This guide provides current information and equations for calculating the speed of sound in sea water as a function of temperature, salinity, pressure (or depth) and latitude, as well as a calculator for converting between pressure and depth.

To use the calculator below, enter the values of water temperature, salinity and either pressure or depth, if you wish to use the NPL Equation you will need to enter latitude. The values for the speed of sound are calculated automatically. The five alternatives are derived using equations from the sources specified.

Temperature (Celsisus), T  
Salinity (Parts per thousand), S  
Pressure (kPa) P or Depth (m), D
Latitude (Degrees) Φ

Mackenzie Equation A function of T, S and D
Coppens Equation A function of T, S and D
UNESCO Equation* A function of T, S and P
Del Grosso’s Equation* A function of T, S and P
NPL Equation A function of T, S, D and Φ

*The UNESCO and Del Grosso equations used above are the versions reformulated by Wong and Zhu in 1995 in order to bring them in line with the 1990 International Temperature Scale

For further details on the sound speed equations please read the following page on the underlying physics. Alternatively click on the equations listed above in order to skip to the relevant sections

Range of validity

Equation Temperature (Celsius), T Salinity (parts per thousand), S Pressure kPa Depth m
Mackenzie 2 - 30 25 - 40 - 0 - 8000
Coppens 0 - 35 0 - 45 - 0-4000
(0 - 4km
UNESCO 0 - 40 0 - 40 0 - 100000
(0 - 1000 Bar)
-
Del Grosso 0 - 30 30 - 40 0 - 98066
(0 - 1000 kg/cm2)
-
NPL *

*The NPL equation was developed to be valid for use in any ocean or sea conditions found on earth with a salinity below 42‰.

Conversion Between Pressure and Depth

Both the UNESCO equation and Del Grosso’s equation use pressure as a variable instead of depth because they are based on measurements made in a small laboratory’s pressurised chamber. Use the calculator below to convert between these two variables.

Further information can be found on the page underlying physics.

Latitude (degrees) Φ
Pressure (kPa) Depth (m)
Depth (m) Φ Pressure (kPa)

A list of references can be found on the page underlying physics.

Any comments or suggestions about further speed of sound equations?

Please contact Stephen Robinson or Ben Ford

HSE
 
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