The conversion factor depends on the temperature at which you want the conversion (usually about 20 to 25 degrees Centigrade). At an ambient pressure of 1 atmosphere, the general equation is:
ppmv = (mg/m3)(273.15 + °C) / (12.187)(MW)
where: ppmv = ppm by volume (i.e., volume of gaseous pollutant per 106 volumes of ambient air)
mg/m3 = milligrams of gaseous pollutant per cubic meter of ambient air
MW = molecular weight of the gaseous pollutant
°C = ambient air temperature in degrees Centigrade
As an example, for gaseous pollutant NOx, convert 20 mg/m3 to ppmv at 25 °C:
ppmv = (20)(273.15 + 25) / (12.187)(46.01) = 10.6
where: 46.01 = molecular weight of NO2 (i.e., NOx expressed as nitrogen dioxide)
NOTES:
(1) The pollution laws and regulations in the United States typically reference their pollutant limits to an ambient temperature of 20 to 25 °C as noted above. However, in other nations, the reference ambient temperature for pollutant limits may be 0 °C or other values.
(2) 1 percent by volume = 10,000 ppmv (i.e., parts per million by volume).
(3) For all practical purposes, degrees Centigrade and degrees Celsius are synonymous.