Relative Humidity Calculator

Article — Relative Humidity Calculator

Relative Humidity Calculator: From Temperature and Dew Point

Relative humidity is the ratio of actual water vapour pressure to saturation vapour pressure at the same temperature, expressed as a percentage. The Magnus formula computes both vapour pressures from temperature, so RH follows from either temperature and dew point or temperature and actual vapour pressure.

Relative humidity is the humidity number most people see on weather apps and thermostats, but it is also the one that confuses the most. The same air feels dramatically different at 30 percent RH on a winter afternoon versus 30 percent RH on a summer night. Both readings describe the same ratio, but the absolute amount of water vapour involved differs by a factor of four.

What relative humidity measures

Relative humidity (RH) is the percentage of saturation reached by water vapour in the air. At 100 percent RH, the air holds as much vapour as it can at the current temperature, and condensation begins on any cooler surface. At 0 percent RH, the air is bone dry — a condition that occurs naturally only in laboratory desiccators.

The reason RH changes with temperature is that the saturation vapour pressure (e_s) rises exponentially with temperature. Warm air can hold much more vapour than cold air, so a fixed amount of water gives a much lower RH in warm air than in cold air. Heat an outdoor 5 °C room to 22 °C without adding water and the RH drops from 80 to around 25 percent — exactly what happens in winter heating.

The relative humidity formula

The defining equation is RH = e / e_s × 100 %, where e is the actual vapour pressure of water in the air and e_s is the saturation vapour pressure at the current temperature. The Magnus formula gives e_s as a function of temperature: e_s = 6.1094 exp(17.625 T / (243.04 + T)) hPa, where T is in degrees Celsius.

To compute RH you need two pieces of information. The most common combination is air temperature plus dew point: RH = e_s(Td) / e_s(T) × 100 %. The other common path is air temperature plus actual vapour pressure measured by a psychrometer or hygrometer.

Relative vs absolute humidity

Absolute humidity (AH) is the mass of water vapour per unit volume of air, in g/m³. It depends only on the actual vapour content and not on temperature. Relative humidity is a ratio that scales with temperature. AH = 216.7 × e / (T + 273.15), with e in hPa and T in °C.

Why two metrics? RH controls how humid air feels because sweat evaporates fast at low RH and slowly at high RH. AH controls how much water can condense when the air cools — important for window fogging, fog formation, and HVAC dehumidification. Both numbers describe the same air; they answer different questions.

Comfortable indoor relative humidity

ASHRAE Standard 55 specifies a comfortable indoor RH range of 30 to 60 percent, with 40 to 50 percent as the sweet spot. Below 30 percent the air feels dry: skin chaps, eyes itch, mucous membranes dry out, and respiratory infections spread more readily. Above 60 percent the air feels muggy, mould risk climbs, and dust mites thrive.

• < 30 % dry skin, static electricity, respiratory irritation
• 30 to 40 % typical winter indoor range with heating
• 40 to 60 % ASHRAE comfort zone year-round
• 50 to 65 % typical summer indoor range
• > 60 % mould risk rises sharply
• > 70 % dust mites multiply, condensation on cool surfaces

Relative humidity, mould, and dust mites

Mould spores germinate when surface relative humidity exceeds about 80 percent for several hours, which corresponds to room RH around 65 to 70 percent. Bathrooms, kitchens, and basements are the typical mould trouble spots because their RH lingers high. EPA guidance recommends keeping indoor RH below 60 percent and below 50 percent in mould-prone areas.

Dust mites require RH above 50 percent to survive. Their populations drop dramatically when bedroom RH stays below 45 percent for two weeks or more. This is why dust-mite allergy sufferers benefit from a dehumidifier as much as from HEPA filtration.

Relative humidity in HVAC and storage

For HVAC engineers, RH determines the latent cooling load. Removing water vapour from indoor air requires condensing it on a cold coil, and that condensation releases the latent heat of vaporisation. On a humid summer day, the latent load can equal the sensible (temperature-only) load.

For archives and museums, RH stability matters more than the exact value. Paper, parchment, and wood swell and shrink with RH; daily swings of 10 percent or more cause embrittlement and cracking. The British Library targets 45 to 55 percent RH with daily variation under 5 percent.

For data centres, ASHRAE recommends 40 to 60 percent RH, balanced between static electricity risk at low RH and corrosion risk at high RH. Modern equipment tolerates wider ranges than older gear, but the standard remains the default specification.

Vapour pressure deficit and growing

Greenhouse growers and cannabis cultivators rarely talk about RH. They talk about vapour pressure deficit (VPD), the difference between saturation and actual vapour pressure: VPD = e_s − e. VPD drives transpiration in plants. Too low (below 0.4 kPa) and plants do not transpire enough to pull nutrients up from the roots; too high (above 1.6 kPa) and plants close their stomata, halting growth.

The sweet spot for most leafy crops is 0.8 to 1.2 kPa VPD. This corresponds to about 65 to 75 percent RH at 22 °C, but the right RH shifts with temperature. Commercial growers tune VPD with climate computers that adjust both temperature and humidity simultaneously.

Common relative humidity mistakes

Other recurring slips: assuming high RH always means muggy air (a 10 °C autumn morning at 95 percent RH feels crisp, not muggy), forgetting to specify temperature when quoting RH for material specs, and confusing RH with relative saturation in industrial drying. For instrument calibration and HVAC design, always pair RH with temperature and pressure.