Marine Sound Propagation Calculator
Calculate the speed of sound in seawater from temperature, salinity, and depth using the Mackenzie equation.
About this calculator
This calculator estimates the speed of sound in seawater from Water Temperature, Salinity, and Depth using the Mackenzie (1981) equation, the practical nine-term polynomial oceanographers and sonar engineers use in place of the far more complex full acoustic equation of state. Speed of Sound is the headline result, and all three inputs push it upward as they increase across this calculator's declared ranges -- though which one matters most shifts depending on where you sit in those ranges, since the formula mixes linear, quadratic, and cross terms between temperature and depth. Depth doubles as a pressure proxy, the way it does throughout this calculator's oceanography hub, because the added weight of overlying water measurably speeds sound transmission.
Est. SOFAR Channel Depth is a rough heuristic, not a direct calculation from a real vertical profile: it estimates where the sound-speed minimum -- the "sound fixing and ranging" channel that lets whale calls and explosive charges travel thousands of kilometers with little loss -- sits, based only on how far Water Temperature departs from a typical deep-ocean value near 4°C, so it does not respond to Salinity or Depth at all. Absorption at 1 kHz and the Transmission Loss it feeds are computed for a fixed reference frequency and a fixed 1 km range using a simplified Francois-Garrison-style formula; the real absorption mechanism also depends on temperature, depth, and pH through chemical relaxation frequencies that this simplified version omits, so those two outputs hold constant no matter what you enter for Water Temperature, Salinity, or Depth.
Inputs
Results
Speed of Sound
1,491.44 m/s
Figures current as of 1981. Source: Kenneth V. Mackenzie, "Nine-term equation for sound speed in the oceans," Journal of the Acoustical Society of America, vol. 70, no. 3, pp. 807-812 (1981) — the practical empirical polynomial in temperature, salinity, and depth that this calculator's Speed of Sound output reproduces exactly.
How to Use This Calculator
- Enter Water Temperature, Salinity, and Depth.
- Review the Speed of Sound (m/s) result.
- Use Absorption at 1 kHz (dB/km) and Transmission Loss (1 km) (dB) to inform your decision.
How the result changes with Salinity
| Salinity | Speed of Sound |
|---|---|
| 18 | 1,470.4 m/s |
| 26 | 1,480.3 m/s |
| 42 | 1,500.1 m/s |
What each input means
- Water Temperature
- In-situ water temperature in degrees Celsius. Sound speed increases ~4.5 m/s per °C.
- Salinity
- Practical Salinity Units. Sound speed increases ~1.3 m/s per PSU increase.
- Depth
- Water depth in meters. Pressure increases sound speed ~1.6 m/s per 100 m depth.
How this is calculated
Worked example, using the default values
- Identify Input ParametersWater Temperature = 10, Salinity = 35, Depth = 100 = 3 input(s) provided
- Calculate Speed of SoundSpeed of Sound1491.44 = 1491.44
- Calculate Absorption at 1 kHzAbsorption at 1 kHz0.06 = 0.06
- Calculate Transmission LossTransmission Loss60.1 = 60.1
Figures and sources
- Mackenzie nine-term equation for speed of sound in seawater (1981) — Kenneth V. Mackenzie, "Nine-term equation for sound speed in the oceans," Journal of the Acoustical Society of America, vol. 70, no. 3, pp. 807-812 (1981) — the practical empirical polynomial in temperature, salinity, and depth that this calculator's Speed of Sound output reproduces exactly.
Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does sound travel faster as Water Temperature rises?
Across this calculator's full -2°C to 35°C range, raising Water Temperature raises Speed of Sound at any fixed Salinity and Depth -- warmer water is more compressible in a way that lets pressure waves propagate faster, which the Mackenzie equation's temperature terms capture empirically. This is why tropical surface water carries sound noticeably faster than the same water mass would at polar temperatures, all else being equal.
Does Depth or Salinity matter more for Speed of Sound?
Neither one dominates uniformly. Over this calculator's full ranges, Depth (0-11,000 m) and Water Temperature can each shift Speed of Sound by well over 100 m/s at the extremes, while Salinity's 0-42 PSU range contributes a smaller swing on its own -- so which input matters most depends on where you are in the range, not on a single fixed ranking.
Why doesn't Est. SOFAR Channel Depth change when I adjust Salinity or Depth?
That's intentional, not a bug: this output is a simplified heuristic that estimates the sound channel axis purely from how far Water Temperature departs from about 4°C, since that's the dominant driver of where the sound-speed minimum sits in most open-ocean profiles. It does not read Salinity or Depth at all, so adjusting either one leaves this particular output unchanged while Speed of Sound itself still responds normally.
Is the Absorption at 1 kHz value affected by Water Temperature or Depth?
No -- it's computed for a fixed 1 kHz reference frequency using a simplified Francois-Garrison-style formula that, in this implementation, depends only on that fixed frequency. The real underwater-acoustics literature ties absorption to temperature, depth, and pH as well through chemical relaxation effects, so treat this output as a rough reference value rather than a site-specific measurement.
Is this the exact Mackenzie equation used in professional sonar work?
Yes -- the nine-term formula and all published 1981 Mackenzie coefficients, from Kenneth V. Mackenzie's paper in the Journal of the Acoustical Society of America (vol. 70, pp. 807-812), are reproduced exactly. The original equation was fitted and validated over 2-30°C, 25-40 PSU, and 0-8,000 m, while this calculator accepts a wider range (down to -2°C and out to 11,000 m), so values near or beyond those calibration bounds should be read as a reasonable extrapolation rather than a lab-verified figure.
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