AN607

Rev. 1.7

27

Humidity-Related Calculations

While the above expressions are physically based, they are difficult to solve and manipulate. Hence, many

approximate formulas have been developed. The two most common are the Antoine Equation and the Magnus

equation. Many of these formulas contain coefficients that can vary depending on their source, its age and, in some

cases, the context of the equations use.

Antoine Equation

This equation calculates saturation vapor pressure. Additionally; coefficients are available for this equation for a

wide variety of vapors other than water. The coefficients used in the following equation are for an air-water system

and are optimized for use over the temperature range 0 to 100 °C.

Magnus Equation

This equation calculates saturation vapor pressure as does the Antoine Equation. It has the advantage that it can

Where:

–2

T is temperature in °C

Over the range of –40 to +50 °C, the best fit constants are as follows:

For air with a vapor pressure P’, the dew point is defined as the temperature at which the water vapor would be

saturated. Thus,

Utilizing the relationship

Reference

17.625

243.04

610.94

Alduchov, Oleg A., Robert E. Eskridge, 1996: Improved Magnus Form

Approximation of Saturation Vapor Pressure. J. Appl. Meteor., 35, 601–609

p

s

23.19

3830

T

44.83

–

------------------------

–





exp

=

t

dp

3830

23.19

Ps



ln

–

--------------------------------------

44.83

+

=

Where:

Pressure in Pascals Nm

2

–



Temperature in °K (°C + 273.15)

P

sC

1

e

A1T

B

1

T

+

-----------------





=

T

d

B

1

In

P



C

1

-------





A1

P



C

1

-------





ln

–

--------------------------------



=