What the wet-bulb temperature is
The wet-bulb temperature is the temperature a wetted, well-ventilated sensor settles at in a given air stream. Water evaporating from the wick carries latent heat away; sensible heat flows in from the warmer air around it. The wick cools until those two rates balance, and that balance point is the wet bulb.
Three things follow directly from that definition, and each of them is useful. First, the wet bulb is always at or below the dry bulb, and always at or above the dew point — the three coincide only at saturation. Second, the depth of the gap is a direct measure of how dry the air is: at 75 °F, a 12.4 °F depression means 50% relative humidity, while a 21.8 °F depression means 20%. Third, and most usefully, the wet bulb is the floor that any evaporative process can reach. A direct evaporative cooler, a cooling tower, a misting fan and a sweating human being are all working down toward the wet bulb and none of them can get past it.
The wet bulb also carries almost all the information about total heat. Lines of constant wet bulb on a psychrometric chart run within a fraction of a Btu of the lines of constant enthalpy, which is why one wet-bulb reading tells an equipment manufacturer what a coil will do. Evaporator capacity tables are published against entering wet bulb for exactly this reason: two air streams at the same wet bulb but different dry bulbs present the coil with nearly the same total load, split differently between sensible and latent.
Why the wet bulb has to be solved rather than calculated
Getting the humidity ratio from a wet-bulb reading is one line of arithmetic. Going the other way is not, and the reason is visible in the formula: the term W*s is the saturation humidity ratio evaluated at the wet-bulb temperature itself. The unknown appears inside a saturation-pressure correlation as well as three times outside it, and that correlation is an exponential of a polynomial in absolute temperature. No rearrangement exists.
So the calculator does what a psychrometric chart does graphically: it searches. It computes the humidity ratio of your air from the relative humidity or the dew point, then hunts for the wet-bulb temperature whose energy balance reproduces that humidity ratio, narrowing the interval by bisection until the answer is settled to under a thousandth of a degree. Because the humidity ratio predicted by the balance rises monotonically with the trial wet bulb, the search is guaranteed to converge on the single correct root — there is no second solution to fall into.
The physical meaning of the numerator and denominator is worth reading. The numerator is the latent heat the saturated wick can carry off, (1093 − 0.556t*) Btu per pound of water evaporated at that temperature, times the water it can hold, less the sensible heat 0.240(tdb − t*) the air gives up in cooling to the wick temperature. The denominator normalises the result back to one pound of dry air. Set the depression to zero and the sensible term vanishes, leaving W = W*s, which is exactly what saturation means.
Barometric pressure matters more than people expect. The humidity ratio divides by (p − pv), so the same relative humidity at altitude means more water per pound of dry air. Run 75 °F and 50% RH at 24.896 in. Hg, the standard pressure at 5,000 ft, and the humidity ratio rises from 64.65 to 77.93 gr/lb while the wet bulb falls from 62.55 °F to 61.76 °F. Both moves are real: there is more water in the air, but the reduced pressure makes evaporation easier, and the second effect wins. This is why evaporative cooling works so well in Denver and Albuquerque.
Worked example: 75 °F dry bulb at 50% relative humidity
Standard sea-level pressure, 29.921 in. Hg or 101,325 Pa.
- Saturation pressure at the dry bulb. 75 °F is 23.889 °C; the ASHRAE correlation gives pws = 2,965.3 Pa.
- Actual vapour pressure. At 50% RH, pv = 0.50 × 2,965.3 = 1,482.6 Pa.
- Humidity ratio of the sample. W = 0.621945 × 1,482.6 ÷ (101,325 − 1,482.6) = 0.0092357 lb/lb, which is 64.65 gr/lb. This is the target the wet bulb has to reproduce.
- First trial: t* = 62 °F. Saturation pressure at 62 °F is 1,897.4 Pa, so W*s = 0.621945 × 1,897.4 ÷ (101,325 − 1,897.4) = 0.0118685 lb/lb. The balance gives W = [(1093 − 0.556 × 62) × 0.0118685 − 0.240 × 13] ÷ (1093 + 0.444 × 75 − 62) = (12.5631 − 3.1200) ÷ 1064.30 = 0.0088727 lb/lb, or 62.11 gr/lb. Too low, so the true wet bulb is higher.
- Second trial: t* = 63 °F. Saturation pressure 1,965.4 Pa gives W*s = 0.0123026 lb/lb, and the balance returns 0.0095324 lb/lb, or 66.73 gr/lb. Now too high, so the answer is bracketed between 62 and 63 °F.
- Interpolate. 62 + (64.65 − 62.11) ÷ (66.73 − 62.11) = 62 + 2.54 ÷ 4.62 = 62.55 °F. The bisection in the calculator lands on 62.553 °F, so the linear interpolation across a single degree is already good to three hundredths.
The wet-bulb depression is 75 − 62.55 = 12.45 °F, the dew point is 55.1 °F, and the enthalpy is 0.240 × 75 + 0.0092357 × (1061 + 0.444 × 75) = 18.00 + 10.11 = 28.11 Btu/lb of dry air.
How to use the wet bulb once you have it
For refrigerant charging, the indoor wet bulb is one of the two inputs to a superheat target. Fixed-orifice systems are charged by comparing measured superheat with a target read from a chart indexed by return-air wet bulb and outdoor dry bulb. A wet-bulb reading two degrees high shifts the target by several degrees of superheat, which is enough to leave a system undercharged — the target superheat calculator shows how steeply that table moves. Systems with a thermostatic or electronic expansion valve are charged on subcooling instead, using the subcooling calculator.
For coil selection, entering wet bulb sets total capacity and the dry-bulb spread sets the split. Manufacturer tables run capacity against entering wet bulb precisely because constant-wet-bulb lines are nearly constant-enthalpy lines. Two rooms at 80 °F/67 °F and 75 °F/67 °F present a coil with almost identical total load; the second simply demands more of it as latent. Split the load with the sensible heat ratio calculator.
For evaporative equipment, the wet bulb is the hard limit. A direct evaporative cooler at 85% effectiveness leaving 95 °F db / 66 °F wb air delivers 95 − 0.85 × (95 − 66) = 70.4 °F. A cooling tower is quoted as an approach, the gap between leaving water and the design wet bulb, and 7 °F is a common design approach — see the cooling tower range and approach calculator. Neither can be pushed below the wet bulb by adding capacity, which is why a tower undersized on approach cannot be rescued by a bigger fan.
For heat stress, do not confuse wet bulb with wet-bulb globe temperature. WBGT is a weighted composite — outdoors it is 0.7 times natural wet bulb, plus 0.2 times globe temperature, plus 0.1 times dry bulb — and the natural wet bulb it uses is an unaspirated reading, not the thermodynamic wet bulb this calculator returns. The two are close in moving air and diverge in still air, so a WBGT screening threshold cannot be applied to this output directly.
Wet-bulb temperature at sea level for common indoor and outdoor states
| Dry bulb (°F) | 20% RH | 30% | 40% | 50% | 60% | 70% | 80% | 90% | 100% |
|---|---|---|---|---|---|---|---|---|---|
| 60 | 43.4 | 45.8 | 48.0 | 50.2 | 52.3 | 54.4 | 56.3 | 58.2 | 60.0 |
| 70 | 50.0 | 53.0 | 55.8 | 58.4 | 61.0 | 63.4 | 65.7 | 67.9 | 70.0 |
| 75 | 53.2 | 56.5 | 59.6 | 62.6 | 65.3 | 67.9 | 70.4 | 72.8 | 75.0 |
| 80 | 56.4 | 60.1 | 63.5 | 66.7 | 69.6 | 72.5 | 75.1 | 77.6 | 80.0 |
| 85 | 59.6 | 63.6 | 67.3 | 70.8 | 74.0 | 77.0 | 79.8 | 82.5 | 85.0 |
| 90 | 62.8 | 67.2 | 71.2 | 74.9 | 78.3 | 81.5 | 84.5 | 87.3 | 90.0 |
| 95 | 66.0 | 70.7 | 75.1 | 79.1 | 82.7 | 86.1 | 89.3 | 92.2 | 95.0 |
| 100 | 69.1 | 74.3 | 79.0 | 83.2 | 87.1 | 90.7 | 94.0 | 97.1 | 100.0 |
Read the AHRI rating points off this table: 80 °F at 40% RH is a 63.5 °F wet bulb, and the 80/67 indoor point sits between the 50% and 60% columns at 51% RH. At altitude the whole table shifts, so use the calculator with your station pressure rather than these sea-level values.
A thermometer in a wet sock is not a wet-bulb reading
The energy balance assumes the wick loses heat overwhelmingly by evaporation, and that requires air moving across it at roughly 400 ft/min or faster — a proper sling, or a fan-aspirated psychrometer. A wetted sensor sitting still in a room reads somewhere between the true wet bulb and the dry bulb, always high. Three more field mistakes push the reading the same way: tap water leaves mineral scale that glazes the wick and blocks evaporation, a wick that has dried out at the top reads sensible temperature instead, and a bulb in line of sight of a hot compressor or a sunlit window picks up radiant gain the balance never accounted for. Sling until the reading stops falling, then take the lowest value.
Assumptions and limits of this calculation
- It returns the thermodynamic wet bulb, not a psychrometer reading. The two agree to within a few hundredths of a degree for a properly aspirated wick at normal HVAC conditions, which is far inside instrument error, but they are not the same defined quantity.
- Moist air is treated as an ideal gas mixture. That holds comfortably at atmospheric pressure across the temperature range this tool covers; it is not a real-gas model for compressed air work.
- The inch-pound constants change below freezing. Above a 32 °F wet bulb the balance uses 1093, 0.556 and 0.240; below it, 1220, 0.04 and 0.48, with saturation taken over ice. The calculator switches automatically at 32 °F.
- Station pressure, not sea-level pressure. Forecast barometric readings are corrected to sea level. Using one at altitude overstates the humidity ratio and shifts the wet bulb by close to a degree at 5,000 ft.
- It is a point calculation. Air stratifies, and a return grille, a room centre and a supply plenum will read differently. Sample where the number is going to be used.
- Relative humidity above 100% is rejected. Supersaturated states do not persist in ducts or rooms; the tool holds the calculation at saturation and flags it rather than returning a fictional answer.
Which psychrometric property to reach for
Any two independent properties fix the state of moist air at a known barometric pressure, so the choice between them is practical rather than theoretical. Reach for the wet bulb when the question is about total heat or about evaporation — coil capacity, tower approach, evaporative-cooler leaving temperature, refrigerant charging. Reach for the dew point when the question is about condensation on a surface, using the dew point calculator. Reach for the humidity ratio when the question is about a quantity of water — pounds per hour off a coil, or the moisture a dehumidifier has to remove.
Relative humidity is the weakest of the four for engineering work, because it changes when you merely heat the air. It survives because occupants understand it and because the mould and comfort literature is written in it. If you have relative humidity and need the others, this calculator and the relative humidity calculator convert in both directions, and the moist air enthalpy calculator takes the state through to total heat.
One historical note explains a persistent confusion. Before the thermodynamic wet bulb was defined, the psychrometer was the definition, and older texts published psychrometric tables from measured depressions with an empirical psychrometric constant. Modern practice inverts that: the thermodynamic wet-bulb temperature is defined by the adiabatic-saturation process, and the instrument is understood as an approximation to it. That is why an ASHRAE table and a nineteenth-century psychrometric table disagree in the last digit, and why a well-designed aspirated psychrometer matters more than a well-chosen empirical constant.