The closest simple dew-point formulas stay within 0.07 °C of a reference calculation

The dew point is the temperature air must cool to before its water vapour saturates, and most calculators take it from a Magnus formula with three fitted numbers. We checked seven published sets of those numbers against a reference built from IAPWS above freezing and from Wexler's and Sonntag's formulations below it. Wherever temperature and dew point both lay between −40 and 50 °C, Alduchov and Eskridge's pair (17.625, 243.04) stayed within 0.054 °C. Sonntag's 1990 pair and Alduchov's 1988 pair stayed within 0.07 °C. On Singapore-like air every set agreed to 0.03 °C. One point of relative humidity moved the answer 0.18 to 0.30 °C. Alduchov and Eskridge made the qualitative point in 1997, writing that the errors they discuss are much less than hygrometers' observational errors; Lawrence's 2005 paper is earlier work on the same conversion. The figures above, in degrees and for tropical air, are our own.

Three published pairs stay within a sliver of the reference

A Magnus formula gives saturation vapour pressure as a·exp(b·T/(c + T)), with T in °C. For the dew point, set the actual vapour pressure, RH/100 times that value, equal to the same function at a lower temperature. The prefactor divides out: with γ = ln(RH/100) + b·T/(c + T), Td = c·γ/(b − γ). Whether a set starts from 6.1094, 6.112 or 6.11 hPa, only b and c reach the dew point.

Our sweep put the largest vapour-pressure error of Alduchov and Eskridge's pair at 0.375%, at −40 °C, consistent with the maximum under 0.384% their OSTI report of 1 November 1997 gives. Sonntag's peaked at 0.313%, at 28 °C. Yet over 15,995 grid points neither strayed past 0.07 °C in dew point, because part of each error cancels when the same curve is read at both T and Td. The report credits the form to Magnus in 1844, and its Table II prints six earlier sets; we ran those and the report's own pair.

Tetens's 1930 pair towers over the others at very dry points

We computed these gaps on the same grid. Tetens's worst case is 6.5 °C at 2% humidity; Buck-1's is −3 °C at 4%. Tetens's pair is 3.2% out in vapour pressure at −40 °C and only 0.31 °C out in dew point at its worst.

Between 22 and 35 °C, at 40 to 100% humidity, the seven sets never differ by more than 0.0275 °C, under a third of a display rounded to 0.1°.

A one-point humidity error outweighs any choice of coefficients

A one-point change in relative humidity moves the dew point by 0.184 °C at 25 °C and 90%, rising to 0.302 °C at 34 °C and 55%. A 0.1 °C change in air temperature moves it by 0.09 to 0.10 °C. These figures show what an input error does to the answer; they say nothing about how well any sensor reads.

The dew point calculator on this site uses Alduchov and Eskridge's pair. Code committed on 7 November 2026 makes it print that sensitivity and a five-set comparison beside each result. Enter 30 °C and 70%: it gives 23.9 °C, the five sets span 0.010 °C, and one point of humidity is worth about 0.24 °C. Before that commit it stated its accuracy as a few tenths of a degree, accepted any temperature (at −243.04 °C it printed "NaN"), and labelled every dew point of 24 °C or more "Severe, dangerous", a band no source we opened supports.

Frost point overtops dew point once the air is below freezing

Below 0 °C a Magnus formula for water gives the dew point over supercooled water. Cooled air reaches saturation over ice first, so frost forms at the frost point, which is warmer. Alduchov and Eskridge report a 1966 WMO recommendation to calculate humidity over water at negative temperatures, the convention assumed here.

Their report also gives an ice formula, 6.1121·exp(22.587·t/(273.86 + t)), for −80 to 0 °C, with a maximum relative error under 0.213%. With it, we found a frost point of −11.39 °C for air at −10 °C and 80%, 1.41 °C above the dew point. The gap grows with the cold, from 0.73 °C at −5 °C and 90% to 3.23 °C at −30 °C and 60%. The ice pair in WMO's Guide to Instruments and Methods of Observation (WMO-No. 8, 2023 edition), as WMO training material quotes it, lands within 0.02 °C of these.