PPM calculator
Enter the amounts, get ppm, ppb and percent.
What does ppm mean?
Parts per million by mass: the mass of a substance per million units of mass of the whole solution — ppm = mass of solute ÷ mass of solution × 10⁶ (OpenStax Chemistry 2e). Parts per billion (ppb) uses 10⁹.
Is 1 ppm the same as 1 mg/L?
For dilute solutions in water, practically yes: a liter of such a solution has a mass of about 1 kg, so 1 mg per liter is about 1 mg per kilogram. The EPA and USGS treat mg/L as ppm for drinking water and fresh water. For other liquids or strong solutions it is not.
How do ppm, ppb and percent relate?
1% = 10,000 ppm, and 1 ppm = 1,000 ppb. So 0.5% is 5,000 ppm, and 15 ppb is 0.015 ppm — the conversion OpenStax uses for lead in drinking water.
Example
5 mg of a substance in 2 kg of solution: 5 mg ÷ 2,000,000 mg × 10⁶ = 2.5 ppm, or 2,500 ppb.
Does it matter which units I enter?
Choose the unit for each amount; the calculator converts both to the same unit before dividing. Both must be masses.
How do I convert ppm to percent?
Divide by 10,000. 250 ppm is 0.025%, and 5,000 ppm is 0.5%. To go the other way, multiply the percent by 10,000.
Is ppm the same for gases?
For gases ppm is usually by volume (ppmv), a different quantity from the by-mass version here. The two agree only for particular gas mixtures, so do not use this calculator for air concentrations.
The definition
A mass fraction is the mass of the substance divided by the total mass of the mixture. Multiply it by 100 for percent, by one million for ppm and by one billion for ppb. Both masses must be in the same unit before dividing, which is why the calculator converts milligrams, grams, kilograms, ounces and pounds into a common unit first. The denominator is the whole solution, solute plus solvent, not the solvent alone.
Worked examples
Dissolve 0.75 g of a salt in a total of 5 kg of solution. In milligrams that is 750 ÷ 5,000,000 = 0.00015, which is 150 ppm or 0.015%. A drinking-water result of 15 ppb is 15 ÷ 1,000 = 0.015 ppm, or 15 ppb, which in dilute water is 0.015 mg per liter. And 250 mg in 1 kg of solution is 250 ppm, equal to 0.025%.
When ppm equals mg/L, and when it does not
In dilute aqueous solutions, one liter has a mass of very nearly one kilogram, so milligrams per liter and milligrams per kilogram coincide. The shortcut fails for strong solutions, which are denser than water (a liter of brine weighs more than a kilogram), and for solvents other than water, such as alcohol or oil. In those cases measure the masses, as this calculator does, instead of using the volume.
Common mistakes
Mixing a mass with a volume is the main one: the calculator expects two masses. A second is using the solvent’s mass alone as the denominator, which overstates the concentration of a strong solution. A third is a decimal-place slip when moving between ppm, ppb and percent; remember that 1 ppm is 1,000 ppb and 0.0001%. Finally, with very small numbers, check that the unit you chose for each mass is the one you meant: a result that is a thousand times too big is most often milligrams entered as grams.
Sources: OpenStax Chemistry 2e, section 3.4 (other units for solution concentrations: mass percentage, ppm and ppb); unit factors from NIST SP 811. Related: molarity calculator, dilution calculator, molality calculator and percent to molarity calculator.