How This Calculator Finds Wet-Bulb Temperature

Wet-bulb temperature is the one property on this site that can't be solved with a simple formula plugged straight in — it has to be searched for. Here's exactly how the calculator does it, and how the number relates to an actual field measurement.

The psychrometer equation

Wet-bulb temperature T_wb is defined implicitly by the psychrometer equation:

e_s(T_wb) − 0.000662 × P × (T_db − T_wb) = e

where e is the actual (known) vapor pressure, P is barometric pressure in kPa, and e_s(T_wb) is the Tetens saturation formula evaluated at the unknown T_wb. T_wb appears on both sides of this equation — once inside the exponential saturation function and once in the linear correction term — so there's no way to algebraically isolate it. The calculator solves it numerically by bisection: it picks a bracketing range of candidate wet-bulb temperatures, repeatedly narrows the range in half by checking which side the equation's residual is closer to zero on, and converges on the answer in a handful of iterations.

Worked example

At T_db = 25°C, 50% RH, sea-level pressure: known vapor pressure e = 0.5 × e_s(25) = 0.5 × 3.17 = 1.58 kPa. Solving the psychrometer equation for this case gives T_wb ≈ 18.0°C — the same value you'd read off a standard ASHRAE psychrometric chart at that dry-bulb/RH intersection, which is a good sanity check that the bisection solver and a printed chart agree.

How a real wet-bulb measurement is taken

In the field, wet-bulb temperature isn't calculated — it's measured directly with a sling psychrometer: two identical thermometers mounted side by side, one left dry (the dry-bulb reading) and one with a wetted cotton wick slipped over its bulb. Spinning the assembly (or using a battery-powered aspirated version) for 60–90 seconds drives air across the wet wick, evaporating water and cooling that thermometer below the dry-bulb reading. The cooling stops once the air right at the wick's surface is fully saturated — that equilibrium reading is the wet-bulb temperature, and the physics of that evaporative equilibrium is exactly what the psychrometer equation above models mathematically.

Technique matters: insufficient airflow across the wick, a dirty or mineral-caked wick, or using water that isn't close to the air's own temperature can all introduce a degree or more of error. A well-maintained aspirated psychrometer is accurate to roughly ±0.2–0.3°C; a casually used sling version is more commonly ±0.5°C or so in practiced hands.

Why wet-bulb sits between dew point and dry-bulb

For any air that isn't already saturated, wet-bulb temperature always falls strictly between dew point and dry-bulb temperature: T_dp ≤ T_wb ≤ T_db. At 100% RH all three are equal. See the dew point vs. wet-bulb page for a worked comparison table across several humidity levels at the same dry-bulb temperature.

FAQ

Why can't wet-bulb be solved directly like dew point?

Dew point only requires inverting the saturation formula once. Wet-bulb requires solving an equation where the unknown appears inside the saturation function and in a separate linear term at the same time — there's no algebraic shortcut, so it has to be searched for numerically.

Does the calculator's bisection method introduce meaningful error?

No — bisection is run to a tight enough tolerance that the remaining error is a small fraction of a degree, far smaller than the accuracy of a typical field thermometer or sling psychrometer reading.

Can I use this instead of carrying a sling psychrometer?

Only if you already know two of the other properties (RH, dew point) by some other means — this calculator computes wet-bulb from already-known air properties, it doesn't replace the physical measurement a psychrometer provides when RH itself is unknown.

→ Run a calculation (free)