What this calculator does
This tool converts a known air temperature and dew point into relative humidity (RH). Relative humidity expresses how much water vapor is in the air compared with the maximum the air could hold at that temperature. When the dew point equals the air temperature, the air is saturated and RH is 100%; the larger the gap between them, the drier the air feels.
How to use it
Enter the current air temperature in degrees Celsius and the dew point in degrees Celsius. The calculator returns the relative humidity as a percentage. Because dew point can never exceed air temperature in real conditions, RH is capped at 100%.
The formula explained
The calculator uses the widely accepted Magnus approximation for saturation vapor pressure. The ratio of the saturation vapor pressure at the dew point to that at the air temperature gives the relative humidity:
$$\text{RH} = 100 \times \frac{\exp\!\left(\dfrac{17.625 \cdot \text{Dew Point}}{243.04 + \text{Dew Point}}\right)}{\exp\!\left(\dfrac{17.625 \cdot \text{Air Temp}}{243.04 + \text{Air Temp}}\right)}$$ where \(T\) is air temperature and \(T_d\) is dew point, both in °C. The constants 17.625 and 243.04 are the Alduchov–Eskridge coefficients, which improve accuracy over the classic 17.27/237.7 set.
Worked example
For an air temperature of 25 °C and a dew point of 15 °C: the numerator is \(\exp(17.625 \cdot 15 / 258.04) = \exp(1.02447) \approx 2.7857\), and the denominator is \(\exp(17.625 \cdot 25 / 268.04) = \exp(1.64384) \approx 5.1759\).
$$\text{RH} = 100 \times \frac{2.7857}{5.1759} \approx 53.83\%$$
FAQ
Why is RH never above 100%? Once the air is saturated, extra moisture condenses out as dew or fog, so relative humidity is physically limited to 100%.
Does this work in Fahrenheit? No — convert temperatures to Celsius first, since the Magnus coefficients here are defined for °C.
How accurate is it? The Alduchov–Eskridge form is accurate to within about 0.4% over the −40 °C to 50 °C range typical of weather conditions.
