospheres (atm), made up of:

Oxygen (O₂): mole fraction 0.21
Nitrogen (N₂): mole fraction 0.78
Carbon dioxide (CO₂): mole fraction 0.01

Multiply each mole fraction by the total pressure:

Oxygen: $0.21 \times 2 = 0.42$ atm
Nitrogen: $0.78 \times 2 = 1.56$ atm
Carbon dioxide: $0.01 \times 2 = 0.02$ atm

As a check, the three partial pressures add back up to the total: $0.42 + 1.56 + 0.02 = 2.00$ atm.

This matters in practice. In hyperbaric oxygen therapy, doctors raise the total pressure a patient breathes at, which raises the oxygen partial pressure even though the oxygen percentage in the gas mixture stays the same. More oxygen partial pressure pushes more oxygen into the blood.

How to use the partial pressure calculator

Enter the total pressure of the mixture and pick a unit: atmospheres (atm), kilopascals (kPa), or millimeters of mercury (mmHg).
Name each gas and enter its mole fraction. Mole fractions must be between 0 and 1, and they must add up to 1 across all components, within a small rounding tolerance.
Select "Calculate Partial Pressures" to see a results table and a chart showing how the total pressure splits across the gases.
Select "Copy Results" to copy the numbers for a lab report or spreadsheet.

The calculator checks the input before it shows results. It flags an error if the total pressure is zero or negative, if any component is missing a name, or if the mole fractions do not sum to 1.

Pressure unit conversions

The calculator works in three units: atm, kPa, and mmHg. The conversions between them are:

1 atm = 101.325 kPa
1 atm = 760 mmHg

Chemistry courses usually use atmospheres. Medicine tends to report blood gases in mmHg. Engineering fields often use kPa. The calculator does not currently support bar or psi.

Where partial pressure is used

Respiratory physiology. Oxygen moves from the lungs into the blood, and carbon dioxide moves the other way, because of partial pressure differences, not total pressure. Air in the lungs typically has an oxygen partial pressure of roughly 100 mmHg, while blood arriving from the body carries oxygen at a lower partial pressure, so oxygen flows into the blood along that gradient.

Chemical engineering. Reaction rates in gas-phase processes, such as ammonia synthesis, depend on the partial pressures of the reacting gases, not just the total pressure of the system. Designers of distillation columns and gas separation equipment also work directly with partial pressures.

Environmental science. Atmospheric carbon dioxide is now above 420 parts per million and still rising. Its partial pressure, small as it is, drives much of the extra warming linked to the gas. Dissolved oxygen in lakes and rivers likewise depends on the partial pressure of oxygen in the air above the water, through a relationship called Henry's law.

When Dalton's law does not apply well

Dalton's law assumes gas molecules do not interact. That assumption breaks down at high pressure or low temperature, where molecules are packed closely enough for intermolecular forces to matter. Natural gas processing at high pressure, for example, often needs a more advanced quantity called fugacity in place of simple partial pressure. Dalton's law also does not describe a liquid's vapor pressure, which depends on temperature and the substance itself rather than on mole fraction in a gas mixture.

Frequently asked questions

What is Dalton's law of partial pressures? It states that in a mixture of gases that do not react with each other, the total pressure equals the sum of the pressures each gas would exert if it alone filled the container at the same temperature.

How do I calculate the partial pressure of a gas? Multiply the gas's mole fraction by the total pressure of the mixture: $P_i = X_i \times P_{total}$ . For example, a gas with mole fraction 0.30 in a mixture at 4 atm has a partial pressure of $0.30 \times 4 = 1.2$ atm.

Why must mole fractions add up to 1? Mole fraction measures the share of all gas particles that one component makes up. Since every particle belongs to some component, the shares must account for the whole mixture, so they sum to exactly 1.

Can a partial pressure be greater than the total pressure? No. Because mole fractions cannot exceed 1, a partial pressure can never exceed the total pressure of the mixture. A result larger than the total usually means a mole fraction was entered as a percentage (like 21) instead of a decimal (0.21).

What pressure units does the calculator support? Atmospheres (atm), kilopascals (kPa), and millimeters of mercury (mmHg). The calculator does not convert to or from bar or psi.

What is the difference between partial pressure and vapor pressure? Partial pressure is one gas's share of the total pressure in a mixture, and it depends on mole fraction. Vapor pressure is the pressure a pure substance's vapor exerts when it is in balance with its own liquid or solid, and it depends only on temperature.

History

John Dalton proposed the law of partial pressures in 1801 and published it in his 1808 book, A New System of Chemical Philosophy. His work came alongside other early gas laws, including Boyle's law (1662), relating pressure and volume, and Charles's law (1787), relating volume and temperature. Together with Avogadro's law (1811), these ideas led to the ideal gas law, $PV = nRT$ , which still forms the basis for most everyday gas calculations.

Partial Pressure Calculator | Gas Mixtures & Dalton's Law