Wet-Bulb Temperature Calculator (Stull)

Understanding the wet-bulb temperature calculator — concept and principle

The wet-bulb temperature is the lowest temperature that air can reach by evaporating water into it at constant pressure; it is what a thermometer wrapped in a wet wick reads when air flows past it. This calculator estimates it from air temperature and relative humidity using Stull's 2011 formula. It is used for heat stress and cooling equipment.

Evaporation cools the wet bulb: 30 °C air at 50% RH gives about 22.30 °C, 7.7 K lower.

How it is calculated

T_w = T·atan[0.151977·(RH + 8.313659)^½] + atan(T + RH) − atan(RH − 1.676331) + 0.00391838·RH^1.5·atan(0.023101·RH) − 4.686035

T: air temperature in °C.
RH: relative humidity in percent (for example 50, not 0.5).
The arctangents are evaluated in radians.

Stull fitted this expression to psychrometric data. It is valid for RH 5–99% and T from −20 to 50 °C at sea-level pressure, with errors mostly within about ±0.3 °C.

The principle

When water evaporates from a wet surface it absorbs latent heat, cooling the surface. The surface settles at a temperature where heat flowing in from the warmer air exactly balances the heat used for evaporation. Dry air allows more evaporation and therefore a larger depression below the air temperature; saturated air allows none, so at 100% RH the wet-bulb equals the air temperature. Exact solutions need iteration; Stull's fit avoids that.

Worked example

Inputs: T = 30 °C, RH = 50%.
First term: 30 × atan(0.151977 × √58.313659) ≈ 25.7871.
atan(80) ≈ 1.5583 and atan(48.3237) ≈ 1.5501.
0.00391838 × 50^1.5 × atan(1.15505) ≈ 1.1876.
T_w ≈ 25.7871 + 1.5583 − 1.5501 + 1.1876 − 4.6860 ≈ 22.30 °C.

Each point is the calculator re-run with only “Air temperature (°C)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Air temperature (°C)	Wet-bulb temperature (°C)
7.5	2.95160391
15	9.40039001
22.5	15.84876113
30	22.29683396
37.5	28.74468519
45	35.19236728
60	48.08736245

How to read the result

The wet-bulb temperature always lies between the dew point (about 18.4 °C here) and the air temperature. It indicates how well sweating can cool the body: as it rises, evaporative cooling becomes less effective. A sustained wet-bulb temperature of 35 °C has been proposed as a theoretical upper limit of human heat tolerance, and real-world danger begins well below that, especially with exertion. For cooling equipment, the wet-bulb sets the lowest outlet temperature an evaporative cooler or cooling tower can approach.

Common mistakes

Entering RH as a fraction (0.5) instead of a percentage.
Using the formula far from sea-level pressure or outside its validity range.
Confusing wet-bulb temperature with WBGT, a different heat-stress index that also includes radiation and wind.
Using a calculator in degree mode for the arctangents.

Keep in mind: This is an empirical approximation, not a health assessment. Heat-illness risk depends on activity, clothing, sun, acclimatisation and individual health; follow official heat warnings and occupational guidance.

Frequently asked questions

Why is the wet-bulb lower than the air temperature?

Evaporation removes latent heat from the wet surface; the drier the air, the more evaporation and the larger the difference.

Is wet-bulb the same as the heat index?

No. The heat index estimates how hot it feels; the wet-bulb is a physical temperature.

Sources: Stull, R. (2011), "Wet-Bulb Temperature from Relative Humidity and Air Temperature", Journal of Applied Meteorology and Climatology, 50, 2267–2269 · Sherwood and Huber (2010), "An adaptability limit to climate change due to heat stress", PNAS, 107(21), 9552–9555

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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