Sound Speed in Seawater Calculator (Mackenzie)
Find the speed of sound in seawater from temperature, salinity and depth, then the wavelength at your frequency and the travel time over your distance.
🔊 What is the Speed of Sound in Seawater?
The speed of sound in seawater is how fast a pressure wave travels through the ocean. It is about 1500 m/s, more than four times faster than sound in air, and it is not a constant. It rises with temperature, with salinity and with pressure (and so with depth). Because those three properties vary from place to place and from the surface to the seabed, the ocean has a whole range of sound speeds, typically between about 1450 and 1550 m/s. This calculator evaluates the nine-term Mackenzie (1981) equation, a widely used empirical formula that turns temperature, salinity and depth into a sound speed.
Sound speed matters whenever anyone measures or communicates underwater. Echo sounders convert a round-trip delay into water depth, sonar systems convert delay into range, acoustic positioning systems triangulate divers and vehicles, and bathymetric surveys correct every beam for the sound speed profile. Marine biologists use it to predict how far whale calls and ship noise travel, and navies use it to model how sound refracts and where it can be heard or hidden. Oceanographers also use acoustic travel times over basin scales to estimate average ocean temperature, a technique called acoustic thermometry.
Two features of the ocean make the profile interesting. Near the surface, temperature falls quickly with depth through the thermocline, so sound speed falls. Deeper down the temperature is nearly constant at a few degrees Celsius and pressure keeps increasing, so sound speed rises again. The depth where the two trends balance is the sound speed minimum, known as the sound channel or SOFAR axis, often near 1000 m. Sound waves bend toward lower speed, so energy launched near the axis is trapped and can travel for thousands of kilometres. The depth chart in the calculator shows this idea with an illustrative thermocline. It is not measured data and your real profile will differ.
A common misconception is that saltier or colder water always means slower sound. In fact, salinity increases the speed, cooling reduces it, and depth increases it, so the three effects must be combined. Another is that the equation works everywhere. It does not: Mackenzie fitted it for 2 to 30 °C, 25 to 40 ppt and 0 to 8000 m, and the calculator warns you when an input leaves that range. For the related density of the same water, see the seawater density calculator, and for sound in other media see the speed of sound calculator.
📐 Formula
The equation is an empirical least-squares fit, not a derivation from first principles. Its standard error is about 0.07 m/s against the data it was fitted to, which is far smaller than the uncertainty of a typical field measurement of temperature and salinity.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Mackenzie Check Value
T = 25 °C, S = 35 ppt, D = 1000 m, f = 10 kHz, X = 1000 m
Example 2 — Cool Surface Water Survey
T = 10 °C, S = 35 ppt, D = 0 m, f = 12 kHz, X = 5000 m
Example 3 — Cold Deep Water at 4000 m
T = 2 °C, S = 35 ppt, D = 4000 m, f = 3 kHz, X = 10000 m
Example 4 — Warm Shallow Sea with a 200 kHz Sonar
T = 28 °C, S = 33 ppt, D = 50 m, f = 200 kHz, X = 300 m
❓ Frequently Asked Questions
🔗 Related Calculators
What is the speed of sound in seawater?
About 1500 m/s on average, which is roughly 5400 km/h. It ranges from about 1450 m/s in cold polar water to about 1545 m/s in warm tropical water, and rises with temperature, salinity and depth.
What is the Mackenzie equation for sound speed?
It is a nine-term empirical formula published by K. V. Mackenzie in 1981 that gives sound speed c in m/s from temperature T in degrees C, salinity S in ppt and depth D in metres. It reproduces measured sound speeds to a few tenths of a metre per second within its range.
How does temperature affect the speed of sound in water?
Warmer water is less dense and less compressible in the acoustic sense, so sound speeds up. Near 10 C and 35 ppt the gradient is about 3.6 m/s per degree C, falling to about 2.4 m/s per degree C near 25 C.
How does salinity affect sound speed?
The speed rises by about 1.2 to 1.3 m/s per unit of salinity near 0 to 10 C and about 1.08 m/s per unit near 25 C. The effect is small in the open ocean but matters in estuaries and near ice melt.
Why does sound speed increase with depth?
Pressure increases the stiffness of water. In the Mackenzie equation the depth term adds about 16.3 to 17.6 m/s for every kilometre of depth, so deep water can carry sound faster even though it is colder.
What is the SOFAR channel?
The Sound Fixing and Ranging channel is a layer where sound speed reaches its minimum, typically near 1000 m depth at mid latitudes. Sound waves bend toward the minimum, so low frequency sound can travel thousands of kilometres trapped in this waveguide.
How do I calculate acoustic wavelength underwater?
Divide the sound speed by the frequency. At 1500 m/s a 10 kHz signal has a wavelength of about 0.15 m, and a 100 Hz signal has a wavelength of about 15 m. The wavelength sets the size of objects a sonar can resolve.
How do I find the travel time of sound over a distance?
Divide the distance by the sound speed. Over 1000 m at 1550 m/s the one-way time is about 0.645 s. Echo sounders and sonars use the round-trip time, which is twice that, to convert a measured delay back into range or depth.
Is the Mackenzie equation valid in the deep ocean?
Published validity limits differ slightly by source: the NPL guide gives 2 to 30 C, 25 to 40 ppt and 0 to 8000 m, while the paper's abstract gives -2 to 30 C, 30 to 40 ppt and 0 to 8000 m. This calculator warns outside the NPL range, which covers nearly the whole open ocean. Hadal trenches below 8000 m and water colder than 2 C are outside the range and give extrapolated values.
How does Mackenzie compare with the Chen and Millero or Del Grosso equations?
All three are empirical fits to measured data. Mackenzie is popular because it needs only temperature, salinity and depth and has a short form. Differences between the equations are typically below about 0.5 m/s in the normal ocean range.
Should I use depth or pressure in this calculator?
This calculator uses geometric depth in metres, as in the original Mackenzie equation. Pressure in decibars is numerically close to depth in metres, with a difference of a few percent that depends on latitude and density.