Various governmental agencies involved with environmental protection and with occupational safety and health have promulgated regulations limiting the allowable concentrations of gaseous pollutants in the ambient air or in emissions to the ambient air. Such regulations involve a number of different expressions of concentration. Some express the allowable concentrations as volume of a specific gaseous pollutant per million volumes of ambient air or, more simply as parts per million by volume (ppmv). Others express the allowable concentrations as m*** of a specific gaseous pollutant per volume of ambient air or usually as milligrams per cubic meter (mg/m³).

The equations for conversion between ppmv and mg/m³ depend on the temperature at which the conversion is wanted (usually about 20 to 25 °C). At an ambient air pressure of 1 atmosphere of 101.325 kiloPascal (kPa), the general conversion equation is:

ppmv = (mg/m³) × (0.08205) × (T) / (M)

and for the reverse conversion:

(mg/m³) = (ppmv) × (M) (12.187) / (T)

where:

ppmv = air pollutant concentration, in parts per million by volume
mg/m³ = milligrams of air pollutant per cubic meter of air
T = ambient air temperature, in kelvins (K) = 273.15 + °C
0.08205 = Universal Gas Law constant, in [atm·L]/(mol·K)
M = molecular weight of the air pollutant (dimensionless)

Notes:

-- Pollution regulations in the United States typically reference their air pollutant limits to an ambient temperature of 20 to 25 °C as noted above. In most other nations, the reference ambient temperature for pollutant limits may be 0 °C or other values.
-- 1 percent by volume = 10,000 ppmv
-- atm = absolute atmosperic pressure in atmospheres
-- mol = gram mole
-- L = liter