# What is the wet bulb temperature?

Estimates the wet-bulb temperature from the air temperature and relative humidity at sea-level pressure, with the Stull (2011) formula.

- Page: https://www.acalculator.org/physics/wet-bulb-calculator
- JSON spec: https://www.acalculator.org/physics/wet-bulb-calculator.json
- Version: 3c3a0634eef4

## Default answer

Example with the default inputs (Air temperature 67.9999999999999 °F, Relative humidity 50%): At 68 °F and 50% relative humidity, the wet-bulb temperature is 56.7 °F.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| t | Air temperature | The dry-bulb air temperature, from −20 °C to 50 °C (−4 °F to 122 °F). |
| rh | Relative humidity | The relative humidity, from 5% to 99%. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| wetBulb | Wet-bulb temperature | The temperature a wet thermometer reads as water evaporates from it, at sea-level pressure. |

## Method

Tw = T·atan[0.151977·(RH + 8.313659)^½] + atan(T + RH) − atan(RH − 1.676331) + 0.00391838·RH^(3/2)·atan(0.023101·RH) − 4.686035, with T and Tw in °C, RH in percent and atan in radians (Stull 2011).

## Assumptions

- Air pressure is standard sea-level pressure, 101.325 kPa. At high altitude the true wet-bulb temperature is a little lower.
- The formula is an empirical fit for relative humidity from 5% to 99% and air temperature from −20 °C to 50 °C; Stull gives its error as −1 °C to +0.65 °C, with a mean absolute error under 0.3 °C.
- Where the formula gives a wet-bulb temperature above the air temperature: below 0 °C (cold, dry air, which Stull leaves out) the page gives no answer; at 0 °C or above (only near 99% humidity above 43 °C, by at most 0.04 °C) it shows the air temperature.

## Worked examples

1. t = 293.15, rh = 50% gives wetBulb = 286.849342. Source: Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1 (example: 20 °C and 50% give 13.7 °C); NCAR Command Language, wetbulb_stull (13.69934 °C), https://www.ncl.ucar.edu/Document/Functions/Contributed/wetbulb_stull.shtml.
2. t = 308.15, rh = 75% gives wetBulb = 304.250777. Source: From Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1.
3. t = 303.15, rh = 20% gives wetBulb = 289.050483. Source: From Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1.
4. t = 318.15, rh = 99% gives wetBulb = 318.15. Source: Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. J. Appl. Meteor. Climatol., 50, 2267–2269, https://doi.org/10.1175/JAMC-D-11-0143.1.

## FAQ

### What is the wet-bulb temperature?

The temperature a thermometer wrapped in a wet cloth reads as air flows past it. Evaporation cools it, so it reads lower than the air unless the air is saturated. It shows how well sweat can cool the body.

### How is the wet-bulb temperature calculated here?

With Stull’s 2011 empirical formula, a fit of arctangent terms in air temperature (°C) and relative humidity (%). At 20 °C and 50% it gives 13.7 °C (56.7 °F).

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

Water evaporating from the wet cloth takes heat from it. The drier the air, the more water evaporates and the bigger the gap. At 100% humidity there is no gap.

### How accurate is the Stull formula?

Stull reports errors from −1 °C to +0.65 °C over its range, with a mean absolute error under 0.3 °C. It assumes sea-level pressure (101.325 kPa).

### Why does the page give no answer for some cold, dry air?

In very cold, dry air the fit breaks down, which Stull’s paper notes. Below 0 °C, where the formula would give a wet-bulb temperature above the air temperature, which cannot happen, the page gives no answer.

### Is wet-bulb temperature the same as WBGT?

No. The wet-bulb globe temperature (WBGT) used for heat safety also counts sunshine and wind. This page gives the plain (natural psychrometric) wet-bulb temperature only.

## Sources

- Stull, R., 2011: Wet-Bulb Temperature from Relative Humidity and Air Temperature. Journal of Applied Meteorology and Climatology, 50, 2267–2269 (equation 1; valid for RH 5% to 99% and T −20 °C to 50 °C, except cold and dry air). https://doi.org/10.1175/JAMC-D-11-0143.1 (retrieved 2026-10-02)
- NCAR Command Language, wetbulb_stull: the Stull (2011) method, its range, and the example 20 °C, 50% → 13.69934 °C. https://www.ncl.ucar.edu/Document/Functions/Contributed/wetbulb_stull.shtml (retrieved 2026-10-02)