# Vapor Pressure of Water Calculator

By Hanna Pamuła, PhD candidate
Last updated: Mar 12, 2021

The vapor pressure of water calculator is a handy tool which can help in determining the vapor pressure of water and ice. Just type in the temperature and the pressure will appear in no time - don't hesitate, give it a go! If you're not sure what vapor pressure is, keep scrolling and you'll find the vapor pressure definition, five different vapor pressure formulas and details about most often used one - Antoine equation.

## What is vapor pressure? Vapor pressure definition Vapor pressure is the pressure exerted by a vapor which is in thermodynamic equilibrium with its condensed phases (solid or liquid) in a closed system at a given temperature. The equilibrium - in other words, steady state - between evaporation and condensation occurs when:

Rate of evaporation of the liquid = Rate of condensation of the gas

Vapor pressure is one of the fluid characteristics: it's a measure of the tendency of a material to change into the gaseous/vapor state. The vapor pressure of a liquid can be measured in many ways, e.g. by a manometer connected to the flask with measured liquid.

## Factors influencing vapor pressure

There are two factors which influence the vapor pressure:

• Temperature

The higher the temperature is, the more molecules have enough energy to escape from the liquid or solid, which leads to higher vapor pressure values.

temperature of a liquid increases (T↑) --> kinetic energy of its molecules increases (Ek↑) --> number of molecules transitioning into a vapor increases --> vapor pressure increases (P↑)

At lower temperatures, fewer molecules have sufficient energy.

• Substance nature (types of molecules)

For substances with stronger intermolecular forces, the vapor pressure will be relatively low. In contrary, for relatively weak forces the vapor pressure is relatively high.

The important thing to mention is the fact that the surface area of liquid/solid substance in contact with the gas doesn't affect the vapor pressure. So it doesn't matter if we put our liquid into a wide flask or a thin graduated cylinder - the vapor pressure remains the same.

## Vapor pressure formulas

There are many different formulas thanks to which you can calculate the vapor pressure of water. The most well known and established is the Antoine equation, but other methods also exist (and they perform better in typical conditions). In our calculator you'll find implemented:

1. Simple formula

`simple_pressure = e^(20.386 - (5132 / (temperature + 273))`, where vapor pressure is expressed in mmHg and temperature in kelvins.

1. Antoine formula

`Antoine_pressure = 10^[A - (B / (C + temperature))]`

The temperature T is expressed in degrees Celsius and the vapor pressure P is in mmHg. Jump to the next section to read more about the constants in the Antoine formula.

1. Magnus formula, also known as August-Roche-Magnus or Magnus-Tetens equation

`Magnus_pressure = 0.61094 * e^[(17.625 * temperature) / (temperature + 243.04)] `

where T is expressed in °C and P in kPa.

1. Tetens formula

`Tetens_pressure = 0.61078 * e^[(17.27 * temperature) / (temperature + 237.3)]`

where T is expressed in °C and P in kPa.

1. Buck formula, also known as Arden Buck equation

`Buck_pressure = 0.61121 * e^[(18.678 - (temperature / 234.5)) * (temperature / (257.14 + temperature))]`

where T is expressed in °C and P in kPa.

You can also use another equation, called the Goff-Gratch formula, but as it's more complicated (and approximately as accurate as Buck formula), we didn't implement it in our vapor pressure of water calculator. The table below shows the comparison of the accuracies between different formulas, for several temperatures from 0-100 °C range (32-212°F). The reference values come from Lide table with vapor pressure of water (all pressures given in kPa).

T (°C) T (°F) P (Lide Table) P (Simple) P (Antoine) P (Magnus) P (Tetens) P (Buck)
0 32 0.6113 0.6593 (+7.85%) 0.6056 (-0.93%) 0.6109 (-0.06%) 0.6108 (-0.09%) 0.6112 (-0.01%)
20 68 2.3388 2.3755 (+1.57%) 2.3296 (-0.39%) 2.3334 (-0.23%) 2.3382 (+0.05%) 2.3383 (-0.02%)
35 95 5.6267 5.5696 (-1.01%) 5.6090 (-0.31%) 5.6176 (-0.16%) 5.6225 (+0.04%) 5.6268 (+0.00%)
50 122 12.344 12.065 (-2.26%) 12.306 (-0.31%) 12.361 (+0.13%) 12.336 (+0.08%) 12.349 (+0.04%)
75 167 38.563 37.738 (-2.14%) 38.463 (-0.26%) 39.000 (+1.13%) 38.646 (+0.40%) 38.595 (+0.08%)
100 212 101.32 101.31 (-0.01%) 101.34 (+0.02%) 104.077 (+2.72%) 102.21 (+1.10%) 101.31 (-0.01%)

As you can notice, the Antoine equation is reasonably accurate for higher temperatures, but the low ones are calculated with quite a big error. The Tetens equation works well for 0-50 °C range, but Buck beats all of them, for every checked value. For temperatures higher than 100 °C, the values start to differ significantly and the Antoine equation is usually the most accurate one.

## Antoine equation

The Antoine equation is derived from the Clausius–Clapeyron relation. It's a semi-empirical formula describing the relation between vapor pressure and temperature. It works for many substances, although you need to know the coefficients. There are usually two sets of parameters used for a single component:

`Antoine_pressure = 10^(A - (B / (C + temperature)))`

• one for describing the vapor pressure curve up to the normal boiling point. For water, it's the range 0-100 °C (32-212 °F)

A = 8.07131, B = 1730.63, C = 233.426, so the Antoine equation is:

`Antoine_pressure = 10^(8.07131 - (1730.63 / (233.426 + temperature)))`

• the second for the range from the normal boiling point to the critical point (100-374 °C - or 212°-705 °F - for water)

A = 8.14019, B = 1810.94, C = 244.485, so the formula looks as follows:

`Antoine_pressure = 10^(8.07131 - (1730.63 / (233.426 + temperature)))`

The Antoine equation is sometimes simplified (omitting C coefficient) or extended by three additional terms, what can increase the flexibility of the equation.

## Vapor pressure of water

The vapor pressure of water is the pressure at which water vapor is in thermodynamic equilibrium with its condensed state. If we raise the pressure and keep the temperature, the water will condense.
Have a look at this handy vapor pressure for water table to find the pressure for different temperatures quickly:

T [°C] T [°F] P [kPa] P [torr] P [atm]
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

Two formulas have a version for vapor pressure of water over ice (so for temperatures below 0 °C). Type negative temperatures into the calculator and vapor pressure will be determined according to Buck and Tetens formulas.

## Vapor pressure of water calculator - how to use

Now as you know what vapor pressure is and you heard about different vapor pressure formulas, it's high time for a practical demonstration. This calculator is one of the easiest to use, as you need to enter only one value, so you shouldn't have any problems with using it! But just in case, we're showing the example:

1. Enter the temperature. Assume we want to calculate the vapor pressure of water in 86 °F (30 °C).

2. Poof! The vapor pressure of water calculator found the pressure according to five formulas. The most often used is the Antoine equation (4.232 kPa), but the Buck formula (4.245 kPa) is usually the most accurate one for temperature ranges we typically look for.

3. If you want to get the result in different pressure unit, simply click on the unit name and choose the one you need: Pa, hPa, torrs, mmHg or any other unit.

Hanna Pamuła, PhD candidate
Temperature
°F
Pressure
Buck formula
0.44165
kPa
Tetens formula
0.4412
kPa
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