Wet-Bulb Calculator

What the wet-bulb temperature measures

Wrap a wet cloth around the bulb of a thermometer and blow air across it. The water evaporates, evaporation pulls heat out of the bulb, and the reading drops below the air temperature. Where it settles is the wet-bulb temperature.

How far it drops depends on how dry the air is. In desert air, water evaporates fast and the wet bulb reads far below the air temperature. In muggy air, the air is already carrying so much vapor that evaporation slows to a crawl, and the wet bulb sits close to the air temperature. The gap between the two readings is called the wet-bulb depression, and it is a direct measure of how much cooling evaporation can still deliver.

At 100 percent relative humidity the two thermometers read the same, because no net evaporation is possible. That is the ceiling of the scale. The floor is set by how dry the air gets.

The classic instrument is a sling psychrometer: two thermometers mounted on a handle, one with a wet wick, swung through the air for a minute or two. Weather stations, HVAC technicians and industrial hygienists still use them, and the calculator on this page reproduces the number they read.

The Stull (2011) formula behind the numbers

There is no tidy algebra that turns an air temperature and a humidity into a wet-bulb temperature, so meteorologist Roland Stull fitted an empirical formula to a full set of psychrometric calculations. His paper, Wet-Bulb Temperature from Relative Humidity and Air Temperature, Journal of Applied Meteorology and Climatology, 2011, is the source this calculator uses.

The formula, with T in °C, RH as a percent, and the arctangents in radians:

Tw = T x atan(0.151977 x sqrt(RH + 8.313659)) + atan(T + RH) - atan(RH - 1.676331) + 0.00391838 x RH^1.5 x atan(0.023101 x RH) - 4.686035

Stull found it with gene-expression programming, a search method that tries thousands of function shapes until one fits. Over its valid range the fit stays within -1.0 to +0.6 °C of the true psychrometric value, with a mean absolute error of 0.28 °C, and it explains 99.95 percent of the variance. Those are the paper's own numbers, and they are why so many weather models and heat stress tools use this one equation.

Two things the table should make obvious. The formula never asks for pressure, because it was fitted at standard sea level pressure. And the ranges are not suggestions: outside them the fit was never tested, and the error can grow fast.

Worked example: 68 °F at 50 percent humidity

The paper works one example by hand: air at 20 °C, which is 68 °F, with a relative humidity of 50 percent. Plugging in gives a wet-bulb temperature of 13.7 °C, or 56.7 °F. Here is the arithmetic term by term.

The wet-bulb depression is 20 - 13.7 = 6.3 °C, or 11.3 °F. In practical terms, a wet surface in that air can cool itself about 11 °F below the air temperature before it stops losing water. A shirt dried outdoors, a swamp cooler pad, and human skin all work off that same gap.

Run the same numbers in Fahrenheit and nothing changes: 68 °F at 50 percent gives 56.7 °F. The calculator accepts either unit and converts internally, because the formula itself is written in Celsius.

Reading the depression: what the gap between the two readings means

The table below shows wet-bulb temperatures for common summer air temperatures. The interesting number is not the wet bulb alone but the gap under it.

Take the 90 °F row. At 20 percent humidity the wet bulb is 63.3 °F, a depression of 26.7 °F, and evaporating water does a lot of work: sweat cools you, a misting fan feels cold, a swamp cooler drops the room. At 80 percent humidity the wet bulb is 84.7 °F, a depression of only 5.3 °F, and the same tools barely help.

That is why two 90 °F afternoons can feel like different planets. The air temperature is the same, the humidity is not, and the wet-bulb depression is the number that separates them. Drying laundry, curing concrete, painting, and wildfire danger all track this gap more closely than the thermometer does.

Why wet bulb matters for heat stress

Your body cools itself by sweating, and sweat only cools while it evaporates. The wet-bulb temperature measures exactly the condition that process needs, which makes it the number that matters when the air itself becomes dangerous.

The National Weather Service uses wet-bulb temperature inside the Wet Bulb Globe Temperature, or WBGT, its heat stress index for people working or training outdoors. WBGT weighs the wet-bulb reading at 0.7, the globe temperature, which captures sun and radiant heat, at 0.2, and the air temperature at 0.1. Military installations, school athletics programs and job sites set their work and rest rules from it.

The hard ceiling is startling. A 2010 study in PNAS by Sherwood and Huber argued that a sustained wet-bulb temperature of 35 °C, which is 95 °F, is about the limit of what a human body can survive even in the shade with water and rest, because skin can no longer shed metabolic heat. Today's hottest places stay below roughly 31 °C, and later lab tests on volunteers have found that real tolerance for light activity sets in below the 35 °C mark. You will not see those numbers on a summer forecast, but the calculator flags any result at or above 35 °C so the limit is visible.

You do not need extremes for wet bulb to matter. At a wet bulb in the mid 70s °F, hard outdoor work already calls for longer rest breaks and more water than the air temperature alone would suggest.

Wet bulb, dew point, and heat index: which number to use

All three numbers come from the same air, but they answer different questions.

A useful habit: use the heat index for how a lazy afternoon in the shade feels, use the dew point for whether the morning will fog the windows, and use the wet bulb for anything that depends on evaporation, from swamp coolers to cooling towers to how hard you can safely exercise. The calculator prints the wet-bulb temperature and the depression, and the related tools on this site cover the other two.

One connection is worth memorizing: the dew point can never exceed the wet-bulb temperature, and the wet-bulb temperature can never exceed the air temperature. If a reading ever breaks that order, one of the inputs is wrong.

Where the formula stops working

The Stull formula is a statistical fit, not physics, so it carries three sets of limits.

First, pressure. The fit assumes standard sea level pressure of 101.325 kPa. In Denver, at about 85 kPa, water evaporates a little more readily and the true wet-bulb temperature sits below the formula's answer. The paper notes the gap grows at higher elevations, so treat results in mountain country as an upper estimate. The same caution applies to aircraft cabins and pressurized rooms.

Second, the fitted range. Air temperatures below -20 °C or above 50 °C, and humidities below 5 percent or above 99 percent, sit outside the data the formula was fitted to. The corner where cold air meets dry air is the worst region, and the paper excludes it outright. The calculator warns you when an input leaves the range rather than pretending the answer is solid.

Third, the physics the fit ignores. Below freezing, saturation over ice differs from saturation over liquid water, and the fit was built on liquid water throughout. Blizzards and freezing rain calculations use proper psychrometric equations instead. And because the formula is a curve fit, it has no error bars you can reason from; the paper's own check is that the mean absolute error across the valid range is 0.28 °C, with the worst spots near the edges.

Using the wet-bulb number at home

The depression is the number to watch for evaporative cooling. A swamp cooler cannot cool air below its wet-bulb temperature, so in 100 °F air at 20 percent humidity, where the wet bulb is 70.1 °F, it can deliver air in the low 70s. In 100 °F air at 80 percent humidity it can do almost nothing, which is why the technology belongs in dry climates.

The same logic runs in the other direction for drying. Laundry, firewood, fresh paint and curing concrete all lose water faster as the depression widens. A dry 70 °F day with a wet bulb in the 40s dries a load on the line faster than a humid 85 °F day with a wet bulb near 80.

Snowmaking rides on it too. The paper behind this formula notes that snow guns can work in air slightly above freezing as long as the wet-bulb temperature is below about -2 °C, because the droplets cool by evaporation as they fall. Ski areas watch the wet bulb, not the thermometer, when they decide to run the guns.

Finally, be honest about the inputs. The formula is exact arithmetic on whatever humidity and temperature you feed it, and a wall hygrometer can be off by several percentage points, which moves the wet-bulb answer by a degree or two. For heat safety decisions, cross-check with a weather service reading or a real sling psychrometer before you change plans.