What equation does this tool use?

The Mackenzie (1981) equation: c = 1448.96 + 4.591T − 0.05304T² + 0.0002374T³ + 1.340(S − 35) + 0.0163D + 1.675×10⁻⁷D² − 0.01025T(S − 35) − 7.139×10⁻¹³TD³, where T is temperature (°C), S is salinity (ppt), and D is depth (m). It is accurate to ±0.07 m/s for 0–30 °C, 25–40 ppt, and 0–8000 m.

Why does sound travel faster in warmer water?

Higher temperature increases molecular kinetic energy, which raises the bulk modulus of elasticity relative to density — the two factors that determine wave speed. A 1 °C rise adds roughly 4.5 m/s.

How does depth affect sound speed?

Increasing depth raises hydrostatic pressure, which compresses the water and increases its bulk modulus faster than its density rises, so sound speeds up. Below the SOFAR channel minimum (around 600–1000 m), speed increases by about 1.63 m/s per 100 m.

What is salinity in ppt?

Parts per thousand (ppt, or ‰) is the mass of dissolved salts per kilogram of water. Open-ocean seawater is typically 34–36 ppt; the Baltic Sea is 6–8 ppt; fresh lakes are near 0 ppt.

What is the SOFAR channel?

The Sound Fixing and Ranging (SOFAR) channel is a depth layer where sound speed reaches a local minimum (typically 800–1200 m). Sound refracts toward this minimum and can travel thousands of kilometers with little spreading loss — whales and navies both exploit it.

Is 1500 m/s a good rule of thumb?

Yes — 1500 m/s is a common engineering estimate for typical open-ocean conditions (around 15 °C, 35 ppt, shallow depth). For precise sonar work, always use the actual temperature–salinity–depth profile.

Sound Speed in Water Calculator

Name: Sound Speed in Water Calculator
Availability: InStock
Author: Nham Vu

Enter water temperature, salinity, and depth to compute the speed of sound using the Mackenzie (1981) equation.

Water Parameters

Temperature (°C)

Valid range: −2 to 35 °C

Salinity (ppt)

0 = freshwater · 35 = typical ocean · 40+ = hypersaline

Depth (m)

0 = surface · 8000 = deep ocean

Quick presets

Result

Speed of Sound

— m/s

— ft/s

Mackenzie term contributions

Mackenzie (1981) equation · accuracy ±0.07 m/s for 0–30 °C, 25–40 ppt, 0–8000 m

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Summary

Enter water temperature, salinity, and depth to compute the speed of sound using the Mackenzie (1981) equation.

How it works

Enter the water temperature in degrees Celsius (0–30 °C is the typical ocean range).
Enter salinity in parts per thousand (ppt). Use 0 for freshwater, 35 for typical open-ocean seawater.
Enter depth in meters (0 at the surface, up to ~8,000 m for deep ocean trenches).
The calculator applies the Mackenzie (1981) nine-term polynomial to compute sound speed.
Results update instantly in both m/s and ft/s with a breakdown of each term's contribution.

Use cases

Calibrate sonar and hydrophone systems for a specific water column.
Estimate acoustic travel time for underwater ranging and positioning.
Study how thermoclines and haloclines affect sonar performance.
Compute sound speed profiles for oceanography coursework or research.
Verify manufacturer specs for underwater acoustic modems.
Plan dive or ROV missions in waters with known temperature/salinity profiles.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu