The formula
How to calculate relative humidity
Relative humidity is the ratio between how much water vapour the air currently holds and the maximum it could hold at that same temperature, expressed as a percentage. This calculator works it out the way a weather station with a dew-point sensor often does: from air temperature and dew point, rather than from a direct humidity sensor.
This is the same Magnus-Tetens relationship used on this site's dew point calculator, solved the other way round — instead of finding the temperature at which the air would saturate, it compares the actual vapour content (implied by the dew point) against the maximum the air could hold at its current temperature.
What to enter:
- Air temperature (°C)
- Dew point (°C)
Everything recalculates as you type, and the numbers in the address bar update with it, so a link to this page carries your figures with it.
Units matter more here than the arithmetic itself: the formula assumes a specific set of units for each input, stated next to the field, and converting into those units first is usually the difference between a correct result and one that is wrong by a clean power of ten.
Why relative humidity matters
The formula behind relative humidity is standard and appears in the same form across textbooks and reference material; what a calculator adds is speed and the ability to see instantly how the result responds to a change in any one of the inputs, which is far slower to do by hand.
It is useful for checking a manual calculation before submitting or acting on it, and equally useful for building intuition about a formula by adjusting one input at a time and watching how the result moves in response — a much faster way to understand a relationship than working through several versions of the algebra by hand.
It is worth remembering that a formula is only ever as good as the assumptions built into it, and most of the standard equations used across science and statistics carry at least one simplifying assumption — a linear approximation, an idealised gas, a normally distributed error term — that holds well in most ordinary cases and breaks down at the extremes. The result here reflects the standard formula exactly; whether that formula's assumptions are appropriate for your particular situation is a separate judgement worth making deliberately rather than assuming automatically.
Where a calculation like this one is part of a larger piece of work, it is generally worth running it with a round, easy-to-check set of numbers first — inputs of exactly 1, 10 or 100 — purely to confirm the formula is being applied correctly, before switching to the real measured values the actual result depends on.
Worked example
Work through the defaults on this page:
- Air temperature: 20 °C
- Dew point: 10 °C
That gives:
- Relative humidity: 52.6 %
The figures above are the calculator's own default values, shown purely so the working is visible rather than hidden — the same steps apply exactly to your own numbers, entered in the fields at the top of this page.
Reading the result
When dew point and air temperature are equal, relative humidity is 100% — the air is fully saturated. The wider the gap between the two, the lower the relative humidity: a 20 °C day with a 10 °C dew point sits around 50%, while the same 20 °C day with a 18 °C dew point is above 85%.
Where this goes wrong. Relative humidity moves through the day even when the actual moisture in the air (and so the dew point) barely changes, purely because air temperature swings — the same air reads as high relative humidity at a cold dawn and low relative humidity in the afternoon heat. Dew point, not relative humidity, is the figure that tracks actual moisture content.
A result that is wrong by an exact factor of ten, a hundred or a similar round number is almost always a units error rather than a mistake in the formula itself — checking each input against the unit stated beside it is the fastest way to track it down.
Not in stable air — 100% is by definition full saturation. Values reported slightly above 100% sometimes appear in raw instrument data (supersaturation is physically possible only briefly, in the absence of condensation nuclei) but any calculator or forecast reporting over 100% as a normal figure is describing measurement noise, not real air.
Many automated weather stations measure temperature and dew point directly with separate sensors, since dew point instruments (which detect the exact temperature condensation begins) are a well-established, stable measurement — relative humidity is then a calculated figure derived from the two, rather than a third independent measurement.
The headline figure is relative humidity. With 20 °C air temperature and 10 °C dew point, that comes to 52.6 %. Change any field and the figure moves with it.
Generally, no more than the least precise input justifies — a result reported to six decimal places from inputs measured to two significant figures is implying a precision the calculation does not actually have. The calculator shows full precision so you can round appropriately for your own use.
Yes — the equation shown in the formula section above is the standard form used in textbooks and reference material for this calculation, not a simplified or approximate version.
Yes, in the sense that it applies the correct standard formula and returns an accurate result for the inputs given — but check your own course or publication's requirements for how results should be rounded, presented and referenced, since those conventions vary and are not something a calculator can know on your behalf.