Parts Per Million (ppm) Converter
Parts Per Million (ppm) Converter
Convert between ppm, ppb, mg/L, µg/mL, µg/L and per cent — and see where the familiar equivalence of ppm with mg/L stops being true.
ppm converter
Any unit → ppm5%, converted to ppm
Formula and the exact relationships
1% = 10,000 ppm · 1 ppm = 1,000 ppb
In dilute aqueous solution (density taken as 1.00 g/mL): 1 ppm = 1 mg/L = 1 µg/mL = 1 mg/kg, and 1 ppb = 1 µg/L
- ppm
- parts per million — a dimensionless ratio of one part in 10⁶, by mass unless stated otherwise
- ppb
- parts per billion, one part in 10⁹ on the short scale used throughout analytical chemistry. 1 ppm = 1,000 ppb
- density 1.00 g/mL
- the assumption that turns a mass ratio into a mass concentration. It holds for dilute aqueous solutions and fails for other solvents, for concentrated solutions and for gases
- 1% = 10,000 ppm
- exact and unit-free: a percentage is parts per 10², so the step to parts per 10⁶ is a factor of 10⁴
Worked example
5%, converted to ppm
1% = 10,000 ppm, so the conversion is × 10,000
5 × 10,000 = 50,000 ppm
In dilute aqueous solution that would be 50,000 mg/L, or 50 g/L
At 5% the density of the solution is already measurably above 1.00 g/mL, which is exactly why concentrations this high belong in per cent rather than ppm
The same concentration written six ways
| Percent | ppm | ppb | mg/L | µg/L |
|---|---|---|---|---|
| 1% | 10,000 | 10,000,000 | 10,000 | 10,000,000 |
| 0.01% | 100 | 100,000 | 100 | 100,000 |
| 0.0001% | 1 | 1,000 | 1 | 1,000 |
| 0.00001% | 0.1 | 100 | 0.1 | 100 |
| 0.0000001% | 0.001 | 1 | 0.001 | 1 |
Where 1 ppm = 1 mg/L stops being true
| Situation | What ppm means there | What to do instead |
|---|---|---|
| Dilute aqueous solution | A mass ratio that coincides with 1 mg/L because the density is 1.00 g/mL | Use the equivalence freely, and state the assumption in the method |
| Non-aqueous solvent | Still a mass ratio, but 1 L no longer weighs 1 kg | Multiply by the solvent density: mg/L = ppm × density in g/mL |
| Concentrated solution | A mass ratio; the solution’s density has drifted away from 1.00 g/mL | Express as % w/w or as a measured mass concentration |
| Solid or tissue | 1 ppm = 1 mg/kg by mass, with no volume involved | Report as mg/kg — the equivalence to mg/L does not apply |
| Gas or vapour | A VOLUME ratio, µL per L of air | mg/m³ = ppm × molecular weight ÷ molar volume (24.45 L/mol at 25 °C and 101.325 kPa) |
A ratio that only looks like a concentration
Parts per million is a dimensionless ratio: one part of solute in a million parts of solution. That is all it says. It becomes a concentration only when something supplies the missing link between mass and volume, and in practice that something is the density of water. One litre of dilute aqueous solution weighs very close to 1 kg, so one part in a million of it is 1 mg in 1 L — which is why 1 ppm, 1 mg/L, 1 µg/mL and 1 mg/kg are used interchangeably in the clinical and water laboratory. The equivalence is a consequence of the matrix, not a definition.
Take the matrix away and the shorthand fails. In a non-aqueous solvent a litre no longer weighs a kilogram, so ppm and mg/L differ by the density in g/mL. In a concentrated solution the density has moved away from 1.00 g/mL for the same reason, which is one argument for writing anything above about 1% as a percentage instead. For solids and tissue, ppm means mg/kg and there is no volume in the picture at all. For gases the convention changes outright: ppm in air is a volume ratio, µL per litre, and converting it to mg/m³ needs the molecular weight and the molar volume — about 24.45 L/mol at 25 °C and 101.325 kPa.
The arithmetic between the units is exact and unit-free, which makes the errors clean and large. A percentage is parts per hundred, so 1% is 10,000 ppm and 1 ppm is 0.0001%. A part per billion is a thousandth of a part per million, so 1 ppm is 1,000 ppb and 1 ppb is 1 µg/L. Every step in that ladder is a factor of a thousand or ten thousand, and a slip anywhere in it produces an answer wrong by an order of magnitude that no amount of careful analysis downstream will reveal.
That matters most where the numbers are small and the limits are legal. Guideline and regulatory values for drinking water and for trace elements in blood are quoted at the ppb and µg/L level, so reading a ppb result as ppm overstates it a thousandfold and the reverse understates it by the same factor. The defences are the ordinary ones: carry the unit alongside the number at every step, prefer the SI mass concentration in reports where ppm and ppb are ambiguous, and state the matrix — aqueous, solid or gas — whenever a ppm figure is written down.
Frequently asked questions
Is 1 ppm the same as 1 mg/L?
For dilute aqueous solutions, yes, because 1 L of such a solution weighs almost exactly 1 kg. It is an approximation resting on a density of 1.00 g/mL, and it fails for other solvents, for concentrated solutions and for gases.
How do I convert per cent to ppm?
Multiply by 10,000. A percentage is parts per hundred and ppm is parts per million, so the step between them is a factor of 10,000: 1% is 10,000 ppm and 5% is 50,000 ppm.
What is the difference between ppm and ppb?
A factor of one thousand. One part per million is 1,000 parts per billion, and in dilute aqueous solution 1 ppb equals 1 µg/L. Confusing the two is a thousandfold error, which matters because water and trace element limits are usually quoted in ppb.
Does ppm work the same way for gases?
No. In gas and vapour analysis ppm is a volume ratio — microlitres per litre of air — not a mass ratio. Converting to mg/m³ requires the molecular weight and the molar volume, about 24.45 L/mol at 25 °C and 101.325 kPa.
How do I express ppm for a solid sample?
As mg/kg. One part per million by mass is 1 mg of analyte in 1 kg of material, and no volume is involved, so the mg/L equivalence used for water does not apply to soil, food or tissue.
Related calculators
References
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure). 9th ed. — on the expression of dimensionless quantities and the deprecation of ppm as a unit symbol.
- Thompson A, Taylor BN. Guide for the Use of the International System of Units (SI). NIST Special Publication 811 — section on ppm, ppb and other dimensionless ratios.
- World Health Organization. Guidelines for Drinking-water Quality. 4th ed. incorporating the first addendum — guideline values expressed in mg/L and µg/L.