Ppm stands for parts per million and is a special unit of concentration. Ppm is used to express very small concentrations and typically used to provide threshold exposures for toxic compounds or the level of contamination in water. Note that ppm is a relative unit; for example, 5 ppm might refer to 5 mg of substance per 1,000,000 mg of water or 5 g per 1,000,000 g. You may need to convert ppm to other units of concentration, such as grams per cubic meter (M3) to make calculations in chemistry.
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Express the ppm concentration as a mass fraction using the gram unit. For example, if the concentration is 5 ppm then 5 ppm = 5 g/1,000,000 g.

Divide the denominator of the fraction by 1,000 to convert it to kilograms. In this example, the denominator is 1,000,000 g/1,000 = 1,000 kg; hence, 5 ppm = 5 g/1,000 kg.

Find out the density of the water at the given temperature using the table in the Resources section; for instance, at 30 degrees Celsius the density of the water is 995.7 kg/cubic meter.

Divide the mass in kilograms at the denominator of the fraction by the density to convert the denominator to cubic meters. In this example, the denominator is 1,000 kg/995.7 kg/cubic meter = 1.004 cubic meters.

Divide the numerator by the denominator (in cubic meters) to convert ppm to grams per cubic meter. In this example, 5 ppm = 5 g/1.004 cubic meters = 4.98 g/cubic meter.
References
 Analytical Chemistry Resources: PPM
 "Chemistry: Textbook"; Raymond Chang; 2007
 CIA: The World Factbook: Weights and Measures