A Frost Point Calculator is a meteorological tool that determines the exact temperature at which water vapor in the air will turn directly into ice crystals, a process called deposition. This is different from the dew point, which is the temperature at which vapor condenses into liquid water. At temperatures below freezing, the frost point is always slightly higher than the dew point because ice is a more stable state than supercooled liquid water. This calculator uses the measured dew point and applies a specific thermodynamic formula to find the corresponding frost point. This value is critically important in aviation to predict carburetor icing and in meteorology for forecasting frost formation, which can impact agriculture and transportation.
formula of Frost Point Calculator
The calculation of the frost point is a two-step process that first requires finding the actual vapor pressure of the air.
1. Calculating the Actual Vapor Pressure (e)
First, you must determine the actual vapor pressure in the air. The best way to do this is by using the Dew Point Temperature, as the dew point is the temperature where the actual vapor pressure equals the saturation vapor pressure over liquid water.
Formula (using Dew Point):
e = 6.112 * exp( (17.67 * Td) / (Td + 243.5) )
- e: The actual vapor pressure of the air (in millibars, mb, or hectopascals, hPa).
- exp: The exponential function, eˣ.
- Td: The Dew Point temperature, in degrees Celsius (°C).
- 6.112, 17.67, 243.5: These are established constants for the Magnus-Tetens formula for saturation vapor pressure over water.
2. Calculating the Frost Point (Tf)
Once you have the actual vapor pressure (e), you can use the inverse of the saturation vapor pressure formula over ice to solve for the frost point temperature.
Formula (solving for Frost Point):
Tf = (272.62 * ln(e / 6.112)) / (22.46 – ln(e / 6.112))
- Tf: The Frost Point temperature, in degrees Celsius (°C).
- ln: The natural logarithm function.
- e: The actual vapor pressure calculated in the first step.
- 272.62, 6.112, 22.46: These are established constants for the Magnus-Tetens formula for saturation vapor pressure over ice.
Dew Point vs. Frost Point
This table illustrates the relationship between the dew point and the frost point at various sub-freezing temperatures. Notice that the frost point is always slightly higher than the dew point, and the difference between them increases as the temperature gets colder.
| Dew Point (°C) | Calculated Vapor Pressure (mb) | Calculated Frost Point (°C) |
| 0°C | 6.11 mb | 0.0°C |
| -5°C | 4.22 mb | -4.4°C |
| -10°C | 2.86 mb | -8.8°C |
| -15°C | 1.91 mb | -13.2°C |
| -20°C | 1.25 mb | -17.7°C |
| -30°C | 0.51 mb | -26.7°C |
Example of Frost Point Calculator
A meteorologist on a cold winter night measures the following atmospheric conditions.
- Dew Point Temperature (Td): -12°C
The meteorologist wants to calculate the frost point to determine the temperature at which frost will begin to form.
Step 1: Calculate the actual vapor pressure (e) using the dew point.
e = 6.112 * exp( (17.67 * Td) / (Td + 243.5) )
e = 6.112 * exp( -212.04 / 231.5 ) ≈ 2.44 millibars
Step 2: Calculate the frost point (Tf) using the vapor pressure.
Tf = (272.62 * ln(2.44 / 6.112)) / (22.46 – ln(2.44 / 6.112))
Tf = -250.3 / (23.378) ≈ -10.7°C
Therefore, even though the dew point is -12°C, frost will begin to form on surfaces once their temperature drops to -10.7°C.
Most Common FAQs
The dew point is the temperature to which air must be cooled for its water vapor to condense into liquid water droplets (dew). The frost point is the temperature to which air must be cooled for its water vapor to deposit directly into ice crystals (frost). At temperatures below 0°C (32°F), the frost point is always higher than the dew point.
This is due to the different energy states of liquid water and ice. It takes less energy for water vapor molecules to arrange themselves into a solid crystalline structure (ice) than it does for them to form a liquid droplet that is supercooled (below freezing but still liquid). Because ice is a more stable, lower-energy state, water vapor will deposit as frost at a slightly warmer temperature than it will condense as supercooled dew.
The frost point is a critical parameter for pilots, especially those flying piston-engine aircraft. If the air temperature drops to the frost point inside the carburetor, ice can form rapidly, blocking the flow of the air-fuel mixture to the engine and potentially causing engine failure. Pilots use charts and calculators to be aware of conditions that are favorable for carburetor icing.