Percent, ppm and ppb are volume fractions: 1 % equals 10,000 ppm and 1 ppm equals 1000 ppb. To reach mg per cubic metre, multiply ppm by the gas's molar mass and divide by the molar volume, which is 22.414 L/mol at 0 C and 1013.25 hPa. The result changes with temperature and pressure, so always state the reference conditions.
Assumes ideal-gas behaviour, which is accurate to well under 1 % at the pressures used for sample gas. Concentrations here are by volume (mole fraction), not by mass.
How the conversion works
Percent, ppm and ppb are all fractions of the whole. One percent is one part in 100, one ppm is one part in a million (so 1 % is 10,000 ppm), and one ppb is one part in a billion (so 1 ppm is 1000 ppb). These conversions need no gas properties and never change.
Mass concentration is different. A cubic metre of gas holds a number of molecules set by its temperature and pressure, and each gas has a different mass per molecule. The ideal-gas relation gives the volume of one mole, so mg/m3 equals ppm times molar mass divided by molar volume.
mg/m3 = ppm x M / Vm Vm = 22.414 x (T + 273.15) / 273.15 x 1013.25 / P
Here M is molar mass in g/mol, T is temperature in C, P is pressure in hPa and Vm is in litres per mole.
Worked examples
50 ppm of carbon monoxide (M = 28.01) at 0 C and 1013.25 hPa: Vm = 22.414 L/mol, so mg/m3 = 50 x 28.01 / 22.414 = 62.5 mg/m3.
100 ppm of sulphur dioxide (M = 64.07) restated at 25 C: Vm = 24.465 L/mol, so mg/m3 = 100 x 64.07 / 24.465 = 261.9 mg/m3. The same ppm at 0 C would be 285.9 mg/m3.
The second example shows why limits quoted in mg/m3 must name a temperature and pressure. The gas is unchanged; only the volume it is divided into moved.
Assumptions and limits
- Ideal-gas behaviour: fine for sample gas near atmospheric pressure.
- Volume fractions: analysers report mole fractions, not mass fractions.
- Dry or wet basis is not handled here; see Dry basis vs wet basis in gas measurement.
- Oxygen-corrected emission values need a second step: Emission correction to reference oxygen.
Frequently asked questions
How do I convert ppm to mg/m3?
Multiply ppm by the gas molar mass and divide by the molar volume, 22.414 L/mol at 0 C and 1013.25 hPa. For carbon monoxide, 1 ppm is about 1.25 mg/m3 at those conditions.
Why do two sources give different mg/m3 for the same ppm?
They use different reference temperatures. 0 C and 25 C differ by about 9 % in molar volume.
Is ppm by volume the same as ppm by mass?
No. They differ by the ratio of molar mass to the molar mass of the carrier gas. Gas analysers report ppm by volume.
How many ppm is one percent?
10,000 ppm. So 0.5 % is 5000 ppm and 100 ppm is 0.01 %.