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Dew point from air temperature and relative humidity (Magnus formula)
- where
- intermediate Magnus term (dimensionless)
- relative humidity (%)
- air temperature (°C)
- dew point temperature (°C)
- dew point spread, air minus dew point (°C)
Explain this equation
Finds the dew point: the temperature at which moisture in the air starts to condense on a surface. You need it before painting exterior work, cold walls or metal, because paint must not go onto a damp surface.
T is the air temperature and RH the relative humidity from a hygrometer. γ is a working value that combines how full of moisture the air is with how much moisture air at that temperature can hold. Td is the resulting dew point and D is how far the air is above it.
The Magnus formula approximates how the saturation vapour pressure of water rises roughly exponentially with temperature. The constants 17.625 and 243.04 °C are the fitted Alduchov–Eskridge values. Taking the natural log and rearranging gives the temperature at which the actual moisture would saturate the air.
Sense check: at 20 °C and 50% RH the dew point is about 9.3 °C. At 100% RH the dew point equals the air temperature, and the spread is zero.
Watch out: the surface, not the air, is what matters. Use the surface margin calculator to compare.
Works out the temperature at which moisture in the air will condense on a surface, from a hygrometer reading of air temperature and relative humidity.
Enter your values to see the result.
Good to know
Uses the Magnus form with the Alduchov–Eskridge constants (17.625 and 243.04 °C), accurate to about 0.1 °C between −40 °C and 50 °C (Lawrence 2005). At 20 °C and 50% RH the dew point is about 9.3 °C; at 10 °C and 80% RH it is about 6.7 °C. Any surface colder than the dew point gets wet, which ruins adhesion and can cause surfactant leaching and blooming on fresh paint.
Common mistake
Taking the reading in a warm van or doorway. Measure the air next to the surface you are about to paint, especially on exterior work early and late in the day.
Limits
Valid for −40 °C to 50 °C over liquid water. Below 0 °C this is the dew point over water, not the frost point. Accuracy is limited by the hygrometer, typically ±2–3% RH.
Sources
- M. G. Lawrence, The relationship between relative humidity and the dewpoint temperature in moist air, Bulletin of the American Meteorological Society 86(2), 2005, pp. 225–233 (Magnus form with Alduchov–Eskridge constants 17.625 and 243.04 °C)
- O. A. Alduchov, R. E. Eskridge, Improved Magnus form approximation of saturation vapor pressure, Journal of Applied Meteorology 35(4), 1996, pp. 601–609
- BS EN ISO 8502-4:2017 Preparation of steel substrates before application of paints: guidance on estimation of the probability of condensation (surface at least 3 °C above dew point)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Coverage depends on the product, surface and application. Always follow the paint and wallcovering manufacturers’ data sheets and BS 6150 / BS 8000-12. Check prices and VAT with your own records and HMRC.