Percent, Per Mille and Parts per Million

Percent, per mille and parts-per notation are all ways of writing a dimensionless ratio as a multiple of a power of ten. This sheet defines each one and shows how to convert between them.

Definitions

Ratio notations as powers of ten
NameSymbolValueUnicode
Percent%1/100 = 10⁻²U+0025
Per mille (per thousand)‰1/1,000 = 10⁻³U+2030
Per ten thousand (basis point)‱1/10,000 = 10⁻⁴U+2031
Parts per millionppm10⁻⁶—
Parts per billionppb10⁻⁹ (short-scale billion)—
Parts per trillionppt10⁻¹² (short-scale trillion)—

Sources: OpenStax: Prealgebra 2e §6.1 Understand Percent

Conversion chart

To convert, multiply by the ratio of the two units' powers of ten. Moving one row down multiplies the number by 10, 1,000 or more.

Equivalent values
FractionPercentPer milleppmppb
1100%1,000‰1,000,0001,000,000,000
0.110%100‰100,000100,000,000
0.011%10‰10,00010,000,000
0.0010.1%1‰1,0001,000,000
0.00010.01%0.1‰100100,000
1 × 10⁻⁶1 × 10⁻⁴%0.001‰11,000
1 × 10⁻⁹1 × 10⁻⁷%1 × 10⁻⁶‰0.0011

Worked examples and usage notes

  • 250 ppm = 250 × 10⁻⁶ = 0.025% = 0.25‰
  • 3.5% = 35‰ = 35,000 ppm
  • A 0.25 percentage-point change in an interest rate is 25 basis points (25‱)
  • “ppt” is ambiguous: it can mean parts per trillion (10⁻¹²) or, in oceanography and some older texts, parts per thousand (10⁻³). State the power of ten when it matters
  • NIST and ISO treat % as acceptable with the SI but advise against ppm, ppb and ppt because they are language-dependent; write 2 µg/g or 2 × 10⁻⁶ instead
  • Always say what the ratio is of: mass fraction (mg/kg), volume fraction (µL/L) or amount fraction (µmol/mol) can differ for the same sample

Sources: NIST: NIST Guide to the SI (SP 811), Chapter 7: Rules and Style Conventions

References

Frequently asked questions

How many ppm is 1 percent?

1% = 10,000 ppm, because 1% is 10⁻² and 1 ppm is 10⁻⁶, a factor of 10⁴ apart.

What is the per mille sign?

‰ (U+2030) means parts per thousand. 5‰ = 0.5% = 0.005.