Density of Air-free Water

The Density of Air-free Water calculator computes the density of air-free water based on the temperature.

INSTRUCTIONS: Choose units and enter the following:

• (T) Temperature

Density of Water (ρ): The calculator returns the density in kilograms per cubic meter.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Density of Air-free water calculator uses the 1990 International Temperature Scale (ITS-90)¹  to compute air-free water's density at an input temperature and the standard pressure of 1 atmosphere.  The formula for the density of air-free water is:

            `ρ = (999.85308 + 6.32693E-2 * T - 8.523829E-3 * T^2 + 6.943248E-5 * T^3 - 3.821216E-7 * T^4) `

where:

• ρ = density of air-free water
• T = temperature

Note: The valid temperature range for this equation is between 5° and 40° Celsius.

Usage

In gravimetric calibrations of volume water is used as the calibrating fluid by dividing mass by density.  Therefore to perform precise calibration we must know the density of water precisely and its density's dependence on temperature.  This equation gives a very precise reformulation which has been compared to the 1975 formulation published by Kell²

If this equation is used as an Equation in an Equation (EIE) , it can be made a constant by specifying the input temperature as a constant in the EIE.  As NIST does for density at Standard temperature and pressure (STP), we assume the standard pressure is 1 atmosphere and the standard temperature as `20^o C`.  Therefore to use this high precision density equation to represent a standard density for water, use this equation as an EIE and set the single input as to the constant `20^o C`.  Note also that the output from this equation as an EiE will be in SI units.

Limits

The research done at NIST that resulted in the 4th degree polynomial in temperature verified accuracy of the densities across a limited range: `5^o C` to `40^o C`, so the range of this equation has the same temperature input range.

See Also

• Specific Weight of Water (SI) at STP
• Specific Weight of Water (US) at STP
• Density of Air-free Water

1. ^ Jones, Frank and Harris GeorgiaITS-90 Density of Water Formulation for
   Volumetric Standards Calibration, Journal of Research of the National Institute of Standards and Technology: Vol 97, Number 3, May-June 1992
2. ^ G. S. Kell, J. Chera. Eng. Data 20, 97 (1975).