What this calculator does
Dry-bulb temperature is just the everyday air temperature: what an ordinary thermometer reads when its bulb is dry, with no wind or evaporation cooling it. Most of the time nobody needs to calculate it, it is simply measured. But if you have a wet-bulb reading (from a sling psychrometer, a weather station, or a psychrometric chart problem) and a relative humidity figure, you can work backwards to the dry-bulb temperature that produced them.
This calculator solves that reverse problem. It takes the same Stull (2011) empirical relationship used to estimate wet-bulb temperature from dry-bulb and humidity, and searches numerically for the dry-bulb temperature that would produce the wet-bulb reading you entered, at the humidity you entered.
The formula
The Stull approximation relates wet-bulb temperature Tw to dry-bulb temperature T and relative humidity RH through an equation that cannot be rearranged neatly to solve for T directly. Instead this calculator tries dry-bulb temperatures across a wide range and narrows in (bisection search) on the one that produces your wet-bulb reading at your humidity, to within a tenth of a degree.
| Term | Meaning |
|---|---|
| Dry-bulb temperature (T) | The ordinary air temperature, unaffected by moisture or evaporation. |
| Wet-bulb temperature (Tw) | The lowest temperature reached by evaporating water into the air at constant pressure, read from a thermometer with a wet wick over its bulb. |
| Relative humidity (RH) | How much water vapour the air holds compared with the maximum it could hold at that temperature, as a percentage. |
| Wet-bulb depression | The gap between dry-bulb and wet-bulb temperature. It widens as the air gets drier, and closes to zero at 100% relative humidity. |
The inputs explained
| Field | What to enter |
|---|---|
| Wet-bulb temperature (°C) | The wet-bulb temperature you measured or were given. |
| Relative humidity (%) | The relative humidity at the time of the wet-bulb reading, as a percentage. |
When to use it
Checking a psychrometric chart problem
Textbook and trade exam questions sometimes give a wet-bulb reading and humidity and ask for the dry-bulb temperature. This calculator checks that answer without reading values off a chart by eye.
Working from weather station data
Some automatic weather stations log wet-bulb temperature and relative humidity directly. Converting back to dry-bulb temperature puts the reading in the more familiar everyday unit.
HVAC and cooling tower calculations
Evaporative cooling and cooling tower performance are often specified against wet-bulb temperature. Recovering the corresponding dry-bulb reading helps translate a spec back into a temperature people can picture.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How dry-bulb temperature changes with humidity, for a fixed wet-bulb reading
The same wet-bulb reading of 20°C, solved across a range of relative humidity values.
| Relative humidity | Dry-bulb temperature | Wet-bulb depression (dry-bulb minus wet-bulb) |
|---|---|---|
| 20% | 36.0 °C | 16.0 °C |
| 40% | 29.4 °C | 9.4 °C |
| 60% | 25.6 °C | 5.6 °C |
| 80% | 22.6 °C | 2.6 °C |
| 100% | 20.0 °C | 0.0 °C |
How dry-bulb temperature changes with the wet-bulb reading, at fixed humidity
A range of wet-bulb readings, all at 50% relative humidity.
| Wet-bulb temperature | Dry-bulb temperature | Wet-bulb depression (dry-bulb minus wet-bulb) |
|---|---|---|
| 10°C | 15.7 °C | 5.7 °C |
| 15°C | 21.5 °C | 6.5 °C |
| 20°C | 27.3 °C | 7.3 °C |
| 25°C | 33.1 °C | 8.1 °C |
| 30°C | 39.0 °C | 9.0 °C |
Questions
Why not just measure dry-bulb temperature directly?
In practice you almost always would, since it is just an ordinary thermometer reading. This calculator is for the specific case where you only have a wet-bulb reading and a humidity figure and need to recover the dry-bulb value, such as checking a chart problem or working from logged station data.
Can wet-bulb temperature ever be higher than dry-bulb?
No. Wet-bulb temperature is always equal to or below dry-bulb temperature, reaching equality only at 100% relative humidity when no evaporative cooling can occur. If you enter values that are not physically consistent, the calculator reports that no valid solution was found.
How accurate is this method?
It relies on the Stull (2011) empirical approximation, the same one commonly used to estimate wet-bulb temperature from dry-bulb and humidity. It is accurate to within about 0.3°C over roughly -20 to 50°C and 5 to 99% relative humidity, which covers ordinary weather conditions.
What happens at very low humidity?
At low relative humidity the wet-bulb depression becomes large, meaning a modest wet-bulb reading can correspond to a much hotter dry-bulb temperature. Extremely dry, hot conditions sit near the edge of where the underlying approximation was validated.
To go the other direction and estimate wet-bulb temperature from a dry-bulb reading and humidity, see the wet-bulb temperature calculator.