What relative humidity actually measures
Relative humidity is a ratio of pressures. Water vapour in air behaves as its own gas and exerts its own partial pressure, and at any temperature there is a ceiling on that pressure — the saturation vapour pressure. Relative humidity is the fraction of that ceiling you are currently using, expressed as a percentage. At 80 °F the ceiling is 1.0330 in. Hg; if the air actually holds vapour at 0.5279 in. Hg, the relative humidity is 0.5279 ÷ 1.0330 = 51%.
The consequence people miss is that relative humidity is a moving target. The ceiling roughly doubles for every 20 °F of warming, so heating a sealed room raises the denominator while leaving the numerator alone, and the relative humidity collapses even though not one molecule of water has left. That is exactly why a house at 70 °F in January reads 15% RH: the outdoor air was near saturation at 20 °F, and 20 °F saturated air is very dry air once you warm it up.
Because of that, relative humidity on its own is a poor way to describe a quantity of moisture. When you need the amount, use the humidity ratio — pounds of water vapour per pound of dry air, usually written in grains, where 7,000 grains make a pound. This calculator reports both, and the humidity ratio calculator goes further into that quantity. Heating and sensible cooling leave the humidity ratio untouched; only condensation, humidification or mixing change it.
The formula, and why a psychrometer works at all
The definition is the easy part: divide the actual vapour pressure by the saturation vapour pressure at the dry-bulb temperature. Everything difficult sits in getting those two pressures.
The saturation pressure comes from a correlation, not a formula you can derive at the bench. This calculator uses the Hyland–Wexler equations published in Chapter 1 of the ASHRAE Handbook—Fundamentals, which give the saturation pressure of water over liquid water above 32 °F and over ice below it. They are the equations behind the printed psychrometric chart and behind the saturation-pressure tables in the same chapter, and they hold from −148 °F to 392 °F.
The actual vapour pressure comes from whichever second measurement you have. If you know the dew point, you are done in one step, because the dew point is by definition the temperature at which the current vapour pressure would be the saturation pressure: pv = pws(tdp).
A wet-bulb reading takes more work. Wrap a thermometer bulb in a wetted wick and blow air across it, and the water evaporating off the wick pulls its latent heat out of the passing air stream. The wick cools until the sensible heat arriving from the air exactly balances the latent heat leaving with the vapour. That balance point is the wet-bulb temperature, and the energy balance behind it is the second formula in the block above: the numerator is the latent heat the saturated wick can supply minus the sensible heat the air gives up, and the denominator normalises it back to a pound of dry air. The quantity W*s is the saturation humidity ratio evaluated at the wet-bulb temperature, which is why the calculation needs the saturation correlation twice.
Barometric pressure enters through the humidity ratio, not through the pressure ratio. Converting a vapour pressure to a humidity ratio divides by (p − pv), so at 5,000 ft the same vapour pressure corresponds to a noticeably larger humidity ratio. Run the default 80/67 reading at 24.90 in. Hg and the answer moves from 51.1% to 53.4% — a real difference, and the reason a sea-level chart taped inside a service van is wrong in Denver.
Worked example: 80 °F dry bulb, 67 °F wet bulb at sea level
This is the standard indoor rating condition for air-conditioning equipment, so it is worth being able to reproduce it by hand. Barometric pressure is 29.921 in. Hg (101,325 Pa).
- Saturation pressure at the wet bulb. 67 °F is 19.444 °C. Hyland–Wexler gives pws* = 2,259.5 Pa, or 0.6672 in. Hg.
- Saturation humidity ratio at the wet bulb. W*s = 0.621945 × 2,259.5 ÷ (101,325 − 2,259.5) = 0.0141855 lb/lb, which is 99.30 gr/lb.
- Apply the energy balance. With tdb = 80 °F and twb = 67 °F, the numerator is (1093 − 0.556 × 67) × 0.0141855 − 0.240 × (80 − 67) = 1055.748 × 0.0141855 − 3.1200 = 14.9762 − 3.1200 = 11.8562. The denominator is 1093 + 0.444 × 80 − 67 = 1061.52. So W = 11.8562 ÷ 1061.52 = 0.0111690 lb/lb, or 78.19 gr/lb.
- Back out the vapour pressure. pv = 101,325 × 0.0111690 ÷ (0.621945 + 0.0111690) = 1,787.4 Pa, which is 0.5279 in. Hg.
- Saturation pressure at the dry bulb. 80 °F is 26.667 °C, and Hyland–Wexler gives 3,498.1 Pa, or 1.0330 in. Hg.
- Divide. RH = 100 × 1,787.4 ÷ 3,498.1 = 51.1%.
Two more numbers fall out for free. The dew point is the temperature whose saturation pressure equals 1,787.4 Pa, which is 15.73 °C or 60.3 °F. The enthalpy is 0.240 × 80 + 0.0111690 × (1061 + 0.444 × 80) = 19.20 + 12.25 = 31.45 Btu per pound of dry air. Read those off a psychrometric chart and you will get 51%, 78 gr/lb, 60 °F and 31.4 Btu/lb — the chart and the equations are the same physics.
How to read the number you get
For occupied comfort, ASHRAE Standard 55 caps the humidity ratio rather than the relative humidity. The upper boundary of the comfort zone is 0.012 lb of water per lb of dry air — 84 gr/lb — with no lower humidity limit set for thermal comfort. That is the number this calculator warns on. A 78 gr/lb reading at 80 °F sits inside the zone; the same 78 gr/lb at 72 °F reads as 66% RH and still sits inside it, which is precisely why the standard uses the mass ratio.
For building durability, the working range most practitioners aim at is 30% to 60% RH. Below 30% you get static discharge, gapping hardwood and dry sinuses; sustained readings above 60% at surface temperature raise the risk of mould growth and dust-mite populations. The trap is that room-average RH tells you nothing about the surface RH behind a sofa on an exterior wall, which can be 20 points higher because the surface is colder.
For refrigeration work, the wet bulb is the number that matters, not the RH. Manufacturers publish evaporator capacity against entering wet-bulb temperature, and superheat targets are read from an indoor wet-bulb and outdoor dry-bulb pair — see the target superheat calculator. Relative humidity is a convenient way to talk to a homeowner; wet bulb is the way to talk to the equipment.
Judge condensation risk on the dew point alone. Any surface colder than the dew point collects water, regardless of the relative humidity in the room. At the default state, ductwork or a chilled-water line below 60.3 °F sweats. The dew point calculator works the same relationship from the other direction when your meter reports RH instead.
Relative humidity from wet-bulb depression at sea level
| Dry bulb (°F) | 2 °F depression | 4 °F | 6 °F | 8 °F | 10 °F | 15 °F | 20 °F |
|---|---|---|---|---|---|---|---|
| 60 | 89 | 78 | 68 | 58 | 49 | 27 | 6 |
| 70 | 90 | 81 | 73 | 64 | 56 | 37 | 20 |
| 75 | 91 | 82 | 74 | 66 | 59 | 41 | 25 |
| 80 | 92 | 83 | 76 | 68 | 61 | 45 | 30 |
| 85 | 92 | 84 | 77 | 70 | 63 | 48 | 34 |
| 90 | 92 | 85 | 78 | 71 | 65 | 50 | 37 |
| 95 | 93 | 86 | 79 | 73 | 67 | 53 | 40 |
The same depression means a higher relative humidity at a higher dry-bulb temperature: a 10 °F depression is 49% RH at 60 °F but 67% RH at 95 °F. That is why you cannot carry a single rule of thumb about depression across the whole temperature range.
A sling psychrometer that is not slung reads high
The wet-bulb energy balance assumes the wick is losing heat mainly by evaporation, which requires air moving over it at roughly 400 ft/min or more. A wetted wick sitting still in a room reaches a temperature somewhere between the true wet bulb and the dry bulb, and every degree of error there costs you four to five points of relative humidity at ordinary room conditions — read the 2 °F and 4 °F columns of the reference table above at 75 °F: 91% against 82%. Sling until the reading stops falling and then take the lowest value, use distilled water so the wick does not glaze over with mineral scale, and shade the bulb from any radiant source.
Mistakes that put the answer out by more than the instrument does
- Entering sea-level pressure at altitude. Weather reports adjust station pressure to sea level. Use the actual station pressure — about 24.90 in. Hg at 5,000 ft in the standard atmosphere — or your humidity ratio will be low by several grains.
- Treating relative humidity as an amount of water. Two rooms at 40% RH and different temperatures hold different amounts of moisture. Compare humidity ratios, or dew points, when you want to know which space is wetter.
- Reading the wet bulb before it stabilises. The wick keeps cooling for 30 to 60 seconds of continuous air movement. An early reading is always high, and high wet bulb means high reported RH.
- Using a room-average RH to judge a cold surface. Mould and condensation depend on conditions at the surface. Measure the surface temperature and compare it with the dew point this calculator returns.
- Mixing up dew point and frost point below freezing. Below 32 °F the saturation curve over ice differs from the curve over supercooled water. This calculator switches to the ice correlation below 32 °F, which is the ASHRAE convention.
- Assuming a hygrometer is accurate as shipped. Capacitive RH sensors drift, especially after exposure to high humidity or solvents. Check them against a saturated-salt reference or against a slung psychrometer before trusting a reading to a point or two.
Key terms
- Dry-bulb temperature
- Ordinary air temperature, measured by a sensor kept dry and shielded from radiant heat. It says nothing about moisture on its own.
- Wet-bulb temperature
- The equilibrium temperature of a wetted, ventilated sensor, where the sensible heat gained from the air balances the latent heat lost to evaporation. It is always at or below the dry-bulb temperature and at or above the dew point.
- Dew point
- The temperature to which you would have to cool the air, at constant pressure and constant moisture content, for condensation to begin. Surfaces below it collect water.
- Humidity ratio
- Mass of water vapour per unit mass of dry air, in lb/lb or in grains per pound (7,000 gr = 1 lb). Unchanged by heating or sensible cooling.
- Saturation vapour pressure
- The maximum partial pressure water vapour can exert at a given temperature. It rises steeply with temperature, roughly doubling every 20 °F in the comfort range.
- Enthalpy
- Total heat content of the moist air per pound of dry air, referenced to 0 °F dry air and 32 °F liquid water. The quantity a cooling coil actually removes.
Where this fits among the other psychrometric tools
Every psychrometric quantity on this page is a different coordinate for the same point on the chart. Fix any two independent properties at a known barometric pressure and the rest follow. Dry bulb plus wet bulb, dry bulb plus dew point, and dry bulb plus relative humidity are the three pairs a technician normally has, and they are interchangeable inputs to the same state.
Use the wet-bulb route when you have a sling psychrometer and want the most defensible reading in the field, because it depends on a thermometer and a wick rather than on a sensor that drifts. Use the dew-point route when you are working from a data logger, since most loggers compute dew point internally from a calibrated capacitive element. If you need to go the other way — from a known relative humidity to a wet bulb, which is what evaporative cooling and cooling-tower work demand — use the wet bulb temperature calculator.
Downstream, the humidity ratio is what sizes equipment. The difference in humidity ratio across a coil, multiplied by the mass flow of dry air, is the moisture the coil removes; multiplied by the latent heat of vaporisation it becomes the latent load handled by the latent heat load calculator, and it is the basis for both the dehumidifier sizing calculator and the condensate rate calculator. Enthalpy difference across the coil, times mass flow, gives you the total load. Cooling towers work the same wet-bulb physics from the other side, where the wet bulb sets the theoretical limit on how cold the leaving water can be — that is the approach in the cooling tower range and approach calculator.
Two limits are worth stating plainly. This calculator models moist air as an ideal gas mixture with the ASHRAE saturation correlation, accurate to well under a tenth of a percent across normal HVAC conditions but not a real-gas equation of state for high-pressure work. And it assumes the psychrometer reading is a true thermodynamic wet bulb; a badly ventilated or contaminated wick is a measurement problem no equation can repair.