mg/m³ = ppm × M ÷ Vₘ, Vₘ = RT ÷ P — fill in every field except the one you want; the empty field is solved for.
Gas:
mg/m³
ppm
g/mol
Mass concentration (C) = 57.244 mg/m³
- Convert T: 25 °C =
298.15 K - Rearrange:
C = ppm × M × P ÷ (0.082057 × T) - Substitute:
(50 ppm) × (28.01 g/mol) × (1 atm) ÷ (0.082057 × (298.15 K))=57.244 mg/m³
How it works
For an ideal gas, 1 ppm means 1 volume of gas per million volumes of air. The molar volume Vₘ = RT ÷ P (24.47 L/mol at 25 °C and 1 atm) turns that into a mass per cubic metre: mg/m³ = ppm × M ÷ Vₘ. Change the temperature and pressure to match the conditions your limit or instrument uses.
Many occupational-hygiene references use 24.45 L/mol for 25 °C and 1 atm, which differs from the value here by less than 0.1 %. This conversion applies to gases and vapours, not to dusts or aerosols, which are always reported in mg/m³.
Frequently asked questions
- How do I convert ppm to mg/m³?
- Multiply ppm by the molar mass and divide by the molar volume. At 25 °C and 1 atm: mg/m³ = ppm × M ÷ 24.47. So 50 ppm of carbon monoxide (M = 28.01) is about 57 mg/m³.
- Why does the conversion depend on temperature?
- A gas expands when warmed, so the same number of molecules occupies more volume. The same ppm therefore corresponds to fewer milligrams per cubic metre at higher temperature.
- Is ppm by volume the same as ppm by mass?
- No. For gases, ppm almost always means by volume (ppmv, equal to the mole fraction × 10⁶). In water, ppm usually means mg per kg, about mg/L.
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