Frost Point Calculator
Calculate frost point with our free science calculator. Uses standard scientific formulas with unit conversions and explanations.
Formula
Tf = 272.55 * ln(e/6.1115) / (22.452 - ln(e/6.1115))
Where Tf is frost point in Celsius and e is actual vapor pressure in hPa from dew point. This inverts the Buck 1981 ice saturation equation. The frost point is always higher than dew point at subfreezing temperatures because ice has lower saturation vapor pressure than supercooled water.
Worked Examples
Example 1: Winter Night Frost Assessment
Problem: Air temperature is -5 C with dew point -8 C at 1013.25 hPa. Find the frost point and frost risk.
Solution: Vapor pressure from dew point: e = 3.097 hPa Frost point: Tf = 272.55*ln(3.097/6.1115)/(22.452-ln(3.097/6.1115)) Tf = -7.99 C Frost point depression = 2.99 C
Result: Frost Point: -7.99 C | High Frost Risk
Example 2: Aircraft Icing Assessment
Problem: At flight level temperature is -12 C with dew point -14 C at 700 hPa.
Solution: Vapor pressure: e = 1.811 hPa Frost point: Tf = -13.72 C RH over ice = 96.5% Temperature below freezing and close to frost point
Result: Frost Point: -13.72 C | Moderate Icing Possible
Frequently Asked Questions
What is the frost point and how does it differ from dew point?
The frost point is the temperature at which air becomes saturated with respect to an ice surface rather than liquid water. Below freezing the saturation vapor pressure over ice is lower than over supercooled water meaning the frost point is always higher than the dew point when temperatures are below 0 Celsius. For example when the dew point is minus 10 Celsius the frost point is approximately minus 9 Celsius. This difference arises because water molecules escape more easily from a liquid surface than from an ice crystal lattice. The distinction is critical for predicting ice crystal formation.
Why is the frost point important for weather forecasting?
The frost point is essential for predicting frost formation on surfaces, ice crystal growth in clouds, and aircraft icing conditions. When the air temperature drops to the frost point water vapor deposits directly as frost without first becoming liquid. Agricultural forecasters use frost point predictions to issue frost warnings that protect crops during cold nights. Aviation meteorologists use frost point data to assess icing risks at various flight levels. The frost point helps explain the Bergeron process in mixed-phase clouds where ice crystals grow at the expense of supercooled droplets.
How is the frost point calculated from dew point measurements?
The frost point is calculated by first determining actual vapor pressure from the dew point using the Magnus formula for liquid water. Then the Buck 1981 ice saturation formula is inverted to find the temperature at which this vapor pressure equals saturation over ice. The formula involves computing e from dew point then solving for Tf = 272.55 times ln(e/6.1115) divided by (22.452 minus ln(e/6.1115)). This two-step approach accounts for the fundamental thermodynamic difference between saturation over water and ice surfaces.
How does frost point relate to the Bergeron ice crystal process?
The Bergeron process depends directly on the difference between saturation vapor pressures over ice and supercooled water. In a mixed-phase cloud where both ice crystals and supercooled droplets coexist the environment is typically saturated with respect to water. Because ice saturation pressure is lower the same environment is supersaturated with respect to ice causing ice crystals to grow by vapor deposition. Simultaneously water droplets evaporate because vapor pressure drops below water saturation. This process is the primary precipitation formation mechanism in mid-latitude clouds.
When is frost most likely to form on surfaces?
Frost formation is most likely during clear calm nights when radiative cooling of the ground surface is maximized. Clear skies allow infrared radiation to escape to space and calm winds prevent mixing of warmer air from aloft. Frost typically forms when the surface temperature drops to the frost point which can happen even when air temperature at station height is a few degrees above zero. Low-lying areas and valley floors are particularly frost-prone due to cold air drainage. Surfaces with low thermal inertia like car windshields and plant leaves cool fastest and develop frost first.
How does altitude affect the frost point?
As altitude increases atmospheric pressure decreases and the air generally becomes colder and drier causing both dew point and frost point to decrease. The frost point drops with altitude because absolute moisture content typically decreases rapidly above the boundary layer. In the free troposphere the frost point can be 30 to 50 degrees below air temperature indicating very dry conditions. At cruising altitudes of commercial aircraft the frost point is often minus 60 to minus 80 Celsius. Mountain locations experience frost more frequently than lowland stations because of lower temperatures and enhanced radiative cooling.