Relative Humidity & Dew Point Calculator
Calculate relative humidity from dry-bulb and dew point temperatures, or compute the dew point from temperature and relative humidity using the Magnus–Tetens formula.
Formulas Used
Magnus–Tetens Saturation Vapor Pressure:
e_s(T) = 6.1078 × exp( a·T / (b + T) ) a = 17.625 (dimensionless) b = 243.04 °C T in °C, e_s in hPa (≡ mbar)
Relative Humidity from T and T_d:
RH = 100 × e_s(T_d) / e_s(T)
Dew Point from T and RH (Magnus inversion):
γ(T, RH) = ln(RH/100) + a·T / (b + T) T_d = b·γ / (a − γ)
Heat Index (Steadman / Rothfusz, T ≥ 27°C, RH ≥ 40%):
HI = −8.785 + 1.611·T + 2.339·RH − 0.146·T·RH
− 0.0123·T² − 0.0164·RH² + 0.00221·T²·RH
+ 0.000725·T·RH² − 0.00000358·T²·RH²
Assumptions & References
- The Magnus–Tetens formula is valid for temperatures between −40°C and +60°C and is accurate to within ±0.1% over that range.
- Constants a = 17.625 and b = 243.04°C are from Alduchov & Eskridge (1996), Journal of Applied Meteorology, 35, 601–609.
- Relative humidity is defined as the ratio of actual vapor pressure to saturation vapor pressure at the same temperature, expressed as a percentage.
- The dew point formula is the algebraic inversion of the Magnus equation; it assumes the dew point is the temperature at which air becomes saturated at constant pressure.
- The Heat Index regression equation is from Rothfusz (1990), NWS Technical Attachment SR 90-23, and is only valid when T ≥ 27°C (80°F) and RH ≥ 40%.
- All calculations assume standard atmospheric pressure (1013.25 hPa). At significantly different pressures (e.g., high altitude), results may differ slightly.
- Dew point depression (T − T_d) is a common field estimate: a spread of <2.5°C indicates near-saturation; >25°C indicates very dry air.