Relative Humidity Calculator — from dew point, wet bulb or vapour pressure

The relative humidity calculator above converts the humidity measurement you happen to have into the percentage everyone quotes, and shows the intermediate quantities rather than hiding them. Relative humidity is the ratio of the water vapour actually in the air to the maximum the air could hold at its current temperature. Both halves of that ratio are vapour pressures, and once you can compute a saturation vapour pressure from a temperature, every humidity conversion follows from the same one equation.

Arb Digital builds free calculators that name the formula they use and state where it stops being valid. This one uses the Buck equation for saturation vapour pressure over liquid water, which is fitted to be accurate across roughly −80 °C to +50 °C — a range that comfortably covers every ordinary meteorological and building-services application. The alternative Magnus and Tetens forms are simpler and slightly less accurate at the cold end, and the section on the formula below explains what the difference amounts to in practice.

What This Relative Humidity Calculator Does

It takes three different starting points and returns the same set of answers from each. Give it an air temperature and a dew point, and it computes the vapour pressure from the dew point and the saturation vapour pressure from the air temperature. Give it an air temperature and a wet-bulb temperature, and it applies the psychrometric equation to get the vapour pressure first. Give it the two vapour pressures directly, and it simply divides them.

The headline result is the relative humidity as a percentage. The grid holds the four supporting quantities: the actual vapour pressure in hectopascals, the saturation vapour pressure in hectopascals, the absolute humidity in grams of water per cubic metre of air, and the mixing ratio in grams of water per kilogram of dry air. Those last two are the figures that engineers, growers and drying-process operators usually want, because unlike relative humidity they describe an amount of water rather than a ratio.

Station pressure is a separate field because it genuinely matters for two of the three modes. The wet-bulb calculation depends on it directly through the psychrometric constant, and the mixing ratio depends on it because a kilogram of dry air occupies a different volume at different pressures. The dew-point route is almost pressure-independent, which is one reason dew point is the preferred field measurement.

How to Use It

1. Pick the input you actually have. Do not convert your reading into a dew point by hand first — the tool does that internally, and each mode uses the appropriate equation for its own measurement.
2. Enter the air temperature and choose Celsius or Fahrenheit. The unit applies to every temperature field on the page at once, so a Fahrenheit air temperature needs a Fahrenheit dew point beside it.
3. Enter the second measurement. Dew point and wet bulb must both be less than or equal to the air temperature. If a dew point exceeds the air temperature the tool caps the result at 100 per cent and says so, because supersaturated air is not a state you can measure with a thermometer.
4. Set the station pressure if you are not at sea level. At 1,500 m elevation the pressure is around 845 hPa, which shifts the mixing ratio noticeably even though the relative humidity barely moves.
5. Read the grid, not just the percentage. The vapour pressure and absolute humidity figures are what tell you whether the air is genuinely wet. The percentage alone is ambiguous until you know the temperature it was measured at.

The Formula: How Relative Humidity Is Calculated

Relative humidity is RH = 100 × e ÷ e_s, where e is the partial pressure of water vapour in the air and e_s is the saturation vapour pressure at the air temperature. Everything else is a route to those two numbers.

For the saturation vapour pressure this tool uses the Buck equation over liquid water: e_s(T) = 6.1121 × exp[(18.678 − T ÷ 234.5) × (T ÷ (257.14 + T))], with T in degrees Celsius and the result in hectopascals. The coefficients come from Buck's 1981 paper on new equations for computing vapor pressure in the Journal of Applied Meteorology, which fits the range −80 °C to +50 °C.

In dew-point mode, e is just the saturation vapour pressure evaluated at the dew point instead of the air temperature — that is what dew point means. Work the defaults: at 25 °C the Buck equation gives e_s = 31.69 hPa, and at a dew point of 15 °C it gives e = 17.05 hPa. The relative humidity is 100 × 17.05 ÷ 31.69 = 53.8 per cent.

The moisture amounts follow from e. Absolute humidity is e ÷ (R_vT) with R_v = 461.5 J kg⁻¹ K⁻¹ and T in kelvin, which for the defaults gives 1705 ÷ (461.5 × 298.15) = 0.01239 kg m⁻³, or 12.39 grams per cubic metre. The mixing ratio is 621.97 × e ÷ (p − e) = 621.97 × 17.05 ÷ 996.2 = 10.65 grams per kilogram.

In wet-bulb mode the vapour pressure comes from the psychrometric equation e = e_s(T_w) − Ap(T − T_w), with a psychrometric coefficient A of 6.62 × 10⁻⁴ per degree Celsius for a properly ventilated wet bulb above freezing.

Why Relative Humidity Misleads and Dew Point Does Not

Relative humidity is a ratio whose denominator changes with temperature, which makes it a poor description of how much water is in the air. The National Weather Service is blunt about it: the NWS Louisville discussion of humidity notes that relative humidity is highest in the early morning when the air is coolest and lowest in the afternoon when it is warmest, even on a day when the actual moisture content never changed at all.

Run that through this calculator to see the size of the effect. Hold the dew point at 15 °C and set the air temperature to 16 °C: the relative humidity reads about 94 per cent. Raise the air temperature to 30 °C with the same dew point and it falls to about 41 per cent. The vapour pressure figure in the grid does not move by a single hectopascal across that change, because nothing was added to or removed from the air. Only the denominator moved.

That is why forecasters quote dew point when they want to say how humid it feels. A dew point of 15 °C is comfortable, 20 °C is noticeably sticky and 24 °C is oppressive, and those thresholds hold regardless of the air temperature. A relative humidity of 70 per cent means something entirely different in a cold cellar than on a summer afternoon.

Where This Sits Next to Our Dew Point and Heat Index Tools

Arb Digital already publishes two humidity-adjacent calculators, and the boundary between the three is worth stating precisely because they answer different questions from the same physics. The dew point calculator runs the conversion in the opposite direction: it takes a temperature and a relative humidity and returns the dew point. This page takes a dew point, wet bulb or vapour pressure and returns the relative humidity. They are inverses of one another, and which one you need depends entirely on which measurement you started with.

The heat index calculator does something different again. It does not compute a humidity value at all — it takes temperature and relative humidity as inputs and returns an apparent temperature, an estimate of how hot conditions feel when evaporative cooling is impaired. Use this page to get the relative humidity, then take that percentage into the heat index tool. The wind chill calculator is the cold-weather counterpart, and it does not use humidity at all because at low temperatures the air holds too little moisture for it to matter.

Reading Absolute Humidity and Mixing Ratio

These two grid figures both describe an amount of water, but they normalise it differently, and mixing them up causes real errors in ventilation and drying calculations.

Absolute humidity is grams of water vapour per cubic metre of moist air. It is the natural unit when you are thinking about a volume — a room, a greenhouse, a shipping container. Its weakness is that it changes when the air expands or is heated at constant pressure, even though no water has moved, because the same water now occupies a larger volume.

Mixing ratio is grams of water vapour per kilogram of dry air. It is the natural unit for air-handling work, because heating or cooling a stream of air without adding or removing water leaves the mixing ratio unchanged. That conservation property is why psychrometric charts are built around it. If you are sizing a dehumidifier, the mixing ratio difference between inlet and outlet air, multiplied by the mass flow, is the water removal rate.

Ice, Supersaturation and the Limits of the Model

Below freezing the phrase saturation vapour pressure becomes ambiguous, because the saturation pressure over supercooled liquid water is higher than the saturation pressure over ice. At −20 °C the two differ by about 10 per cent. Meteorological convention, and this calculator, report relative humidity with respect to liquid water at all temperatures, which is why a frosty morning can report 95 per cent rather than the 105 per cent an ice-based reference would give.

Values above 100 per cent are physically possible in clean air but not measurable with a thermometer pair, so a dew point entered above the air temperature is treated as an input error and capped. In practice a dew point reading that exceeds the air temperature means one of the two sensors has drifted, and the calibration is worth checking before the arithmetic is.

Common Mistakes to Avoid

• Treating relative humidity as an amount of water — it is a ratio against a temperature-dependent maximum. The same air can read 40 per cent and 90 per cent within a single day without gaining a gram of moisture.
• Mixing temperature units between fields — the unit menu applies to air temperature, dew point and wet bulb together. A Celsius air temperature beside a Fahrenheit dew point gives a nonsense answer that still looks plausible.
• Ignoring station pressure in wet-bulb mode — the psychrometric equation multiplies the wet-bulb depression by the pressure, so using sea-level pressure at altitude biases the result.
• Comparing an ice-referenced reading with a water-referenced one — below freezing the two conventions differ by several per cent and grow further apart as it gets colder.
• Using absolute humidity where mixing ratio belongs — heating air changes its absolute humidity without changing its moisture content. In any air-handling calculation the mixing ratio is the conserved quantity.

Related Free Tools From Arb Digital

Run the conversion the other way with the dew point calculator, then take the percentage from this page into the heat index calculator for apparent temperature, or the wind chill calculator for the cold-weather equivalent. Convert your inputs first with the temperature converter and the pressure converter, and follow the same vapour-pressure curve up to its high end with the boiling point calculator. Everything Arb Digital publishes is listed at the free online tools hub.

Frequently Asked Questions

This tool is provided for educational and study use. It applies standard empirical humidity equations and does not account for instrument calibration, ventilation or local conditions, so treat its output as a physics result rather than a certified measurement.