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Dew point and relative humidity calculator

Convert between temperature, relative humidity and dew point, and see how much a temperature error shifts an RH reading.

The sensitivity table answers the calibration question: if the sensor's temperature reading is wrong by ±0.2, ±0.5 or ±1 °C while the moisture content is unchanged, what RH does it report?

Result

Dew point
9.26°C
Relative humidity
50.0%rh
Absolute humidity
8.62g/m³
e_s(T)
23.33hPa
saturation
e
11.67hPa
actual vapour pressure
dRH/dT
-3.10%rh/°C
at constant moisture
Indicated RH for a temperature measurement error at constant dew point
Temperature errorReads (−)Reads (+)RH error
±0.2 °C50.6 %49.4 %≈ ±0.6 %rh
±0.5 °C51.6 %48.5 %≈ ±1.6 %rh
±1.0 °C53.2 %47.0 %≈ ±3.2 %rh

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Magnus formula over liquid water with Alduchov–Eskridge constants; about 0.4 % in vapour pressure between −40 and 50 °C. Not for frost point over ice.

A worked example

A calibration laboratory holds 21.0 °C and 45 % relative humidity. Items arrive from a 5 °C refrigerator, and the question is whether they will wet on the bench.

What you start with

Air temperature
21.0 °C
Relative humidity
45 %

The arithmetic

  1. 01

    Get the saturation vapour pressure at the air temperature, then scale it by the humidity.

    e = 0.45 × e_s(21.0 °C)

  2. 02

    Solve the same relation backwards for the temperature at which that vapour pressure saturates.

    dew point = 8.61 °C

  3. 03

    Take the sensitivity of the humidity reading to air temperature at this point.

    ∂RH/∂t = −2.76 %RH per °C

Dew point 8.61 °C. Anything brought into the room colder than 8.6 °C will condense.

The item from the 5 °C refrigerator wets, and no amount of wiping fixes a resistance measurement made on a damp sensor. The sensitivity figure is the other half: the humidity reading moves 2.8 points for every degree the air temperature moves, so a specification of ±5 %RH is in practice a specification of ±1.8 °C — which is both easier to control and far easier to measure traceably.

How the calculation works

  1. 01Saturation vapour pressure over water: e_s(T) = 6.1094 exp(17.625 T / (243.04 + T)) hPa.
  2. 02Dew point: T_d = b γ / (a − γ), where γ = ln(RH/100) + a T/(b + T), a = 17.625, b = 243.04 °C.
  3. 03Absolute humidity = 216.7 e / (T + 273.15) g/m³, with e the actual vapour pressure in hPa.
  4. 04RH sensitivity at constant vapour pressure: d(RH)/dT = −RH a b / (b + T)².

Limitations

  • Valid over liquid water from about −40 °C to +50 °C; not for frost point (over ice).
  • Magnus is an approximation (about 0.4 % in e_s); precision hygrometry uses Sonntag or Wexler equations with enhancement factors.

Frequently asked questions

What is the dew point at 20 °C and 50 % RH?
About 9.3 °C. Cooling the air to that temperature at constant moisture content brings it to saturation.
How much does a 1 °C temperature error change RH?
At 20 °C and 50 % RH, roughly 3 %rh per kelvin — a 1 °C error in the sensor's temperature reads as about 3 %rh. This is why humidity calibration starts with thermal equality between sensor and reference.

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