Saturation Vapor Pressure Calculator
Saturation vapor pressure (es) is the maximum water vapor pressure the atmosphere can sustain at a given temperature. It is the fundamental thermodynamic quantity underpinning all moisture-related calculations in meteorology: relative humidity, dewpoint, lifted condensation level, and equivalent potential temperature all depend on es. The Magnus formula provides an accurate and computationally simple approximation to the more exact Clausius-Clapeyron equation. Enter a temperature to see the saturation vapor pressure over liquid water and over ice, along with the actual vapor pressure for a given relative humidity.
Magnus formula
es(T) = 6.112 * exp(17.67 * T / (T + 243.5)) [hPa, over liquid]
es_ice(T) = 6.1078 * exp(21.875 * T / (T + 265.5)) [hPa, over ice]
e(T, RH) = (RH / 100) * es(T)
T is temperature in Celsius. The formula for liquid water (August-Roche-Magnus) is accurate to within 0.1% for -40 to 60 C. The ice formula applies below 0 C. At 0 C, both formulas give the same value (approximately 6.11 hPa). Actual vapor pressure e equals saturation vapor pressure multiplied by relative humidity as a fraction.
Reference saturation vapor pressure values
- -20 C: approximately 1.03 hPa.
- 0 C: approximately 6.11 hPa.
- 10 C: approximately 12.27 hPa.
- 20 C: approximately 23.37 hPa.
- 30 C: approximately 42.43 hPa.
- 40 C: approximately 73.77 hPa.
Note the exponential increase: at 40 C, es is about 7 times larger than at 10 C, consistent with the Clausius-Clapeyron doubling per approximately 10 C.
Saturation vapor pressure: frequently asked questions
What is saturation vapor pressure?
Saturation vapor pressure (es) is the partial pressure of water vapor in air that is in equilibrium with a flat water surface at a given temperature. It represents the maximum amount of water vapor the air can hold at that temperature. When actual vapor pressure equals saturation vapor pressure, the air is saturated (100% relative humidity) and condensation or deposition begins.
What is the Magnus formula?
The Magnus formula is an empirical approximation for saturation vapor pressure: es(T) = 6.1078 * exp(17.27 * T / (T + 237.3)) in hPa (where T is in Celsius). A commonly used variant by August-Roche-Magnus uses different coefficients depending on the temperature range. The WMO standard coefficients are 17.368 and 238.83 for temperatures above 0 C, and different values below 0 C.
Why does saturation vapor pressure increase so rapidly with temperature?
Saturation vapor pressure increases exponentially with temperature following the Clausius-Clapeyron equation. For every 10 C rise in temperature, es approximately doubles. This is why warm air can hold much more moisture than cold air, and why tropical storms have far more available water vapor than midlatitude systems at the same relative humidity.
How is saturation vapor pressure used in meteorology?
Saturation vapor pressure is used to calculate relative humidity (RH = actual/saturation), dewpoint (the temperature where es equals actual vapor pressure), mixing ratio, specific humidity, and equivalent potential temperature. It appears in virtually every thermodynamic parameter used in operational meteorology.
What is the difference between saturation vapor pressure over water vs ice?
Below 0 C, saturation vapor pressure over liquid water is higher than over ice, because liquid water requires less energy to evaporate individual molecules than ice requires for sublimation. This difference is the basis for the Bergeron-Findeisen process in which supercooled water droplets evaporate while ice crystals grow, producing precipitation-sized ice particles.
Official sources
- WMO Technical Regulations: WMO CIMO Guide: Psychrometry.
- NOAA/NWS: Dewpoint vs Relative Humidity.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.