| 0 | 32 | 0.6113 | 4.5851 | 0.0060 | |
| 5 | 41 | 0.8726 | 6.5450 | 0.0086 | |
| 10 | 50 | 1.2281 | 9.2115 | 0.0121 | |
| 15 | 59 | 1.7056 | 12.7931 | 0.0168 | |
| 20 | 68 | 2.3388 | 17.5424 | 0.0231 | |
| 25 | 77 | 3.1690 | 23.7695 | 0.0313 | |
| 30 | 86 | 4.2455 | 31.8439 | 0.0419 | |
| 35 | 95 | 5.6267 | 42.2037 | 0.0555 | |
| 40 | 104 | 7.3814 | 55.3651 | 0.0728 | |
| 45 | 113 | 9.5898 | 71.9294 | 0.0946 | |
| 50 | 122 | 12.3440 | 92.5876 | 0.1218 | |
| 55 | 131 | 15.7520 | 118.1497 | 0.1555 | |
| 60 | 140 | 19.9320 | 149.5023 | 0.1967 | |
| 65 | 149 | 25.0220 | 187.6804 | 0.2469 | |
| 70 | 158 | 31.1760 | 233.8392 | 0.3077 | |
| 75 | 167 | 38.5630 | 289.2463 | 0.3806 | |
| 80 | 176 | 47.3730 | 355.3267 | 0.4675 | |
| 85 | 185 | 57.8150 | 433.6482 | 0.5706 | |
| 90 | 194 | 70.1170 | 525.9208 | 0.6920 | |
| 95 | 203 | 84.5290 | 634.0196 | 0.8342 | |
| 100 | 212 | 101.3200 | 759.9625 | 1.0000 |
Calculations of the (saturation) vapor pressure of water are commonly used in meteorology. The temperature-vapor pressure relation inversely describes the relation between the boiling point of water and the pressure. This is relevant to both pressure cooking and cooking at high altitudes. An understanding of vapor pressure is also relevant in explaining high altitude breathing and cavitation.
There are many published approximations for calculating saturated vapor pressure over water and over ice. Some of these are (in approximate order of increasing accuracy):
| Name | Formula | Description | |||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| "Eq. 1" (August equation) | P=\exp\left(20.386-
\right) | is the vapour pressure in mmHg and is the temperature in kelvins. Constants are unattributed. | |||||||||||||||||||
| The Antoine equation | log10P=A-
| is in degrees Celsius (°C) and the vapour pressure is in mmHg. The (unattributed) constants are given as
| |||||||||||||||||||
| August-Roche-Magnus (or Magnus-Tetens or Magnus) equation | P=0.61094\exp\left(
\right) | Temperature is in °C and vapour pressure is in kilopascals (kPa). The coefficients given here correspond to equation 21 in Alduchov and Eskridge (1996).[2] See also discussion of Clausius-Clapeyron approximations used in meteorology and climatology. | |||||||||||||||||||
| Tetens equation | P=0.61078\exp\left(
\right) | is in °C and is in kPa | |||||||||||||||||||
| The Buck equation. | P=0.61121\exp\left(\left(18.678-
\right)\left(
\right)\right) | is in °C and is in kPa. | |||||||||||||||||||
| The Goff-Gratch (1946) equation.[3] | (See article; too long) | ||||||||||||||||||||
Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapor pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005):
| (°C) | (Lide Table) | (Eq 1) | (Antoine) | (Magnus) | (Tetens) | (Buck) | (Goff-Gratch) | |
|---|---|---|---|---|---|---|---|---|
| 0 | 0.6113 | 0.6593 (+7.85%) | 0.6056 (-0.93%) | 0.6109 (-0.06%) | 0.6108 (-0.09%) | 0.6112 (-0.01%) | 0.6089 (-0.40%) | |
| 20 | 2.3388 | 2.3755 (+1.57%) | 2.3296 (-0.39%) | 2.3334 (-0.23%) | 2.3382 (+0.05%) | 2.3383 (-0.02%) | 2.3355 (-0.14%) | |
| 35 | 5.6267 | 5.5696 (-1.01%) | 5.6090 (-0.31%) | 5.6176 (-0.16%) | 5.6225 (+0.04%) | 5.6268 (+0.00%) | 5.6221 (-0.08%) | |
| 50 | 12.344 | 12.065 (-2.26%) | 12.306 (-0.31%) | 12.361 (+0.13%) | 12.336 (+0.08%) | 12.349 (+0.04%) | 12.338 (-0.05%) | |
| 75 | 38.563 | 37.738 (-2.14%) | 38.463 (-0.26%) | 39.000 (+1.13%) | 38.646 (+0.40%) | 38.595 (+0.08%) | 38.555 (-0.02%) | |
| 100 | 101.32 | 101.31 (-0.01%) | 101.34 (+0.02%) | 104.077 (+2.72%) | 102.21 (+1.10%) | 101.31 (-0.01%) | 101.32 (0.00%) |
A more detailed discussion of accuracy and considerations of the inaccuracy in temperature measurements is presented in Alduchov and Eskridge (1996). The analysis here shows the simple unattributed formula and the Antoine equation are reasonably accurate at 100 °C, but quite poor for lower temperatures above freezing. Tetens is much more accurate over the range from 0 to 50 °C and very competitive at 75 °C, but Antoine's is superior at 75 °C and above. The unattributed formula must have zero error at around 26 °C, but is of very poor accuracy outside a narrow range. Tetens' equations are generally much more accurate and arguably more straightforward for use at everyday temperatures (e.g., in meteorology). As expected, Buck's equation for > 0 °C is significantly more accurate than Tetens, and its superiority increases markedly above 50 °C, though it is more complicated to use. The Buck equation is even superior to the more complex Goff-Gratch equation over the range needed for practical meteorology.
For serious computation, Lowe (1977)[4] developed two pairs of equations for temperatures above and below freezing, with different levels of accuracy. They are all very accurate (compared to Clausius-Clapeyron and the Goff-Gratch) but use nested polynomials for very efficient computation. However, there are more recent reviews of possibly superior formulations, notably Wexler (1976, 1977),[5] [6] reported by Flatau et al. (1992).[7]
Examples of modern use of these formulae can additionally be found in NASA's GISS Model-E and Seinfeld and Pandis (2006). The former is an extremely simple Antoine equation, while the latter is a polynomial.[8]
In 2018 a new physics-inspired approximation formula was devised and tested by Huang [9] who also reviews other recent attempts.