Vapour pressure of water

The vapour pressure of water is the pressure at which water vapour is in thermodynamic equilibrium with its condensed state. At higher pressures water would condense. The water vapour pressure is the partial pressure of water vapour in any gas mixture in equilibrium with solid or liquid water. As for other substances, water vapour pressure is a function of temperature and can be determined with the Clausius–Clapeyron relation.

Vapour pressure of water (0–100 °C)[1]
T, °CT, °FP, kPaP, torrP, atm
0320.61134.58510.0060
5410.87266.54500.0086
10501.22819.21150.0121
15591.705612.79310.0168
20682.338817.54240.0231
25773.169023.76950.0313
30864.245531.84390.0419
35955.626742.20370.0555
401047.381455.36510.0728
451139.589871.92940.0946
5012212.344092.58760.1218
5513115.7520118.14970.1555
6014019.9320149.50230.1967
6514925.0220187.68040.2469
7015831.1760233.83920.3077
7516738.5630289.24630.3806
8017647.3730355.32670.4675
8518557.8150433.64820.5706
9019470.1170525.92080.6920
9520384.5290634.01960.8342
100212101.3200759.96251.0000

Approximation formulas

There are many published approximations for calculating saturated vapour pressure over water and over ice. Some of these are (in approximate order of increasing accuracy):

• ${\displaystyle P=\exp \left(20.386-{\frac {5132}{T}}\right),\ \ \ \ (Eq.1)}$
where P is the vapour pressure in mmHg and T is the temperature in kelvins.
${\displaystyle \log _{10}P=A-{\frac {B}{C+T}},}$
where the temperature T is in degrees Celsius (°C) and the vapour pressure P is in mmHg. The constants are given as
A B C Tmin, °C Tmax, °C
8.071311730.63233.426199
8.140191810.94244.485100374
${\displaystyle P=0.61094\exp \left({\frac {17.625T}{T+243.04}}\right),}$

where temperature T is in °C and vapour pressure P is in kilopascals (kPa)

${\displaystyle P=0.61078\exp \left({\frac {17.27T}{T+237.3}}\right),}$

where temperature T is in °C and  P is in kPa

${\displaystyle P=0.61121\exp \left(\left(18.678-{\frac {T}{234.5}}\right)\left({\frac {T}{257.14+T}}\right)\right),}$

where T is in °C and P is in kPa.

Accuracy of different formulations

Here is a comparison of the accuracies of these different explicit formulations, showing saturation vapour pressures for liquid water in kPa, calculated at six temperatures with their percentage error from the table values of Lide (2005):

T (°C)P (Lide Table)P (Eq 1)P (Antoine)P (Magnus)P (Tetens)P (Buck)P (Goff-Gratch)
00.61130.6593 (+7.85%)0.6056 (-0.93%)0.6109 (-0.06%)0.6108 (-0.09%)0.6112 (-0.01%)0.6089 (-0.40%)
202.33882.3755 (+1.57%)2.3296 (-0.39%)2.3334 (-0.23%)2.3382 (+0.05%)2.3383 (-0.02%)2.3355 (-0.14%)
355.62675.5696 (-1.01%)5.6090 (-0.31%)5.6176 (-0.16%)5.6225 (+0.04%)5.6268 (+0.00%)5.6221 (-0.08%)
5012.34412.065 (-2.26%)12.306 (-0.31%)12.361 (+0.13%)12.336 (+0.08%)12.349 (+0.04%)12.338 (-0.05%)
7538.56337.738 (-2.14%)38.463 (-0.26%)39.000 (+1.13%)38.646 (+0.40%)38.595 (+0.08%)38.555 (-0.02%)
100101.32101.31 (-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 very narrow range. Tetens' equations are generally much more accurate and arguably simpler for use at everyday temperatures (e.g., in meteorology). As expected, Buck's equation for T > 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.

Numerical approximations

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]