per mille
DimensionlessSlopeexact by definition
Per mille is one part in one thousand, exactly 0.001, the same idea as percent with a thousand in the denominator. It is the working unit of stable isotope geochemistry, where δ¹⁸O and δ¹³C are reported per mille against a standard, of historical seawater salinity, and of gradient in some European rail and drainage practice. The factor is exact by definition.
Watch out: The proper symbol is a percent sign with a second zero in the denominator, which has no font metrics in this site's renderer and is spelled out here instead. Be careful with isotope deltas: they are already defined as a per mille deviation from a reference, so a δ value of minus 8 means minus 8 per mille and must not be multiplied by 0.001 twice.
| 1 (Dimensionless) | 0.001 |
| 1 (Slope) | 0.001 |
One part per thousand of rise per run, equal to 1 mm/m. Railway gradients are quoted this way across much of Europe, where a 25 per mille climb is steep main-line grade.
One per mille in every dimensionless unit
| 1,000,000,000 | part per trillion (ppt) | |
| 1,000,000 | part per billion (ppb) | |
| 1,000 | part per million (ppm) | |
| 100 | per cent mille (pcm) | |
| 10 | basis point (bp) | |
| 1 | per mille (per mille)this unit | |
| 0.1 | percent (%) | |
| 0.001 | ratio (—) |
One per mille in every slope unit
| 0.001 | meter per meter (m/m) | |
| 0.1 | percent grade (%) | |
| 1 | millimeter per meter (mm/m) | |
| 1 | per mille (‰)this unit | |
| 0.001 | foot per foot (ft/ft) | |
| 0.012 | inch per foot (in/ft) |