Speed of Sound in Seawater Calculator (Mackenzie Equation, Echo Sounders and Sonar)
How fast sound travels in water of a given temperature, salinity and depth, the water depth that an echo time corresponds to and the error of a sounder fixed at 1500 m/s.
Results
The dashed line marks the value you entered.
What this tool does
Sound travels about 4.4 times faster in water than in air, near 1500 m/s, and the speed rises with temperature (roughly 3–4 m/s per °C), salinity and depth. Echo sounders convert the delay of an echo into depth using a set speed, typically 1500 m/s, so in cold or fresh water the depth they show is a little too large and in warm water too small. Mackenzie's equation is accurate to a fraction of a metre per second for temperatures from −2 to 30 °C, salinities from 25 to 40 and depths down to 8000 m.
Formula
c = 1448.96 + 4.591T − 5.304×10⁻²T² + 2.374×10⁻⁴T³ + 1.340(S − 35) + 1.630×10⁻²D + 1.675×10⁻⁷D² − 1.025×10⁻²T(S − 35) − 7.139×10⁻¹³TD³ (Mackenzie, 1981)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
tw | Water temperature | °C |
sa | Salinity (open-ocean water is about 35) | PSU |
dz | Depth | m |
te | Echo time of the sounder (there and back) | ms |
C | Speed of sound in the water | m/s |
ED | Depth from the echo | m |
ER | Error if the sounder assumes 1500 m/s | m |
XA | Times faster than sound in air (343 m/s) | — |
Worked example
- Water temperature15 °C
- Salinity (open-ocean water is about 35)35 PSU
- Depth100 m
- Echo time of the sounder (there and back)100 ms
- Speed of sound in the water1508.3 m/s
- Depth from the echo75.42 m
- Error if the sounder assumes 1500 m/s-0.42 m
- Times faster than sound in air (343 m/s)4.40
Limitations
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.