Relative Humidity Calculator

What the relative humidity calculator does

Relative humidity tells you how close the air is to being full of moisture. This calculator connects three quantities, the air temperature, the dew point, and the relative humidity, and works out whichever one you leave out from the other two.

Below is what relative humidity is, why temperature matters so much, the equation behind it, and a worked example.

How to use it

1. Choose which quantity to find: the temperature, the dew point, or the relative humidity.
2. Enter the two you know, each with its temperature unit, and the humidity as a percentage.
3. Press Calculate for the missing one, or Reset to clear it.

What relative humidity is

Relative humidity is the amount of water vapour the air is holding, expressed as a percentage of the most it could hold at that temperature. At 100 percent the air is saturated, holding all the moisture it can, and any extra would condense into dew, fog, or rain. At 50 percent it holds half its maximum, and at low values the air is dry and thirsty.

The word relative is the key. It is not a measure of how much water is in the air outright, but of how full the air is relative to its capacity. This is why relative humidity is what we feel and what weather reports quote: it governs how readily sweat evaporates, whether washing dries, and how muggy or parched the day seems. The same actual amount of moisture can mean bone-dry air on a hot afternoon and saturated air on a cold night, because the capacity changes with temperature.

Why warm air holds more moisture

The reason relative humidity depends so strongly on temperature is that warm air can hold far more water vapour than cold air. As air heats, its capacity for moisture rises steeply, so the same amount of water vapour fills a smaller fraction of that larger capacity, and the relative humidity drops. Cool the air down and the opposite happens: capacity shrinks, the moisture fills more of it, and the relative humidity climbs.

This is why a heated room in winter feels dry even though no moisture was removed, simply because warming the air expanded its capacity. It is why dew forms on cool mornings, as overnight cooling pushes the air to saturation. And it is why relative humidity alone never tells you the actual moisture content without the temperature alongside it. The calculator builds this temperature dependence in, which is what lets it convert between temperature, dew point, and relative humidity.

The equation it uses

The calculator uses the August-Roche-Magnus approximation, a well-established formula relating temperature, dew point, and the saturation of the air. The relative humidity comes from comparing two saturation terms, one at the dew point and one at the air temperature:

RH = 100 × exp[ β · T_d ÷ (λ + T_d) ] ÷ exp[ β · T ÷ (λ + T) ]

Here T is the air temperature, T_d is the dew point, and β and λ are constants of the Magnus formula, about 17.625 and 243.04. The same relationship, rearranged, lets the calculator find the dew point from the temperature and humidity, or work in the other direction. It is an approximation, but a very accurate one across the everyday range of weather.

The link to dew point

Relative humidity and dew point are two views of the same thing, the moisture in the air, and the calculator moves freely between them. The dew point is the temperature to which the air would have to cool to become saturated. The closer the dew point is to the current temperature, the more moisture the air already holds relative to its capacity, and so the higher the relative humidity.

When the dew point equals the air temperature, the air is saturated and the relative humidity is exactly 100 percent. As the gap between them widens, with the dew point falling below the temperature, the relative humidity drops. This pairing is why knowing any two of temperature, dew point, and relative humidity fixes the third, and why the calculator can solve for whichever one you are missing.

Working range and precision

The calculator works in the range where the Magnus approximation is reliable, roughly −45 to 60 degrees Celsius, which covers essentially all weather and indoor conditions, and it accepts temperatures in Celsius, Fahrenheit, or kelvin. Relative humidity is capped at 100 percent, since the air cannot hold more than saturation. The relationship is an accurate empirical fit rather than an exact law, but its error across normal conditions is very small. Results are shown to two decimal places.

A worked example

Suppose the air temperature is 25 degrees Celsius and the dew point is 15 degrees Celsius.

Feeding these into the Magnus relationship gives a relative humidity of about 54 percent. The air is holding a little over half the moisture it could at 25 degrees. If the temperature dropped toward 15 degrees while the moisture stayed put, the dew point and temperature would converge and the relative humidity would rise toward 100 percent, which is exactly how evening cooling brings on dew.

Questions people ask

What does relative humidity actually mean?

It is the percentage of the maximum moisture the air could hold at its current temperature. At 100 percent the air is saturated; lower values mean drier air with spare capacity.

Why does relative humidity change with temperature?

Because warm air can hold much more water vapour than cold air. Heating the air raises its capacity and lowers the relative humidity, while cooling it does the reverse, even when the actual moisture is unchanged.

How is relative humidity related to dew point?

The closer the dew point is to the air temperature, the higher the relative humidity. When they are equal, the air is saturated at 100 percent. The calculator converts between the two.

Can relative humidity go above 100 percent?

Not in ordinary conditions. At 100 percent the air is saturated, and any further moisture condenses into dew, fog, or rain rather than staying as vapour.

References

A quick note on where the science comes from. The relationship between temperature, dew point, and relative humidity through the August-Roche-Magnus approximation is standard meteorology, described by the US National Weather Service and in the Wikipedia article on dew point. The HyperPhysics overview from Georgia State University covers the underlying humidity concepts.

1. National Weather Service (NOAA), Discussion of the August-Roche-Magnus approximation and humidity. https://www.weather.gov/epz/wxcalc_rh
2. Wikipedia, Dew point. https://en.wikipedia.org/wiki/Dew_point
3. HyperPhysics, Relative Humidity. http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/relhum.html