Graham’s Law Calculator

This Graham's law calculator works out how much faster one gas effuses or diffuses compared with another, based purely on their molar masses. Graham's law states that the rate of effusion or diffusion of a gas is inversely proportional to the square root of its molar mass, so lighter gas molecules move through a small opening or spread through another gas noticeably faster than heavier ones. You enter the molar mass of gas 1 and the molar mass of gas 2, both in grams per mole, and the calculator returns the rate ratio as rate 1 divided by rate 2, along with the inverse ratio of rate 2 divided by rate 1, and a plain-English note on which gas is faster. Underneath the result you will find the formula itself, rate 1 over rate 2 equals the square root of M2 over M1, plus a worked example comparing helium at 4 g/mol with oxygen at 32 g/mol, showing helium effusing about 2.83 times faster. It suits chemistry students, teachers and lab workers, and explains everyday effects such as why a helium balloon deflates faster than one filled with air, plus industrial processes like gas separation and uranium enrichment. The calculation assumes both gases are at the same temperature and pressure, and results are rounded, so treat the output as a teaching estimate rather than a precision laboratory figure.

Molar mass of gas 1 (g/mol)

Molar mass of gas 2 (g/mol)

Rate 1 / Rate 2 = 2.828427

Rate 2 / Rate 10.353553

Which is fastergas 1 is faster

The formula

Graham’s law: rate1 / rate2 = the square root of (M2 / M1), where M1 and M2 are the molar masses. Lighter gases effuse faster. The rates are at the same temperature and pressure.

Worked example

Helium (4 g/mol) versus oxygen (32 g/mol): rate of helium over oxygen is the square root of 32/4 = the square root of 8, about 2.83, so helium effuses roughly 2.83 times faster. Enter 4 and 32 to confirm.

Frequently asked questions

What is Graham’s law?

The rate of effusion of a gas is inversely proportional to the square root of its molar mass, so lighter gases escape faster.

What is the difference between effusion and diffusion?

Effusion is escape through a tiny hole; diffusion is spreading through another gas. Graham’s law applies to both as a rate ratio.

Why does helium leak faster than air?

Helium has a much smaller molar mass than nitrogen and oxygen, so by Graham’s law it effuses faster.

Who this calculator is for

This calculator is for chemistry students, teachers and lab workers.

What this calculator assumes

You enter values in the units shown.
Standard conditions unless stated.
Results are rounded for display.

Formula and sources

Related calculators

Molarity Calculator: concentration in mol/L.
pH Calculator: acidity from H+ concentration.
Ideal Gas Law Calculator: PV = nRT.

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