Relative Humidity Calculator

Calculate relative humidity, dew point, or air temperature from any two known values using a reversible Magnus-form humidity relationship.

Calculator is for informational purposes only. Terms and Conditions

Relative humidity from air temperature and dew point
\[ RH = 100\,\frac{e_s(T_d)}{e_s(T)} \]

Uses the Alduchov–Eskridge improved Magnus form over liquid water with coefficients 17.625 and 243.04 °C; this implementation is limited to −40 to 50 °C.

1

Choose what to calculate

Select the unknown. The calculator shows only the two values required for that result.

Calculation setup

Choose the unknown. Required fields, equation, result label, and answer units update together.

Enter air temperature and dew point. Relative humidity updates automatically.
2

Enter the known values

Use °F or °C for temperature values. The two active fields can use different temperature units.

Fields marked required must be completed. Temperature inputs must remain within the documented equation range.

Dry-bulb air temperature for the humidity state.

Temperature at which the current water vapor would reach saturation.

3

Result

Primary answer first, followed by calculation checks, warnings, and transparent solution steps.

Relative Humidity
—
%
Enter the required values to calculate.

Result details

  • Check—
Show calculation steps Review conversions, equations, substitutions, assumptions, and checks
  1. Enter valid values to see the complete calculation.
4

Method, Sources, and Assumptions

Calculation basis, authoritative references, empirical limits, and physical checks.

Improved Magnus form

Relative humidity is calculated as actual water-vapor pressure divided by saturation vapor pressure. Saturation pressure uses the Alduchov–Eskridge improved Magnus form over liquid water.

  • The Magnus-form correlation is empirical and this implementation is limited to −40 to 50 °C.
  • The correlation is applied over liquid water and is intended for ordinary atmospheric humidity calculations, not specialized frost-point or supersaturated-state work.
  • Relative humidity is represented on a 0–100 percent scale.

Calculator guide

Relative Humidity Calculator Guide: RH, Dew Point, and Air Temperature

Use the Relative Humidity Calculator above to calculate relative humidity from air temperature and dew point, calculate dew point from air temperature and relative humidity, or solve for air temperature from dew point and RH. Each mode uses two known values and returns the third. Temperature can be entered in °F or °C, and relative humidity is expressed as a percentage.

Relative humidity is the ratio of actual water-vapor pressure to the saturation vapor pressure at the current air temperature. Because saturation pressure changes strongly with temperature, RH is temperature-dependent. Dew point identifies the temperature at which the current vapor state reaches saturation and is often the better quantity for condensation checks.

Primary use
Calculate relative humidity from air temperature and dew point.
Other solve modes
Calculate dew point or solve for air temperature.
Method
Improved Magnus saturation-vapor-pressure correlation with algebraic inversions.

How to Use the Relative Humidity Calculator

Choose the quantity you do not know, then enter the two values you do know. The active inputs, equation, result label, and result units change with the selected solve mode.

  1. Calculate relative humidity

    Select Relative Humidity, then enter air temperature and dew point. For the ordinary unsaturated-air state handled by the calculator, dew point must be less than or equal to air temperature. The result is returned as percent RH.

  2. Calculate dew point

    Select Dew Point, then enter air temperature and relative humidity. The result is returned in the same temperature unit used for the air-temperature input.

  3. Calculate air temperature

    Select Air Temperature, then enter dew point and relative humidity. The result is returned in the same temperature unit used for the dew-point input.

  4. Use °F and °C without changing the physical state

    Each temperature field has its own unit selector. Changing a selector converts the represented temperature; it does not reinterpret the same number as a different unit.

Relative Humidity Formula and Calculation Method

Relative humidity is determined from actual and saturation water-vapor pressure. The calculator evaluates saturation pressure with the Alduchov–Eskridge improved Magnus form and uses algebraic inversions of that same relationship for the dew-point and air-temperature solve modes.

Relative humidity from temperature and dew point

\[ RH = 100\frac{e_s(T_d)}{e_s(T)} \]

Calculate saturation vapor pressure at the dew point, divide it by saturation vapor pressure at the air temperature, then multiply by 100.

Improved Magnus saturation-pressure correlation

\[ e_s(T)=610.94\exp\left(\frac{17.625T}{243.04+T}\right) \]

Temperature \(T\) is in degrees Celsius and the resulting saturation vapor pressure \(e_s\) is in pascals.

The calculator uses coefficients 17.625 and 243.04 °C and constrains entered and calculated temperatures to −40 to 50 °C (−40 to 122 °F).

Solving for dew point

\[ \gamma= \ln\left(\frac{RH}{100}\right) +\frac{17.625T}{243.04+T}, \qquad T_d=\frac{243.04\gamma}{17.625-\gamma} \]

The dew-point mode reverses the same correlation, which makes it possible to check the result by calculating RH again from the solved dew point.

\(RH\)
Relative humidity, expressed on a 0–100 percent scale.
\(T\)
Dry-bulb air temperature, converted internally to °C.
\(T_d\)
Dew-point temperature, converted internally to °C.
\(e_s\)
Saturation vapor pressure at the specified temperature, in pascals.

Relative Humidity Calculation Example

Suppose the air temperature is 72°F and the dew point is 55°F. These are the calculator’s default example values in Relative Humidity mode.

Given values

Air temperature
72°F
Dew point
55°F
Find
Relative humidity

Convert the units

\[ 72^\circ F=22.222^\circ C, \qquad 55^\circ F=12.778^\circ C \]

Calculate the two vapor pressures

\[ e_s(22.222)=2674.52\ \mathrm{Pa}, \qquad e_s(12.778)=1473.43\ \mathrm{Pa} \]

Calculate relative humidity

\[ RH= 100\frac{1473.43}{2674.52} =55.091\% \]

Result

55.1% relative humidity

At 72°F with a 55°F dew point, the current water-vapor pressure is about 55% of the saturation vapor pressure at 72°F.

How to Interpret Relative Humidity Results

Relative humidity describes how close the air is to saturation at its current temperature. It does not, by itself, tell you the total mass of water vapor in the air. Dew point is often the more direct indicator when you care about how close a surface or air stream is to condensation.

100% RH is the saturation boundary

When dew point equals air temperature, actual vapor pressure equals saturation vapor pressure and the calculator returns 100% RH. In the calculator’s normal unsaturated-air scope, dew point cannot be higher than air temperature.

Heating lowers RH if dew point stays constant

Holding dew point at 55°F gives about 77.8% RH at 62°F, 55.1% at 72°F, and 39.6% at 82°F. The water-vapor pressure is held constant in this comparison; only saturation pressure changes with air temperature.

Dew-point depression is a fast sanity check

Dew-point depression is \(T-T_d\). As that difference approaches zero, the state approaches saturation. A negative value would place dew point above air temperature and is rejected in Relative Humidity mode.

Relative Humidity Input Quality and Common Mistakes

Humidity calculations are only as representative as the measurements entered. The most important checks are unit consistency, measurement timing and location, and physical consistency between air temperature and dew point.

Dew point higher than air temperature

For the ordinary unsaturated-air state handled here, dew point must not exceed dry-bulb temperature. If it does, recheck both measurements, their units, and whether they describe the same air sample.

Confusing °F and °C

A temperature of 20°C is 68°F, not 20°F. Use the field’s unit selector so the calculator converts the physical quantity correctly.

Treating RH as moisture content

The same water-vapor pressure can correspond to very different RH values at different air temperatures. Use dew point or a full psychrometric calculation when the moisture state matters more than percentage saturation.

Entering RH outside the calculator range

Relative humidity must be greater than 0% and no more than 100% in the dew-point and air-temperature solve modes. The calculator does not present supersaturated states as ordinary results.

Mixing readings from different conditions

Air temperature and dew point should describe the same state. Combining an indoor temperature with an outdoor dew point, or readings taken far apart in time, can produce a mathematically valid result that represents neither location.

Reading more precision than the measurements support

The method is an empirical vapor-pressure correlation, and real temperature or humidity sensors also have measurement uncertainty. Treat the displayed decimal places as calculation resolution, not proof that the underlying measurements are equally precise.

Relative Humidity Calculator Assumptions and Limits

This is a focused three-variable humidity solver for ordinary atmospheric calculations, education, and quick engineering checks. It is not a replacement for a complete moist-air property model when pressure, altitude, wet bulb, enthalpy, humidity ratio, or equipment behavior matters.

Empirical saturation-pressure correlation

The improved Magnus form approximates saturation vapor pressure. Higher-precision thermodynamic work may use more complete formulations for water and moist air.

Temperature range

The calculator constrains entered and calculated temperatures to −40 to 50 °C, equivalent to −40 to 122 °F.

Liquid-water basis

The implemented Magnus coefficients are used over liquid water. Specialized frost-point or saturation-over-ice calculations below freezing can require a separate ice-based relationship.

Normal unsaturated-air scope

The user-facing solver limits RH to 100% and rejects dew point above air temperature in Relative Humidity mode. Specialized supersaturated or multiphase atmospheric states require a different model.

Related Humidity and Psychrometric Calculators

Use a related calculator when relative humidity is an intermediate value rather than the final quantity you need.

Moist-air properties Psychrometric Calculator

Extend the humidity state into humidity ratio, dew point, wet bulb, enthalpy, vapor pressure, specific volume, density, and pressure-aware checks.

Weather and heat Heat Index Calculator

Use measured air temperature and relative humidity to estimate apparent heat with the NOAA/NWS heat-index method.

Vapor pressure Vapor Pressure Calculator

Work directly with temperature–vapor-pressure relationships when pressure is the quantity you need to calculate or reverse-solve.

Relative Humidity Technical Sources and Verification

The guide uses ASHRAE psychrometric definitions for relative humidity and dew point and the published Alduchov–Eskridge improved Magnus correlation for the calculator’s saturation-vapor-pressure approximation. The worked example was recomputed directly and checked by reversing the result back to dew point.

For the default 72°F air-temperature and 55°F dew-point example, the implemented correlation gives approximately 2674.52 Pa and 1473.43 Pa for the two saturation pressures, producing 55.091% RH before display rounding. Reversing that state with 72°F and 55.091% RH returns approximately 55°F dew point.

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