Relative Humidity Calculator - Dew Point, RH, Saturation Pressure

The relative humidity calculator is a meteorology and HVAC tool that turns a measured air temperature plus dew point into the percent relative humidity, or back-calculates the dew point from a known RH, using the Alduchov and Eskridge (1996) Magnus approximation.

• • Indoor air-quality and comfort checks: Compare a measured dew point to the room air temperature and read the percent RH, then judge whether the room is too dry or too damp for mold risk.
• • Weather observation and forecast decoding: Translate a surface weather reading of dry-bulb and dew point into the RH percent, saturation pressure, and actual vapor pressure that the same reading would yield on a station plot.
• • Condensation and dew-point forecasting: Read the back-calculated dew point from a known RH, then compare it to the wall or window temperature to see whether condensation is about to form.
• • Classroom psychrometric exercises: Use the relative humidity calculator as a small psychrometric tool in meteorology, HVAC, and physics classes.

Relative humidity is the ratio of the actual water vapor pressure in the air to the saturation vapor pressure the air could hold at the same temperature, expressed as a percent. Saturation pressure is set by temperature, which is why the same 15 C dew point can sit at 30 percent RH on a 30 C afternoon and at 100 percent RH on a 15 C winter morning.

The saturation pressure at any temperature T in degrees Celsius is 610.94 * exp(17.625 * T / (243.04 + T)) in pascals, evaluated once at the dry-bulb and once at the dew point, and the percent RH is the ratio.

Once you have the relative humidity, an absolute humidity calculator takes the same actual vapor pressure and turns it into the mass of water vapor per cubic meter of moist air.

The calculator applies the Alduchov and Eskridge (1996) Magnus approximation in two passes. One pass evaluates the saturation pressure at the dry-bulb temperature to set the denominator, and the other evaluates it at the dew point to set the numerator. The same form is reversed in dew-point-from-RH mode.

• T_dry: Air (dry-bulb) temperature in degrees Celsius. Sets the saturation pressure in the denominator.
• T_dew: Dew point temperature in degrees Celsius. Sets the actual vapor pressure in the numerator in RH-from-dew-point mode.
• RH_in: Relative humidity in percent, used in dew-point-from-RH mode. The calculator back-solves the dew point from this input.
• P_sat(T): Saturation vapor pressure at temperature T, in pascals, computed with the Alduchov and Eskridge 1996 Magnus form.
• a, b, c: Magnus constants a = 17.625, b = 243.04 C, c = 610.94 Pa.

In dew-point-from-RH mode, the calculator inverts the same Magnus expression. The combined variable gamma = ln(RH/100) + a * T / (b + T) is plugged into the closed-form T_dew = b * gamma / (a - gamma), which is exact for the Magnus approximation.

The actual vapor pressure is the saturation pressure at the dew point and feeds the mixing ratio, the absolute humidity, and the vapor pressure deficit for the same air parcel.

According to Alduchov and Eskridge 1996 - Improved Magnus Form, the improved Magnus approximation 610.94 * exp(17.625 * T / (243.04 + T)) in pascals matches the ASHRAE saturation pressure table to within 0.4 percent from -40 to 50 degrees C.

When you are ready to translate the same reading into a plant-physiology or HVAC metric, a vapor pressure deficit calculator computes the difference between saturation pressure and actual vapor pressure in the same Magnus form.

Four ideas come up every time you work with relative humidity. They are the same terms you will see on a station plot, in an HVAC control loop, and on a psychrometric chart.

Once you have those four terms in mind, the panel reads like a psychrometric chart: dry-bulb temperature sets the ceiling, dew point sets the actual water content, and the percent RH is the ratio between them.

For the dry-air side of the same air parcel, an air density calculator applies the ideal gas law to the temperature and pressure you already entered so you can compare density against the humidity values.

Pick a mode, type the two temperature or humidity numbers you have, and the calculator handles the Magnus math in real time.

1. 1 Choose the calculation mode: Use RH-from-dew-point when you have a measured dew point, or dew-point-from-RH when you only have a relative humidity reading.
2. 2 Enter the dry-bulb temperature: Type the air temperature in degrees Celsius. It is the reference for the saturation pressure in both directions.
3. 3 Enter the dew point (RH-from-dew-point mode): Type the dew point in degrees Celsius. It sets the actual vapor pressure compared to the dry-bulb saturation pressure.
4. 4 Enter the relative humidity (dew-point-from-RH mode): Switch the role: type the known percent RH and leave the dew point as a default. The calculator back-solves the dew point from the Magnus inverse.

For a classroom exercise, enter 25 in the air temperature input, 15 in the dew point input, and keep the mode on RH-from-dew-point. The panel shows RH = 53.8 percent, P_sat(25) = 3162 Pa, and P_vapor = 1702 Pa, which is the trio an NWS station plot would print for the same reading.

If the next step is a full psychrometric analysis, an ideal gas calculator handles the dry-air partial pressure that completes the ideal gas picture of the same air parcel.

The Magnus form is the same expression ASHRAE and NWS use for psychrometric charts, so the calculator's numbers line up with textbook tables and calibrated weather station readings.

• • Bidirectional RH and dew point: Switch between RH-from-dew-point and dew-point-from-RH without retyping the same air temperature, so the same air parcel can be characterized in either direction.
• ASHRAE-aligned saturation pressure: Use the same Alduchov-Eskridge Magnus constants cited in the ASHRAE Handbook of Fundamentals, so indoor psychrometric work matches the table you are reading.
• Cross-checked dew point and RH: Run the back-calculated dew point alongside the percent RH to confirm the inputs, which catches typos and reverse-mode mistakes before you push values into a load calculation.
• Useful for condensation forecasting: Compare the back-calculated dew point to a wall or window temperature to predict condensation on cold surfaces during shoulder seasons.
• Mobile-friendly for field readings: Type a weather reading from a phone in the field and the Magnus math runs in real time, so percent RH and vapor pressure show up without a spreadsheet.

Indoor RH in the 40 to 60 percent range is the ASHRAE comfort band, which is the same band most condensation forecasts use to keep interior window surfaces above the dew point.

The same dew point output becomes the input to a cloud base calculator, which uses the dry adiabatic lapse rate to estimate the lifting condensation level for the parcel.

The Magnus form is a closed-form approximation, not a measurement. A few practical factors decide whether the number you get matches a calibrated psychrometer.

• • Inputs outside the Magnus valid range of -40 to 50 C can return a numerical value, but the underlying approximation is no longer the ASHRAE-aligned reference.
• • The dew point input is capped at the dry-bulb temperature. If you enter a dew point above the air temperature the calculator clamps it and reports the air parcel as saturated, which prevents a fake RH over 100 percent.

Treat the calculator as a fast Magnus implementation, not a replacement for a calibrated psychrometer. When you need SI-traceable numbers, run a chilled-mirror dew point reading and plug it in.

According to ASHRAE Handbook of Fundamentals, Chapter 1 lists 40 to 60 percent relative humidity as the standard indoor comfort band and reports the saturation pressure at 25 C as about 3167 Pa.

According to Lawrence 2005 - BAMS, the Magnus form provides a simple conversion between relative humidity and dew point that is accurate enough for operational meteorology and HVAC work, which is why the same Alduchov-Eskridge constants are reused across weather-station calculators.

At higher elevation the same percent RH represents less actual water, so an altitude temperature calculator helps you keep the dry-bulb and dew point reading in step with the local atmospheric profile.