Steve Gribble ·

*gribble [at] gmail [dot] com*

#### Air density calculator

This air density calculator lets you estimate rho. Rho is one of the parameters used in cycling power models, specifically when estimating aerodynamic drag forces.

To use this page, you need to provide the calculator with three parameters: air temperature, air pressure, and dew point. You should be able to look up these three parameters for your region from most weather web sites.

**Units**: metric imperial

**Environmental parameters**

Air pressure (hPa)

Dew point (°C)

**rho**(kg/m^{3}) =

**rho**(lb/f^{3}) =#### Air density equations

Air contains a mixture of dry air and water vapor. The amount of water vapor is a function of the relative humidity; it is also related to the dew point temperature of the air. To calculate the density of air, you need to calculate the partial pressure of the dry air and the partial pressure of the water vapor; as it turns out, you can calculate these using measurements of air temperature, air pressure, and dew point temperature as inputs.

First, let's calculate the pressure of water vapor in the
air. The pressure of water vapor is equal to the saturation
pressure of water vapor at the dew point temperature. In
other words, given the dew point temperature (in degrees
Celsius), we need a way to calculate the saturation vapor
pressure **E _{s}** (hPa) at that dew point
temperature. (Another name for a hectoPascal is a millibar,
so 1 hPa = 1 mb.) A very accurate equation for
calculating

**E**was developed by Herman Wobus:

_{s}**E**(hPa) =

_{s}**e**/

_{so}**p**(1)

^{8}where:

**e**= 6.1078

_{so}**p**= c

_{0}+

**T**(c

_{1}+

**T**(c

_{2}+

**T**(c

_{3}+

**T**(c

_{4}+

**T**(c

_{5}+

**T**(c

_{6}+

**T**(c

_{7}+

**T**(c

_{8}+

**T**(c

_{9}) ) ) ) ) ) ) )

**T**= air temperature (degrees Celsius)

c

_{0}= 0.99999683

c

_{1}= -0.90826951 · 10

^{-2}

c

_{2}= 0.78736169 · 10

^{-4}

c

_{3}= -0.61117958 · 10

^{-6}

c

_{4}= 0.43884187 · 10

^{-8}

c

_{5}= -0.29883885 · 10

^{-10}

c

_{6}= 0.21874425 · 10

^{-12}

c

_{7}= -0.17892321 · 10

^{-14}

c

_{8}= 0.11112018 · 10

^{-16}

c

_{9}= -0.30994571 · 10

^{-19}

Given this, the pressure of water vapor **P _{v}** is
found by using the dew point temperature

**T**(C) as

_{dewpoint}**T**in equation (1). So, we get:

**P**(hPa) =

_{v}**E**at

_{s}**T**(2)

_{dewpoint} Next, we need to calculate the pressure of dry air
**P _{d}**, given the measured air pressure

**P**from a weather report and the water vapor pressure

**P**calculated from equation (2). The measured air pressure

_{v}**P**is the sum of the pressures of dry air

**P**and water vapor

_{d}**P**. Rearranging, we get:

_{v}**P**(hPa) =

_{d}**P**(hPa) —

**P**(hPa) (3)

_{v}Now that we know

**P**and

_{v}**P**, we're ready to calculate the air density

_{d}**Rho**(kg/m

^{3}). The density is:

**Rho**(kg/m

^{3}) = (

**P**/ (

_{d}**R**·

_{d}**T**)) + (

_{k}**P**/ (

_{v}**R**·

_{v}**T**)) (4)

_{k}where:

**P**(hPa) is from equation (2)

_{v}**P**(hPa) is from equation (3)

_{d}**R**is 461.4964

_{v}**R**is 287.0531

_{d}**T**is measured temperature in degrees Kelvin, i.e., measured temperature

_{k}**T**(Celsius) + 273.15

Credits go to Richard Shelquist's page on an introduction to air density for the details behind these equations!