Converting ppm, ppb and Percent

Converts between percent and the units used for very dilute concentrations. One ppm is one part in a million and one ppb is one part in a billion. Entering the mass of the solution also gives the mass of solute in milligrams.

For the very dilute concentrations found in drinking water standards or air pollution limits, percentages fill up with leading zeros and become hard to read. Units with a larger denominator solve that.

One ppm is one part per million and one ppb is one part per billion. Per mille, written ‰, is one part per thousand, sitting between percent and ppm.

Lined up, they relate like this.

1percent=10per mille=104ppm=107ppb1 \,\text{percent} = 10 \,\text{per mille} = 10^{4} \,\mathrm{ppm} = 10^{7} \,\mathrm{ppb}

Every one of them expresses a share of the whole. Only the size of the denominator differs, so converting means multiplying or dividing by a power of ten.

Example

The default input is 25 ppm in a solution of 1000 g.

As a percentage that is 0.0025, as per mille 0.025, and as ppb 25000. Writing 25 ppm spares the reader from counting zeros in 0.0025 percent.

The dissolved mass is 25×106×100025 \times 10^{-6} \times 1000 g, which is 0.025 g, or 25 mg. Read it as 25 mg dissolved in a kilogram of water.

In water, ppm is close to mg/L

For dilute aqueous solutions, 1 ppm can be read as roughly 1 mg/L. A litre of water weighs about a kilogram, and a millionth of that is a milligram.

This is why water quality limits appear sometimes in mg/L and sometimes in ppm — the substitution works. It stops working once the solution is concentrated, or the solvent is not water, because then the density is no longer 1.

Points to watch

Establish whether a figure is a ratio of masses or of volumes. Liquids and solids normally use mass, but atmospheric work uses volume and sometimes writes ppmv to make the distinction. The familiar figure of 420 ppm of carbon dioxide in the atmosphere is by volume.

This calculator treats the value as a mass ratio. Entering the mass of the solution gives the dissolved mass in milligrams.