The saturation vapour pressure of water is the pressure of water vapour in equilibrium with liquid water (or ice) at a given temperature – the most water vapour the air can hold before it condenses. It climbs steeply with temperature: 0.61 kPa at 0 °C, 2.34 kPa at 20 °C, 7.38 kPa at 40 °C and 101.3 kPa at 100 °C, the point at which water boils at sea level.
Meteorologists need it for relative humidity, dew point and cloud formation; HVAC engineers for drying and condensation; chemists for correcting the volume of gases collected over water; biologists for evaporation and transpiration. Because no simple formula is exact everywhere, several empirical equations are in use. The Buck (1981) equation is among the most accurate from −40 to +50 °C, Magnus and Tetens are compact and popular in meteorology, and the Antoine equation with two coefficient sets covers 1–374 °C.
Below 0 °C there are two answers: the vapour pressure over supercooled liquid water and the lower one over ice. Choose which surface you need. With a relative humidity, the calculator also gives the actual vapour pressure, the mass of water vapour per cubic metre of air and the dew point.
How to use the Vapour Pressure of Water Calculator
- Temperature
- Formula for the main result
- Surface below 0 °C
- Relative humidity (for humidity and dew point)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the temperature and pick the formula used for the main result; all five values are shown for comparison. Antoine switches automatically to its high-temperature coefficients above 100 °C; Buck and Tetens switch to their ice versions below 0 °C if you choose the ice surface. The actual vapour pressure is RH × saturation pressure, absolute humidity is e·M/(R·T), and the dew point inverts the Magnus formula.
Worked example
At 25 °C, Buck: (18.678 − 25/234.5) × 25/(257.14 + 25) = 18.571 × 0.08861 = 1.6456, so P = 0.61121 × e^1.6456 = 3.168 kPa. Antoine: log₁₀ P = 8.07131 − 1730.63/(233.426 + 25) = 1.37437, P = 23.68 mmHg = 3.158 kPa. At 50% relative humidity the actual vapour pressure is 1.584 kPa, the air holds 11.5 g of water vapour per m³ and the dew point is about 13.9 °C.
Vapour pressure of water table
| Temperature | Buck (kPa) | Antoine (kPa) | Tetens (kPa) |
|---|---|---|---|
| 0 °C | 0.611 | 0.606 | 0.611 |
| 5 °C | 0.872 | 0.866 | 0.872 |
| 10 °C | 1.228 | 1.221 | 1.228 |
| 15 °C | 1.705 | 1.698 | 1.705 |
| 20 °C | 2.338 | 2.330 | 2.338 |
| 25 °C | 3.169 | 3.158 | 3.168 |
| 30 °C | 4.245 | 4.232 | 4.243 |
| 37 °C | 6.280 | 6.260 | 6.275 |
| 40 °C | 7.382 | 7.358 | 7.375 |
| 50 °C | 12.349 | 12.306 | 12.336 |
| 60 °C | 19.945 | 19.870 | 19.932 |
| 70 °C | 31.201 | 31.087 | 31.216 |
| 80 °C | 47.410 | 47.267 | 47.523 |
| 90 °C | 70.152 | 70.030 | 70.516 |
| 100 °C | 101.308 | 101.337 | 102.212 |
Calculated with the formulas on this page (over liquid water).
Antoine coefficients for water
| Range | A | B | C |
|---|---|---|---|
| 1–100 °C | 8.07131 | 1730.63 | 233.426 |
| 99–374 °C | 8.14019 | 1810.94 | 244.485 |
P in mmHg and T in °C. Multiply mmHg by 0.133322 to get kPa.
Tips
- Use kelvin for every temperature in thermodynamic formulas – the unit menus convert for you.
- Watch the units: ΔH is usually in kJ/mol and ΔS in J/(mol·K).
- Tabulated values are for standard conditions (1 bar, usually 25 °C).
- Everything is calculated in your browser.
Common mistakes to avoid
- Mixing kJ and J between ΔH and ΔS.
- Assuming ΔH and ΔS do not change with temperature over large ranges.
- Using Celsius in ln(T₂/T₁).
Inputs explained
| Field | What to enter |
|---|---|
| Temperature | Units: °C, K, °F |
| Formula for the main result | Choose one: Buck (1981) – recommended, Antoine equation, Magnus (Alduchov & Eskridge), Tetens … |
| Surface below 0 °C | Choose one: Liquid water (supercooled), Ice |
| Relative humidity (for humidity and dew point) | In % |
What each result means
- Saturation vapour pressure = [P]
- Buck = [pb]
- Antoine = [pa]
- Magnus = [pm]
- Tetens = [pt]
- Simple exponential fit = [ps]
- Actual vapour pressure at this relative humidity = [P]×[Relative humidity (for humidity and dew point)]÷100
- Absolute humidity (water vapour per m³ of air) = [P]×[Relative humidity (for humidity and dew point)]÷100×1000×18.015÷(8.314462618×([Temperature] + 273.15))
- Saturation vapour density = [P]×1000×18.015÷(8.314462618×([Temperature] + 273.15))
- Dew point (Magnus) = 243.04×ln([P]×[Relative humidity (for humidity and dew point)]÷100÷0.61094)÷(17.625 – ln([P]×[Relative humidity (for humidity and dew point)]÷100÷0.61094))
- Share of atmospheric pressure (101.325 kPa) = ([P]÷101.325)×100
Formula
Buck: P = 0.61121 · exp[(18.678 − T/234.5) · T/(257.14 + T)] kPa · Antoine: log₁₀ P = A − B/(C + T) (mmHg) · Magnus: P = 0.61094 · exp[17.625T/(T + 243.04)] kPa · Tetens: P = 0.61078 · exp[17.27T/(T + 237.3)] kPa · T in °CWorked example
Inputs — Temperature: 25 °C; Formula for the main result: Buck (1981) – recommended; Surface below 0 °C: Liquid water (supercooled); Relative humidity (for humidity and dew point): 50 %.
Results — Saturation vapour pressure = 3.1685 kPa; Buck = 3.1685 kPa; Antoine = 3.1579 kPa; Magnus = 3.1617 kPa; Tetens = 3.1677 kPa; Simple exponential fit = 3.1842 kPa; Actual vapour pressure at this relative humidity = 1.5843 kPa; Absolute humidity (water vapour per m³ of air) = 11.513 g/m³; Saturation vapour density = 23.026 g/m³; Dew point (Magnus) = 13.89 °C; Share of atmospheric pressure (101.325 kPa) = 3.127 %; Validity = Within the normal range of the chosen formula.
Key terms
- Saturation vapour pressure
- The equilibrium pressure of water vapour over a flat surface of pure water or ice at a given temperature.
- Relative humidity
- The actual vapour pressure as a percentage of the saturation vapour pressure.
- Dew point
- The temperature to which air must be cooled at constant pressure for its water vapour to start condensing.
- Absolute humidity
- The mass of water vapour per unit volume of air, usually in g/m³.
Frequently asked questions
What is the vapour pressure of water at 25 °C?
3.17 kPa (23.8 mmHg, 31.7 hPa). Buck gives 3.168 kPa and Antoine 3.158 kPa.
What is the vapour pressure of water at 100 °C?
101.325 kPa (1 atm) by definition of the normal boiling point; Buck gives 101.3 kPa.
What is the vapour pressure of water at body temperature (37 °C)?
About 6.28 kPa (47.1 mmHg) – the value used in respiratory physiology for alveolar air.
Which formula is most accurate?
Buck (1981) agrees with the reference IAPWS values to within about 0.05% between −40 and 50 °C. Antoine is excellent from 1 to 100 °C; Magnus and Tetens are within about 0.1–0.4% near room temperature.
Why is vapour pressure lower over ice than over supercooled water?
Molecules are more tightly held in ice, so fewer escape. At −10 °C: 0.260 kPa over ice versus 0.286 kPa over liquid water. This difference drives snow and hail growth in clouds.
How do I correct a gas collected over water?
Subtract the water vapour pressure at the water temperature from the total pressure. At 22 °C that is 2.64 kPa (19.8 mmHg).
How is the dew point found?
The actual vapour pressure e = RH × saturation pressure is fed back into the Magnus formula and solved for temperature. At 25 °C and 50% RH the dew point is about 13.9 °C.
Sources
- Buck, A. L. (1981). New equations for computing vapor pressure and enhancement factor. J. Appl. Meteor. 20, 1527–1532
- NIST Chemistry WebBook – Water (phase-change data)
- Alduchov, O. A. & Eskridge, R. E. (1996). Improved Magnus form approximation of saturation vapor pressure. J. Appl. Meteor. 35, 601–609