Relative Humidity Calculator

What relative humidity measures

Relative humidity is a ratio, not an amount. It compares the water vapor in the air with the most water vapor that same air could hold at its current temperature, and it reports the result as a percentage. The National Weather Service describes it as the actual amount of water vapor in the air compared with the total amount of vapor that can exist at its current temperature.

The word relative is the part that trips people up. Warm air holds more moisture than cool air, so the same lump of damp air reads high on a cool morning and low on a hot afternoon. Air at 40 °F and 50 percent carries about 3.3 grams of water per cubic meter, while air at 80 °F and 50 percent carries about 12.6 grams. The two percentages match and the two rooms do not.

That is why this page hands you a dew point along with the percentage. The dew point is the temperature the air has to be cooled to before the vapor in it condenses, and it is the better comfort gauge because it names a temperature instead of a ratio. The calculator runs both ways: give it a temperature and a dew point and it returns the relative humidity, give it a temperature and a humidity and it returns the dew point, and either way it reports the absolute humidity in grams per cubic meter, the vapor pressure, the saturation vapor pressure and the spread between air and dew point.

The Magnus-Tetens formula behind the numbers

The work is done with the Magnus-Tetens approximation, the standard way to turn a temperature into the vapor pressure of saturated air. The saturation vapor pressure is

es(T) = 6.112 × exp(17.625 × T ÷ (243.04 + T))

with T in Celsius and es in hectopascals. The coefficients A = 17.625 and B = 243.04 °C come from Alduchov and Eskridge, whose 1996 paper in the Journal of Applied Meteorology reworked the Magnus form so it fits measured vapor pressure data as closely as possible. The University of Washington glaciology lab teaches the same expression, written in pascals, as the August-Roche-Magnus approximation.

Everything else on this page comes out of that one equation. The vapor pressure in the air is the saturation pressure at the dew point, so relative humidity is 100 × es(Td) ÷ es(T). Running it the other way, the dew point is recovered through a short intermediate value, gamma = ln(RH ÷ 100) + 17.625 × T ÷ (243.04 + T), and then Td = 243.04 × gamma ÷ (17.625 − gamma).

The fit holds over ordinary weather. Alduchov and Eskridge report a relative error below 0.4 percent for the saturation vapor pressure between −40 °C and 50 °C over liquid water, and that range is the one the calculator accepts.

Worked example: temperature and dew point in, relative humidity out

Take a summer afternoon: air at 25 °C with a dew point of 16.7 °C. The saturation vapor pressure at 25 °C is 31.63 hPa, and the saturation vapor pressure at 16.7 °C is 18.98 hPa, which is the vapor pressure the air carries. Relative humidity is 100 × 18.98 ÷ 31.63, which comes out to 60.0 percent. The same air holds 13.8 grams of water per cubic meter, and the spread between the air and the dew point is 8.3 °C, or 14.9 °F.

The same calculation in Fahrenheit gives the same answer for a familiar setup: air at 68 °F with a dew point of 50 °F is 52.5 percent relative humidity, with 9.1 grams of water per cubic meter in it. The National Weather Service reminds readers that a dew point on its own does not fix the relative humidity, because the air temperature has to be known too, and that is exactly what the two boxes in the calculator ask for.

Worked example: temperature and relative humidity in, dew point out

Now the other direction. Air at 30 °C and 50 percent relative humidity. First the intermediate value: ln(50 ÷ 100) = −0.6931, and 17.625 × 30 ÷ (243.04 + 30) = 1.9365, so gamma = 1.2434. Then the dew point is 243.04 × 1.2434 ÷ (17.625 − 1.2434) = 18.4 °C, which is 65.2 °F. That dew point lands in the band the National Weather Service calls oppressive, and the air carries 15.1 grams of water per cubic meter.

The same chain in Fahrenheit puts a familiar number on the screen: air at 80 °F and 50 percent has a dew point of 59.7 °F, and air at 20 °C and 45 percent has a dew point of 7.7 °C, which is 45.9 °F. A relative humidity of 100 percent has one special case worth remembering, because there is no algebra to do: the dew point is then the air temperature, since saturated air is at the dew point by definition.

Why the reading falls when the air warms

Watch what happens when the dew point stays put and only the temperature moves. Hold the dew point at 55 °F, which is 12.8 °C, and warm the air from 60 °F to 100 °F. No moisture leaves the air and none arrives, and yet the relative humidity falls from 83.5 percent to 22.5 percent, because warm air could carry far more vapor than it does. The percentage moved by 61 points while the moisture in the room did not change at all.

The last column drifts down from 11.1 to 10.3 grams per cubic meter, because a cubic meter of warmer air weighs a little less. The dew point never moved, so the moisture per pound of air stayed the same; only the volume it fills changed.

That is the trap built into relative humidity. A number that slides down through the morning while the weather stays just as muggy has recorded a change in the capacity of the air, not a change in the water. The National Weather Service heat index guidance makes the point with two days: 90 °F with a dew point of 69 °F gives 50 percent relative humidity, and 50 °F with a dew point of 50 °F gives 100 percent, yet the 90 °F day feels far more humid because its dew point is 19 °F higher.

Absolute humidity: how much water the air holds

Absolute humidity answers the question the percentage cannot. It reports the mass of water vapor in a cubic meter of air, in grams, and it is computed from the vapor pressure and the temperature: AH = 216.7 × e ÷ (273.15 + T), with e in hectopascals and T in Celsius. Saturated air at 25 °C holds 23.0 grams per cubic meter, which is the ceiling for that temperature, and saturated air at 30 °C holds 30.3 grams, close to the National Weather Service note that a cubic meter of air in the mid 80s Fahrenheit can hold about 30 grams of vapor.

The pair of numbers tells the story best. Air at 68 °F with a dew point of 50 °F sits at 52.5 percent relative humidity and 9.1 grams per cubic meter, while air at 100 °F with a dew point of 75 °F reads 45.2 percent and 20.6 grams per cubic meter. The lower percentage is holding more than twice the water, and anyone who has felt a July afternoon and an October morning knows those are not the same comfort level.

Absolute humidity also matters for drying. Clothes, paint, and lumber lose moisture to the air in proportion to the gap between the water in the material and the water in the room, so a lower absolute humidity dries laundry faster even when the percentage looks the same on two different days.

Reading the result: comfort, fog, and condensation

Comfort follows the dew point more closely than the percentage, so the calculator prints a band taken from the National Weather Service scale: a dew point of 55 °F or lower is dry and comfortable, 55 to 65 °F is becoming sticky with muggy evenings, and 65 °F or higher is a lot of moisture in the air and oppressive. The same office publishes a heat index chart that turns a temperature and a humidity into a felt temperature, and its worked example is blunt, 96 °F with 50 percent relative humidity feels like 108 °F.

Condensation is the other use for a dew point. Water forms on any surface colder than the dew point, which is why a cold drink leaves a wet ring on a summer table, why a bathroom mirror fogs after a hot shower, and why a window in winter grows a film of water on the inside when the glass drops below the room dew point. Fog is the same idea in the open air: when the spread between air temperature and dew point falls to a few degrees, the air sits close enough to saturated for droplets to form.

Where the formula stops working

Three limits are worth knowing. The fitted range runs from −40 °C to 50 °C, and the calculator turns down inputs outside it, because the error grows quickly near the ends of the range. The formula describes vapor over liquid water; below freezing, vapor saturates over ice at a slightly different pressure, and forecasts for frozen precipitation use a separate set of coefficients instead. And a reading of exactly 100 percent means the air is saturated at that temperature, not that the air is wetter than a sponge.

Supersaturation, where the vapor pressure briefly sits above the saturation value, does happen inside cloud droplets and in the lee of mountains, but it does not last in open air, so a reported value above 100 percent usually points to a sensor or a rounding problem rather than to the sky itself.

One last caution. The result can only be as good as the number you typed. A household hygrometer is not a reference instrument, and the weather service builds its official observations from calibrated equipment, so treat the output as the arithmetic of a good reading rather than a replacement for one. The formula itself is good to a few tenths of a degree over the range it covers.