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ppm and ppb Calculator

Work out a concentration in ppm and ppb from a mass of solute, or the solute needed for a target, by mass or for a dilute solution measured by volume.

Formula

ppm=msolutemsolution×106\mathrm{ppm} = \dfrac{m_{\text{solute}}}{m_{\text{solution}}}\times 10^{6}
ppb=msolutemsolution×109\mathrm{ppb} = \dfrac{m_{\text{solute}}}{m_{\text{solution}}}\times 10^{9}
msolution=V×ρm_{\text{solution}} = V \times \rho
dilute aqueous solution:1 ppm≈1 mg/L\text{dilute aqueous solution:}\quad 1\ \mathrm{ppm} \approx 1\ \mathrm{mg/L}
ppm\text{ppm}
parts per million by mass: milligrams of solute per kilogram of solution
ppb\text{ppb}
parts per billion (10⁹) by mass: micrograms of solute per kilogram of solution
ρ\rho
of the solution; 1.00 g/mL for dilute aqueous solutions

How it works

For solids and liquids, ppm and ppb are mass fractions: the mass of solute divided by the mass of the whole solution, scaled by a million or a billion. One ppm is one milligram per kilogram.

A litre of dilute aqueous solution weighs very nearly one kilogram, so 1 ppm is commonly treated as 1 mg/L and 1 ppb as 1 µg/L. That shortcut is a statement about density. When the solution is given by volume the calculator multiplies by the density you enter, which you should change for anything that is not dilute and aqueous.

Worked example

25 mg of a solute is dissolved in water to give 2 L of solution.

  1. Mass of solution = 2,000 mL × 1.00 g/mL = 2,000 g.
  2. ppm = 0.025 g / 2,000 g × 10⁶ = 12.5.

The solution is 12.5 ppm, or 12,500 ppb, which is 12.5 mg/L.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Concentrations are mass fractions. Gas concentrations in ppm are by volume or by mole and are not covered here.
  • A billion is 10⁹.
  • With the default density, the solution is dilute and aqueous.

Common mistakes

  • Using 1 ppm = 1 mg/L for a solvent or a concentrated solution whose density is not 1 g/mL.
  • Applying a mass-based ppm to a gas mixture, where ppm means parts by volume.
  • Writing ppt without saying whether it means parts per thousand or parts per trillion. NIST advises against all three abbreviations for that reason; state mg/kg or µg/L when a report allows it.

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