Vapor Pressure of Water Calculator

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.

Vapor pressure is the pressure exerted by a vapor that 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.

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.

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:

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

2. Antoine formula:

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.

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

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

4. Tetens formula:

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

5. Buck formula, also known as Arden Buck equation:

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 Lide table with the vapor pressure of water (all pressures are given in $\mathrm{kPa}$).

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:

• One for describing the vapor pressure curve up to the normal boiling point. For water, it's the range $0\ \degree\mathrm{C}$ - $100\ \degree\mathrm{C}$ or $32\ \degree\mathrm{F}$ - $212\ \degree\mathrm{F}$.

So the Antoine equation is:

• 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)

So the formula looks as follows:

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

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:

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.

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.