What is the wet bulb temperature?
Type the air temperature and the relative humidity. The wet bulb calculator estimates the wet-bulb temperature at sea-level pressure with Stull’s formula, valid from −20 °C to 50 °C and 5% to 99% humidity.
- Wet-bulb temperature
- 56.7 °F
At 68 °F and 50% relative humidity, the wet-bulb temperature is 56.7 °F.
Wet-bulb temperature: 56.7 °F. At 68 °F and 50% relative humidity, the wet-bulb temperature is 56.7 °F.
How to calculate
Estimates the wet-bulb temperature from the air temperature and relative humidity at sea-level pressure, with the Stull (2011) formula.
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.
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).
- 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
Each example is checked against the calculator on every build.
- Air temperature 68 °F, Relative humidity 50% gives Wet-bulb temperature 56.7 °F.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
- Air temperature 95 °F, Relative humidity 75% gives Wet-bulb temperature 88 °F.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
- Air temperature 86 °F, Relative humidity 20% gives Wet-bulb temperature 60.6 °F.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
- Air temperature 113 °F, Relative humidity 99% gives Wet-bulb temperature 113 °F.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
How it works
With the air temperature T in °C and the relative humidity RH in percent (5 means 5%), Stull’s equation 1 gives the wet-bulb temperature Tw in °C:
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
Each atan is in radians. A temperature typed in °F is first changed to °C, exactly from the typed decimal: T = (°F − 32) × 5/9. The result is shown in °F (US) or °C (Metric): °F = °C × 9/5 + 32.
Rules
- Air temperature from −20 °C to 50 °C (−4 °F to 122 °F), both ends included and checked exactly from the decimal you typed; relative humidity from 5% to 99%. These are the limits Stull gives.
- Air pressure is standard sea-level pressure, 101.325 kPa.
- The wet-bulb temperature cannot be above the air temperature. When the formula gives Tw greater than T:
- with T below 0 °C, the page gives no answer, with a message. This is the cold, dry corner Stull leaves out (for example −20 °C at 10%); it reaches up to about −14 °C.
- with T at 0 °C or above, the page shows Tw = T. This happens only at 98.9% humidity or more with T of 43 °C or more, where the formula overshoots by at most 0.04 °C, within its stated error.
Output format. The wet-bulb temperature shows with 1 decimal, in °F or °C, rounded half up from the computed value.
Worked examples by hand
20 °C at 50%. T × atan(0.151977 × √58.313659) = 20 × 0.859571 = 17.191413; atan(70) = 1.556512; atan(48.323669) = 1.550105; 0.00391838 × 50^1.5 × atan(1.15505) = 1.187558. Tw = 17.191413 + 1.556512 − 1.550105 + 1.187558 − 4.686035 = 13.70 °C (56.66 °F), as in Stull’s paper.
35 °C at 75%. The same steps give 31.10 °C (87.98 °F).
30 °C at 20%. The same steps give 15.90 °C (60.62 °F).
45 °C at 99%. The same steps give 45.0100 °C, above the air temperature, so the page shows 45 °C (113 °F).
Other questions people ask
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.