Relative humidity from wet-bulb and dry-bulb temperature

How the calculation works

1. 01The psychrometer equation: e = e_s(T_w) − A·P·(T_d − T_w), with e the actual vapour pressure, T_w and T_d the wet- and dry-bulb temperatures, P the station pressure and A the psychrometer coefficient.
2. 02Relative humidity is 100·e / e_s(T_d), and the dew point is the temperature at which e_s equals e. Saturation vapour pressure is the Magnus form already used by the dew point calculator.
3. 03A depends on the instrument and on how well the wet bulb is ventilated. The typical values offered (6.62 × 10⁻⁴ K⁻¹ aspirated, 8.0 × 10⁻⁴ K⁻¹ naturally ventilated) can be replaced by your own psychrometer's coefficient.

Limitations

• Valid for liquid water from about −40 to +50 °C. A wet bulb below freezing may be an ice bulb with a different coefficient, which this does not model.
• The humidity is only as good as the two thermometers and the wick. Depression error is amplified: near 50 % RH an error of 0.1 K in the depression is about 1 %RH.
• The coefficient values are typical, not a property of your instrument. For a certified psychrometer, use the coefficient it states.

Frequently asked questions

How do I get relative humidity from wet-bulb and dry-bulb temperature?

Find the actual vapour pressure from the psychrometer equation, then divide by the saturation vapour pressure at the dry-bulb temperature. At 22 °C dry and 16 °C wet, sea-level pressure, aspirated, it comes out near 53 %RH.

What happens if the wet and dry bulb read the same?

The air is saturated: 100 %RH, with a dew point equal to the air temperature. A wet bulb that reads warmer than the dry bulb is a fault, usually a swapped sensor.

Why does pressure matter for a psychrometer?

Because the evaporative cooling that depresses the wet bulb depends on the air density, so the same depression means a different humidity at altitude. The equation includes the station pressure for that reason.

How accurate is a wet-bulb humidity reading?

Typically a few %RH with good practice: calibrated thermometers, clean distilled-water wick and enough airflow. It is a classic way to check an electronic humidity sensor precisely because it depends on temperature measurement rather than on a humidity element that drifts.