Water content in ppm by volume equals the saturation vapour pressure at the dew point divided by the total pressure, times a million. At atmospheric pressure, minus 40 C is about 127 ppm and minus 60 C is about 11 ppm; at 7 bar the same dew points hold seven times less water as a fraction of the gas.
Uses Buck (1996) over liquid water above 0 C and Murphy and Koop (2005) over ice at and below 0 C. At very low dew points, instrument accuracy is far wider than the formula.
How it is calculated
The air can hold only so much water vapour at a given temperature, the saturation vapour pressure. At the dew point the gas is exactly saturated, so the partial pressure of water in the gas equals that saturation pressure. The share of the gas that is water is then that partial pressure divided by the total pressure.
ppmv = 1,000,000 x pv(dew point) / P_total
Below 0 C the saturation pressure is taken over ice, which gives the frost point, the convention nearly all dry-gas specifications use. The calculator inverts the same relation to find the dew point from ppm.
Worked examples
A dryer outlet at atmospheric pressure shows minus 40 C. Saturation pressure over ice at minus 40 C is 12.8 Pa, so ppmv = 12.8 / 101,325 x 1,000,000 = 127 ppm.
A compressed air line at 7 bar absolute with a pressure dew point of minus 40 C holds only 12.8 / 701,325 x 1,000,000 = 18 ppm. Expand it to atmosphere and the same 18 ppm corresponds to an atmospheric dew point of about minus 56 C.
That is why a pressure dew point and an atmospheric dew point of the same gas differ by many degrees. Always state which one is meant.
Reference points
| Dew point (C) | ppm by volume at 1 atm |
|---|---|
| +20 | about 23,000 |
| 0 | about 6,000 |
| -20 | about 1,000 |
| -40 | about 127 |
| -60 | about 11 |
| -80 | about 0.5 |
| -100 | about 0.014 |
Each 10 C of cooling is roughly a three-fold drop in water content in this range.
Limits
- Real gases and mixtures behave slightly differently from the ideal relation; the error is small for dry gas.
- Instrument accuracy matters more than the formula: a catalogue accuracy of plus or minus 2 C at minus 60 C is a factor of about 1.3 either way in ppm.
- Convention differs between dew point (over water) and frost point (over ice) near zero; this tool switches at 0 C.
Frequently asked questions
How many ppm is a dew point of minus 40 C?
About 127 ppm by volume at atmospheric pressure, and about 18 ppm in a gas that is at 7 bar absolute when the dew point is quoted at that pressure.
What is the difference between dew point and frost point?
Below 0 C moisture may condense as liquid or deposit as frost. The frost point, over ice, is slightly higher than the dew point over supercooled water at the same water content. Dry-gas standards use the frost-point convention.
Does pressure change the dew point?
Yes. At a higher total pressure the same ppm corresponds to a higher dew point, because the water partial pressure rises in proportion.
Can I use this for natural gas or hydrogen?
For dry, near-ideal gases at modest pressure it is a good estimate. At high pressure real-gas effects matter and a correction is needed.