Frost Point Calculator
Find the frost point from temperature and humidity.
Result
How it is calculated
The calculation has three steps, with temperature in °C and relative humidity in %. (1) Saturation vapour pressure over liquid water, in hPa: es = 6.1094 × exp(17.625 × T ÷ (243.04 + T)). (2) Actual vapour pressure: e = es × RH ÷ 100. (3) The ice saturation curve e = 6.1115 × exp(22.452 × Tf ÷ (272.55 + Tf)) is solved for the frost point Tf: with a = ln(e ÷ 6.1115) it gives Tf = 272.55 × a ÷ (22.452 − a). The tool shows Tf in °C and e in hPa. Humidity must be above 0 and at most 100, otherwise there is no result. The ice formula is meant for air near or below freezing. For temperatures above 0 °C the tool still gives a number, but it is only a mathematical extension and no frost forms there.
Worked example
The air is at −2 °C with 85% relative humidity. Step 1: es = 6.1094 × exp(17.625 × (−2) ÷ 241.04) ≈ 5.28 hPa. Step 2: e = 5.28 × 0.85 ≈ 4.49 hPa. Step 3: a = ln(4.49 ÷ 6.1115) ≈ −0.309, so Tf = 272.55 × (−0.309) ÷ (22.452 + 0.309) ≈ -3.70 °C. If a surface cools below −3.70 °C, frost starts to form on it.
Common mistakes
- Entering humidity as a fraction (0.85) rather than a percentage (85). The result would imply almost completely dry air.
- Confusing frost point with dew point. Below 0 °C the two differ: the frost point is a little higher than the dew point because saturation over ice is reached at a higher temperature than over supercooled water.
- Using the humidity of a warm room to judge frost outside. Use the temperature and humidity of the air that touches the cold surface.
- Reading the frost point as the air temperature at which frost forms in the air. Frost forms on surfaces that are at or below this temperature.
- Using the tool for temperatures well above freezing, where a value above 0 °C has no physical meaning as a frost point; use a dew point calculator there.
About this calculator
Frost point is the ice-surface counterpart of dew point: it's the temperature to which air must be cooled, at constant pressure and moisture content, for water vapor to become saturated with respect to ice and begin depositing as frost rather than condensing as liquid dew. Because the saturation vapor pressure over ice is slightly lower than over supercooled liquid water at the same sub-zero temperature, the frost point is always a bit higher than the dew point would be if water stayed liquid at that temperature.
Meteorologists use frost point below freezing instead of dew point for accuracy, while refrigeration and cold-storage engineers, aviation professionals (assessing airframe or runway icing risk), and natural-gas pipeline operators (controlling water-dew-point specifications to prevent hydrate formation) rely on it as a practical threshold for when frost or ice will start forming on a surface.
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