The computational cyclist

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

Temperature (°C)
Air pressure (hPa)
Dew point (°C)

rho (kg/m3) =
rho (lb/f3) =

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 Es (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 Es was developed by Herman Wobus:

Es (hPa) = eso / p8        (1)
eso = 6.1078
p = c0 + T (c1 + T (c2 + T (c3 + T (c4 + T (c5 + T (c6 + T (c7 + T (c8 + T (c9) ) ) ) ) ) ) )
T = air temperature (degrees Celsius)
c0 = 0.99999683
c1 = -0.90826951 · 10-2
c2 = 0.78736169 · 10-4
c3 = -0.61117958 · 10-6
c4 = 0.43884187 · 10-8
c5 = -0.29883885 · 10-10
c6 = 0.21874425 · 10-12
c7 = -0.17892321 · 10-14
c8 = 0.11112018 · 10-16
c9 = -0.30994571 · 10-19

Given this, the pressure of water vapor Pv is found by using the dew point temperature Tdewpoint (C) as T in equation (1). So, we get:

Pv (hPa) = Es at Tdewpoint        (2)

Next, we need to calculate the pressure of dry air Pd, given the measured air pressure P from a weather report and the water vapor pressure Pv calculated from equation (2). The measured air pressure P is the sum of the pressures of dry air Pd and water vapor Pv. Rearranging, we get:

Pd (hPa) = P (hPa) — Pv (hPa)        (3)

Now that we know Pv and Pd, we're ready to calculate the air density Rho (kg/m3). The density is:

Rho (kg/m3) = (Pd / (Rd · Tk)) + (Pv / (Rv · Tk))        (4)

Pv (hPa) is from equation (2)
Pd (hPa) is from equation (3)
Rv is 461.4964
Rd is 287.0531
Tk is measured temperature in degrees Kelvin, i.e., measured temperature T (Celsius) + 273.15

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