Dew point (or dew-point temperature) is the temperature at which dew, or condensation, forms, on cooling a gas. Where the condensate is ice, this is known as frost point.

Relative humidity is the ratio of the amount of water vapour, e, in the air to the amount of water vapour, e_s, that would be in the air if saturated at the same temperature and pressure, and can be expressed

relative humidity (in %) = 100 × e/e_s          (1)

Unfortunately, there is no simple, direct formula for converting in either direction between dew point and relative humidity. Conversions between these two parameters must be carried out via the intermediate step of evaluating both the actual vapour pressure of water and the saturation vapour pressure at the prevailing temperature, i.e.

To convert from dew point or frost point to relative humidity:

• Convert dew-point temperature and ambient temperature into water vapour pressures using equation (2) or (3) below (or equation (4) or (5) for greater accuracy)
• Use these values of vapour pressure in equation (1) to find relative humidity

To convert from relative humidity and ambient temperature to dew point or frost point:

• Use equation (2) or (3) below (or equation (4) or (5) for greater accuracy) to find saturation vapour pressure from ambient temperature
• Use equation (1) to calculate water vapour pressure from saturation vapour pressure and known relative humidity
• Use equation (2) or (3) below (or (4) or (5)) to calculate dew or frost point temperature from vapour pressure (requires iteration if using (4) or (5)).

Vapour pressure can be calculated using the Magnus formulae:

At a temperature t (in °C), the saturation vapour pressure e_w(t), in pascals, over liquid water, is

ln e_w(t) = ln 611.2 + (17.62 t)/(243.12+t)          (2)

(e_w(t), is in pascals (Pa): 100 Pa = 1 millibar (mbar))

For the range -45 °C to +60 °C, values given by this equation have an uncertainty of less than ±0.6 percent of value, at the 95% confidence level.

Over ice, e_i(t) is

ln e_i(t) = ln 611.2 + (22.46 t)/(272.62+t)          (3)

For the range -65 °C to +0.01 °C, values given by this equation have an uncertainty of less than ±1.0 percent of value, at the 95% confidence level.

A more accurate but complex alternative formula for vapour pressure (in pascals) from dew point (in kelvin) is as follows for water

ln e_w(T) = -6096.9385 T^-1 + 21.2409642 - 2.711193×10^-2 T + 1.673952×10^-5 T² + 2.433502 ln T          (4)

and for ice

ln e_i(T) = -6024.5282 T^-1 + 29.32707 + 1.0613868×10^-2 T - 1.3198825×10^-5 T² - 0.49382577 ln T          (5)

(Formulae due to Sonntag, 1990, updated from formulae given by Wexler, 1976 and 1977.)

The uncertainties associated with these equations are:

• less than 0.01 percent of value, for water from 0 °C to +100 °C
• ess than 0.6 percent, for supercooled water below 0 °C down to -50 °C
• less than 1.0 percent for ice down to -100 °C

at the 95% confidence level.

The accuracy of these calculations depends slightly on the pressure and temperature of the gas concerned. For air near room temperature and atmospheric pressure, the water vapour enhancement factor, affects the result by approximately 0.5 percent of value.

Further information and tables are given in the publication "A Guide to the measurement of Humidity".