Wet-bulb temperature calculator
The wet-bulb temperature from the air temperature and relative humidity, with the formula Roland Stull published in 2011, and what research says about the wet-bulb temperatures the human body can cope with.
Wet-bulb temperature (example)
28.5 °C · 83.3 °F
In laboratory tests of young, healthy people doing light activity, the limit was 25 to 28 °C wet-bulb in hot, dry air and 30 to 31 °C in warm, humid air. Older people, children and people with health conditions can be at risk at lower values.
For 35.0 °C (95.0 °F) at 60 % relative humidity, at sea-level pressure. Stull gives the formula's error as −1 to +0.65 °C.
Why 35 °C wet-bulb is called the human limit
Sweat cools the body only by evaporating, and evaporation cannot cool anything below the wet-bulb temperature. Sherwood and Huber (2010) argued that a wet-bulb temperature above 35 °C for extended periods should cause hyperthermia (a dangerous rise in body temperature) in humans, because getting rid of the body's own heat becomes impossible. In the climate data they studied, the highest wet-bulb temperatures never went above 31 °C.
That 35 °C is a theoretical ceiling for a healthy body, not a safe level below it. When researchers at Penn State tested young, healthy volunteers doing light activity (the PSU HEAT project, published in the Journal of Applied Physiology in 2022), they found the point where heat stress could no longer be compensated (core temperature kept rising) at 30 to 31 °C wet-bulb in warm, humid air, and 25 to 28 °C in hot, dry air. Older people, babies, people with health conditions and anyone working hard can be harmed at lower values still.
How it is calculated
Stull (2011) found this fit for wet-bulb temperature Tw (°C) from air temperature T (°C) and relative humidity RH (%), at standard sea-level pressure (101.325 kPa). The arctangents are in radians.
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
Stull states it is valid for relative humidity from 5 % to 99 % and air temperature from −20 °C to 50 °C, except when it is both cold and dry, with errors from −1 °C to +0.65 °C (mean absolute error under 0.3 °C). It assumes sea-level pressure, so it reads slightly off at high altitude.
Worked example: 20 °C at 50 % humidity
Tw = 20 · atan(0.151977 · √58.313659) + atan(70) − atan(48.323669) + 0.00391838 · 50^1.5 · atan(1.15505) − 4.686035 = 13.70 °C
About 13.7 °C, the value NCAR's documentation of its implementation of Stull's formula gives for this example.
Reference table (°C)
| Air temperature | RH 20 % | RH 40 % | RH 60 % | RH 80 % | RH 95 % |
|---|---|---|---|---|---|
| 25 °C (77 °F) | 12.5 | 16.4 | 19.5 | 22.3 | 24.4 |
| 30 °C (86 °F) | 15.9 | 20.4 | 24.0 | 27.1 | 29.4 |
| 35 °C (95 °F) | 19.3 | 24.5 | 28.5 | 31.9 | 34.3 |
| 40 °C (104 °F) | 22.7 | 28.6 | 33.0 | 36.7 | 39.3 |
| 45 °C (113 °F) | 26.1 | 32.6 | 37.5 | 41.5 | 44.3 |
This calculator gives an estimate for learning and planning. It is not a forecast or a warning, and it cannot say whether conditions are safe. For decisions, follow your national weather service and local authorities.
Sources
- Stull, R. (2011), Wet-Bulb Temperature from Relative Humidity and Air Temperature, Journal of Applied Meteorology and Climatology 50(11), 2267-2269: the formula and its valid range (the journal page refused our reader; the coefficients were checked against the RESKit implementation)
- NCAR Command Language: wetbulb_stull: validity, errors and the 20 °C / 50 % example (13.7 °C)
- Sherwood, S. C. and Huber, M. (2010), An adaptability limit to climate change due to heat stress, PNAS 107(21), 9552-9555: why 35 °C wet-bulb is the theoretical limit
- Penn State (2022): Humans can't endure temperatures and humidities as high as previously thought: PSU HEAT results: 30-31 °C warm-humid, 25-28 °C hot-dry (Vecellio et al., Journal of Applied Physiology, 2022)
Questions
What is wet-bulb temperature?
It is the lowest temperature air can be cooled to by evaporating water into it. Because sweat cools us by evaporating, the wet-bulb temperature sets a limit on how well the body can cool itself.
Is a wet-bulb temperature of 35 °C the limit for humans?
It is the theoretical limit: Sherwood and Huber (2010) showed that above it, for long periods, the body can no longer get rid of the heat it makes, so its core temperature keeps rising. Laboratory tests on young, healthy volunteers found the real limit was lower, around 30 to 31 °C in warm, humid air and 25 to 28 °C in hot, dry air (Penn State, 2022).