Enter any two of the three variables (actual air temperature, relative humidity, and dew/frost point temperature) into the calculator to determine the missing one. For results above 0°C, the calculated value corresponds to the dew point; for results below 0°C, it corresponds to the frost point.
Frost Point Formula
The frost point is computed by first finding the actual water vapor pressure from air temperature and relative humidity, then solving for the temperature where the air would be saturated with respect to ice. (If the point temperature is above 0°C, the relevant quantity is the dew point instead.) Variables:
\begin{aligned}
e_{s,w}(T)&=6.112\,\exp\left(\frac{17.62\,T}{243.12+T}\right)\\
e&=\frac{RH}{100}\,e_{s,w}(T)\\
FP&=\frac{272.62\,\ln(e/6.112)}{22.46-\ln(e/6.112)}
\end{aligned}- FP is the frost point temperature in degrees Celsius (typically used when FP ≤ 0°C)
- T is the actual air temperature in degrees Celsius
- RH is the relative humidity in percent (as commonly reported, relative to saturation over liquid water)
- e is the actual vapor pressure (in hPa)
In words: compute the saturation vapor pressure over liquid water at the air temperature, multiply by RH/100 to get the actual vapor pressure, then compute the frost point by finding the temperature where saturation over ice equals that vapor pressure.
What is a Frost Point?
The frost point is the temperature at which air becomes saturated with respect to ice, so water vapor can deposit directly as ice (frost) on a surface at or below 0°C. It is closely related to the dew point (saturation with respect to liquid water). When temperatures are below freezing, the frost point is typically slightly higher (less negative) than the dew point for the same moisture content because saturation vapor pressure over ice is lower than over liquid water.
How to Calculate Frost Point?
The following steps outline how to calculate the Frost Point using the formulas above:
- Determine the actual air temperature (T) in degrees Celsius.
- Determine the relative humidity (RH) in percent.
- Compute the saturation vapor pressure over liquid water at T, then compute the actual vapor pressure e = (RH/100) × es,w(T).
- Compute the frost point (FP) by solving for the temperature where saturation vapor pressure over ice equals e.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge (chosen so the point is below freezing):
T – Actual air temperature in degrees Celsius = -5
RH – Relative humidity in percent = 80
Using the formulas above, the frost point is approximately -7.00°C (for the same conditions, the dew point would be approximately -7.91°C).
