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Wet-Bulb Temperature Calculator

Find the wet-bulb temperature to gauge heat stress and cooling potential.

How it is calculated

Enter the air temperature in degrees Celsius and relative humidity as a percentage (0 to 100). The tool applies Stull's 2011 empirical approximation, with T the air temperature and RH the humidity:

Tw = T·atan(0.151977·√(RH + 8.313659)) + atan(T + RH) − atan(RH − 1.676331) + 0.00391838·RH1.5·atan(0.023101·RH) − 4.686035

The angles are in radians. The Fahrenheit value is Tw × 9/5 + 32. Both are rounded to two decimals. Humidity outside 0 to 100 gives no result. This is a fitted approximation, not a full psychrometric calculation, and it ignores air pressure; at 100% humidity it can come out a fraction of a degree above the air temperature.

Worked example

Air at 30 °C and 70% humidity. The four terms are: 30 × atan(0.151977 × √78.31) = 27.943; atan(100) = 1.561; atan(68.32) = 1.556, which is subtracted; and 0.00391838 × 701.5 × atan(1.617) = 2.334. Adding and subtracting, then taking off 4.686, gives a wet-bulb temperature of 25.60 °C, or 25.60 × 9/5 + 32 = 78.07 °F.

Try this example →

Common mistakes

  • Entering the temperature in Fahrenheit; the formula needs Celsius, and the Fahrenheit figure is only an output.
  • Typing humidity as a fraction such as 0.7 instead of 70, which gives a wildly different (and much lower) result.
  • Confusing wet-bulb with the heat index or feels-like temperature; they are different measures built from different formulas.
  • Using the dew point where relative humidity is asked for.
  • Reading the result as exact: the formula is an approximation and ignores pressure, so a measured wet-bulb reading with a psychrometer may differ slightly.

About this calculator

This calculator estimates wet-bulb temperature (Tw) from air temperature and relative humidity using Stull's formula, an arctangent-based empirical approximation from 2011 that's accurate to within about 0.3°C for typical conditions without needing a psychrometric chart. Wet-bulb temperature reflects the lowest temperature achievable through evaporative cooling.

Meteorologists, occupational health officers, and outdoor-event organizers use it to gauge heat stress risk — wet-bulb readings above roughly 32°C (90°F) signal dangerous conditions where sweat can no longer cool the body effectively.

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Comments (1)

  • Editorial team

    Humidity can matter more than the thermometer. Here, a dry 40 °C at 20% humidity gives a wet-bulb of 22.70 °C, while a milder 30 °C at 70% gives 25.60 °C, so the cooler, muggier day leaves less room for sweat to cool you. The fitted formula is built for roughly 5% to 99% humidity, so treat extreme inputs with caution. Which climate are you checking this for?

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