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# How do I convert between dew point and relative humidity?

## Units for saturation and condensation

The dew point, or dew-point temperature, is the temperature at which dew, or condensation, forms as you cool a gas. Where the condensate is ice, this is known as the frost point.

The relative humidity is the ratio of the amount of water vapour, e, in the air to the amount of water vapour, es, that would be in the air if saturated at the same temperature and pressure. It can be expressed

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

Unfortunately, there is no simple, direct formula for converting 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.

### 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

• Use Equation 2 or 3 below (or Equation 4 or 5 for greater accuracy) to find the 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 Equation 4 or 5) to calculate dew or frost point temperature from vapour pressure (requires iteration if using Equations 4 or 5).

Vapour pressure can be calculated using the Magnus formula. This states that at a temperature t (in °C), the saturation vapour pressure ew(t), in pascals (Pa), over liquid water, is

ln ew(t) = ln 611.2 + (17.62 t)/(243.12+t)        (Equation 2)

For information, 100 Pa = 1 millibar (mbar)

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

Over ice, ei(t) is

ln ei(t) = ln 611.2 + (22.46 t)/(272.62+t)          (Equation 3)

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

### And in more detail…

This is a more accurate but complex alternative formula for vapour pressure (in pascals) from dew point (in kelvin) for water:

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

and for ice:

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

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

The uncertainties associated with these equations are:

• < 0.01 % of value, for water from 0 °C to +100 °C
• < 0.6 %, for supercooled water below 0 °C down to -50 °C
• < 1.0 % 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 % of value.

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