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Mass percent and ppm converter

Convert a concentration between percent, per mille, ppm, ppb and ppt, and into mg/L or mol/L using the density and molar mass. Below it, work out the mass percent of a mixture from its recipe.

g/mL

1.000 for dilute water solutions. Needed for mg/L, g/L and mol/L.

g/mol

Adds mol/L to the results, for example 58.44 for sodium chloride.

Mass fraction

  • Percent by mass (% w/w)0.025
  • Per mille (‰, g/kg)0.25
  • ppm (mg/kg)250
  • ppb (µg/kg)250,000
  • ppt, parts per trillion (ng/kg)250,000,000

Mass per volume

  • g/L (mg/mL)0.25
  • % w/v (g per 100 mL)0.025
  • mg/L250
  • µg/L250,000

Amount per volume

  • mol/L (M)add molar mass
  • mmol/L (mM)add molar mass
  • µmol/L (µM)add molar mass

For dilute water solutions, 1 ppm is about 1 mg/L because a litre of water weighs about 1 kg.

How the calculation works

All mass based units are the same quantity, the mass fraction, written with a different multiplier.

w = mass of solute ÷ mass of solution
Mass fraction of a solute
UnitEqualsExample for w = 0.0025
Percent (% w/w)w × 1000.25 %
Per mille (‰)w × 1,0002.5 ‰
ppm (mg/kg)w × 1,000,0002,500 ppm
ppb (µg/kg)w × 10⁹2,500,000 ppb

To go from a mass fraction to a mass per volume you need the density of the solution, because a litre of solution has a mass of density × 1,000 g.

mg/L = ppm × ρ mol/L = w × ρ × 1000 ÷ M
From mass fraction to mass and amount per volume
ρ
density of the solution in g/mL (equal to kg/L)
M
molar mass of the solute in g/mol

For dilute water solutions ρ is close to 1.000 g/mL, so 1 ppm ≈ 1 mg/L. For brines, acids or organic solvents the difference matters, so enter the real density.

Worked example

The same steps the calculator follows, done by hand

A rinse water specification allows up to 250 ppm of sodium chloride (58.44 g/mol). The water has a density of 1.000 g/mL.

  1. 1
    Mass fraction: w = 250 ÷ 1,000,000 = 0.00025, which is 0.025 % w/w or 250 mg/kg.
  2. 2
    Mass per volume: 250 ppm × 1.000 g/mL = 250 mg/L, or 0.25 g/L.
  3. 3
    Molarity: 0.25 g/L ÷ 58.44 g/mol = 0.00428 mol/L, about 4.28 mM.

Mass percent from a recipe

Find the percent by mass when you know how much solute and solvent you mixed

I know
g

Mass percent

5% w/w

50,000 ppm by mass. The total solution is 500 g.

Frequently asked questions

Is ppm the same as mg/L?
Only for dilute water solutions. ppm by mass is mg per kg. mg/L is mg per litre. They match when a litre of solution weighs 1 kg. For a solution with a density of 1.2 g/mL, 100 ppm is 120 mg/L.
What is the difference between % w/w, % w/v and % v/v?
% w/w is grams of solute per 100 g of solution. % w/v is grams per 100 mL of solution. % v/v is mL of a liquid per 100 mL of solution, common for alcohols. Specifications should always state which one is meant.
How do I convert ppm to percent?
Divide by 10,000. So 5,000 ppm is 0.5 % and 1 % is 10,000 ppm.
What does ppt mean?
It is ambiguous. In environmental work it usually means parts per trillion (ng/kg), while some older texts use it for parts per thousand. This converter uses parts per trillion and shows per mille (‰) for parts per thousand.
Does this work for gases?
Not directly. Gas concentrations in ppm are usually by volume (ppmv), which depends on the molar mass of the gas and on temperature and pressure. Use mg/m³ = ppmv × M ÷ 24.45 at 25 °C and 1 atm.

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