# Vapor Pressure of Water Calculator

Created by Hanna Pamuła, PhD
Reviewed by Bogna Szyk and Adena Benn
Last updated: Jan 05, 2023

The vapor pressure of water calculator is a handy tool that 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 unsure what vapor pressure is, keep scrolling. You'll find the definition, five different vapor pressure formulas, and details about the 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:

the 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 the measured liquid.

## Factors influencing vapor pressure

There are two factors that 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 ($T\uparrow$) → kinetic energy of its molecules increases ($E_{\mathrm{k}}\uparrow$) → number of molecules transitioning into a vapor increases → vapor pressure increases ($P\uparrow$)

At lower temperatures, fewer molecules have sufficient energy.

• Substance nature (types of molecules)

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

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
$P_{\mathrm{simple}} = \mathrm{e}^{20.386-\frac{5132}{T+273}}$

Where vapor pressure is expressed in $\mathrm{mmHg}$ and temperature in kelvin.

1. Antoine formula
$P_\mathrm{Antoine} = 10^{A-\frac{B}{C+T}}$

The temperature $T$ is expressed in degrees Celsius and the vapor pressure $P$ is in $\mathrm{mmHg}$. 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
$P_{\mathrm{Magnus}}= 0.61094\!\times\!\mathrm{e}^{\frac{17.625 \times T}{T+ 243.04}}$

Where $T$ is expressed in $\degree\mathrm{C}$ and $P$ in $\mathrm{kPa}$.

1. Tetens formula
$P_{\mathrm{Tetens}}= 0.61078 \!\times\!\mathrm{e}^{\frac{17.27 \times T}{T + 237.3}}$

Where $T$ is expressed in $\degree\mathrm{C}$ and $P$ in $\mathrm{kPa}$.

1. Buck formula, also known as Arden Buck equation
$P_{\mathrm{Buck}} = 0.61121\!\times\!\mathrm{e}^{\left(18.678 - \frac{T}{234.5}\right)\times\frac{T}{257.14+T}}$

Where $T$ is expressed in $\degree\mathrm{C}$ and $P$ in $\mathrm{kPa}$.

You can also use another equation, called the Goff-Gratch formula, but as it's more complicated (and approximately as accurate as the 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 $0\ \degree\mathrm{C}$ - $100\ \degree\mathrm{C}$ range ($32\ \degree\mathrm{F}$ - $212\ \degree\mathrm{F}$). The reference values come from with the vapor pressure of water (all pressures are given in $\mathrm{kPa}$).

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 $0\ \degree\mathrm{C}$ - $50\ \degree\mathrm{C}$ range, but Buck beats all of them for every checked value. The values start to differ significantly for temperatures higher than $100\ \degree\mathrm{C}$, and the Antoine equation is usually the most accurate one.

#### Antoine equation

The Antoine equation is derived from the Clausius–Clapeyron relation (the one we used in our boiling point calculator). It's a semi-empirical formula describing the association 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:

$P_{\mathrm{Antoine}} = 10^{A-\frac{B}{C+T}}$
• One for describing the vapor pressure curve up to the normal boiling point. For water, it's the range$0\ \degree\mathrm{C}$ - $001\ \degree\mathrm{C}$ - or $32\ \degree\mathrm{F}$ - $212\ \degree\mathrm{F}$.
$\begin{split} A& = 8.07131\\ B& =1730.63\\ C&=233.426 \end{split}$

So the Antoine equation is:

$P_{\mathrm{Antoine}} = 10^{8.07131-\frac{1730.36}{233.426+T}}$
• the second for the range from the normal boiling point to the critical point ($100\ \degree\mathrm{C}$ - $374\ \degree\mathrm{C}$ - or $212\ \degree\mathrm{F}$ - $705\ \degree\mathrm{F}$ - for water)
$\begin{split} A& = 8.14019\\ B& =1810.94\\ C&=244.485 \end{split}$

So the formula looks as follows:

$P_{\mathrm{Antoine}} = 10^{8.14019-\frac{1810.94}{244.485+T}}$

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

🙋 Before heading into the next section, be sure to master the conversions between the various pressure measurement units: our pressure conversion tool is a comprehensive guide to do so. You can also try our temperature conversion tool for an easier mnemonic exercise!

## Vapor pressure of water

The vapor pressure of water is the pressure at which water vapor is in thermodynamic equilibrium with its condensed state. The water will condense if we raise the pressure and keep the temperature.
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 $0\ \degree\mathrm{C}$). Type negative temperatures into the calculator and the vapor pressure will be determined according to Buck and Teten's 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 $86\ \degree\mathrm{F}$ ($30\ \degree\mathrm{C}$).

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

3. If you want to get the result in a different pressure unit, simply click on the unit name and choose the one you need: $\mathrm{Pa}$, $\mathrm{hPa}$, $\mathrm{torr}$, $\mathrm{mmHg}$ or any other unit.

## FAQ

### What is vapor pressure?

The vapor pressure of water is the point of equilibrium between the number of water molecules moving between the liquid phase and the gas phase in a closed container. At this point, there are as many molecules leaving the liquid and entering the gas phase as there are molecules leaving the gas phase and entering the liquid phase.

### Does vapor pressure increase with temperature?

Yes, vapor pressure increases with temperature as the molecules receive more energy to escape from the liquid phase and transition to the gas phase. Note that a closed container is required, as otherwise, the molecules in the gas phase will fly away.

### How can I calculate the vapor pressure of water at 80°C degrees?

The vapor pressure of water at 80°C will be 47.27 kPa (Antoine formula) or 46.19 kPa (simple formula).
To find the vapor pressure of water:

1. Use one of the popular approximations, e.g., Antoine formula:
PAntoine = 10A-B/(C+T) = 108.14019-1810.94/(244.485+T).
2. Enter T = 80°C in Celsius degrees: 108.14019-1810.94/(244.485+80).
3. Compute 101.6746 = 47.27 kPa.
4. Compare with the simplified formula:
Psimple = e20.386-5132/(T+273) = e20.386-5132/(80+273) = 46.19 kPa.

### Can a vapor pressure of water be zero?

No, vapor pressure can't be zero when the temperature is above absolute zero. Note that many objects have resided for eons in the vacuum of space, whose temperature is not absolute zero, but have not evaporated because they have non-zero vapor pressure (e.g., asteroids).

### Why is the vapor pressure of water so important?

The vapor pressure of water is crucial for life forms on Earth, as its value is high enough to allow for the process of evaporation but low enough to also allow for the existence of liquid and solid water.

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