Index / Science
Dew Point and Condensation Risk
Three published formulas for saturation vapour pressure, run side by side, with the spread between them printed. Most calculators pick one and do not say which. Below the dew point is the number people are usually actually after: how cold a surface has to be before it runs with water, and how cold before mould has what it needs.
Air
Over water. An empty box is zero, and at zero
there is no dew point at all.
Only the mixing ratio and specific humidity use
this. An empty box falls back to 1013.25, which is standard sea
level.
All three are computed either way. This only
chooses which one the big number is.
Arden Buck
—
Vapour pressure
—
Absolute humidity
—
The three formulas, and how far apart they are
How cold a surface has to be
The rest of the moisture in that air
What this page checked about its own answer
the inversion, put back through the formula
Which formulas, over what range, and what they disagree about
Everything here comes from one quantity: the saturation vapour
pressure of water. There is no exact closed form for it, so every
calculator uses a fit to measurements, and different fits give slightly
different answers. Three are computed here:
Arden Buck (1981), es = 6.1121 exp[(18.678 − T/234.5)(T/(257.14 + T))] hPa, over water. Good to about 0.05% from −20 °C to 100 °C, which is why it is the default here.
Magnus form with Alduchov and Eskridge (1996) coefficients, es = 6.1094 exp[17.625 T/(243.04 + T)] hPa. Stated for −40 °C to 50 °C; past 50 it drifts, reaching about 2.7% high at 100 °C, and the page says so when you go there.
Sonntag (1990), the six-term fit in kelvin. The most accurate of the three across the widest range and the most awkward to type.
Over the range a building lives in, they agree to about a quarter of a percent. The widest gap between them between −30 and 50 °C is 0.26%, at around 25 °C, which is a few hundredths of a degree of dew point. If a number on this page matters to a tenth of a degree, the formula is not what should worry you; the accuracy of the hygrometer is.
The dew point is inverted, not approximated. The usual shortcut rearranges the Magnus form algebraically, which only works for that form and is an approximation for the other two. This page instead searches for the temperature whose saturation pressure equals the actual vapour pressure, by bisection, to within a ten-millionth of a degree — and then puts that temperature back through the formula and prints the residual, so the inversion is checked in front of you.
All of it is over water, not ice. Below freezing, saturation over ice is lower than over supercooled water, so a frost point is not the same number as a dew point. This page reports the dew point over water throughout and does not switch formulas at zero, because switching silently is how two calculators come to disagree by a degree.
The mould threshold is 80% humidity at the surface, which is the figure in BS 5250 and the WHO dampness guidance, sustained rather than momentary. It is a threshold for growth being possible, not a prediction, and it is reached at a surface warmer than the dew point — mould does not need running water.
Absolute humidity uses Rv = 461.5 J/(kg·K) and treats water vapour as an ideal gas, which is worth about 0.2% at room temperature. The mixing ratio uses 621.97 g/kg for the ratio of molar masses, and the pressure in the box.
The wet-bulb temperature is Stull's 2011 empirical fit, which is not derived from the formulas above. It is stated for 1013.25 hPa, −20 to 50 °C and 5% to 99% humidity, and this page prints nothing for it outside that range rather than extrapolating.
Arden Buck (1981), es = 6.1121 exp[(18.678 − T/234.5)(T/(257.14 + T))] hPa, over water. Good to about 0.05% from −20 °C to 100 °C, which is why it is the default here.
Magnus form with Alduchov and Eskridge (1996) coefficients, es = 6.1094 exp[17.625 T/(243.04 + T)] hPa. Stated for −40 °C to 50 °C; past 50 it drifts, reaching about 2.7% high at 100 °C, and the page says so when you go there.
Sonntag (1990), the six-term fit in kelvin. The most accurate of the three across the widest range and the most awkward to type.
Over the range a building lives in, they agree to about a quarter of a percent. The widest gap between them between −30 and 50 °C is 0.26%, at around 25 °C, which is a few hundredths of a degree of dew point. If a number on this page matters to a tenth of a degree, the formula is not what should worry you; the accuracy of the hygrometer is.
The dew point is inverted, not approximated. The usual shortcut rearranges the Magnus form algebraically, which only works for that form and is an approximation for the other two. This page instead searches for the temperature whose saturation pressure equals the actual vapour pressure, by bisection, to within a ten-millionth of a degree — and then puts that temperature back through the formula and prints the residual, so the inversion is checked in front of you.
All of it is over water, not ice. Below freezing, saturation over ice is lower than over supercooled water, so a frost point is not the same number as a dew point. This page reports the dew point over water throughout and does not switch formulas at zero, because switching silently is how two calculators come to disagree by a degree.
The mould threshold is 80% humidity at the surface, which is the figure in BS 5250 and the WHO dampness guidance, sustained rather than momentary. It is a threshold for growth being possible, not a prediction, and it is reached at a surface warmer than the dew point — mould does not need running water.
Absolute humidity uses Rv = 461.5 J/(kg·K) and treats water vapour as an ideal gas, which is worth about 0.2% at room temperature. The mixing ratio uses 621.97 g/kg for the ratio of molar masses, and the pressure in the box.
The wet-bulb temperature is Stull's 2011 empirical fit, which is not derived from the formulas above. It is stated for 1013.25 hPa, −20 to 50 °C and 5% to 99% humidity, and this page prints nothing for it outside that range rather than extrapolating.