Why are seawater and pure water evaluated using separate models?

Empirical polynomials are validated only within their published domains. The Mackenzie (1981) equation is documented for marine salinities of 25–40 ppt, so this tool does not silently extrapolate it to fresh water. Pure water at atmospheric pressure instead uses Lubbers & Graaff (1998).

What are the published validity limits for the Mackenzie (1981) model?

According to UK National Physical Laboratory (NPL) guides, Mackenzie (1981) is valid for temperatures of 2 to 30 °C, salinities of 25 to 40 ppt (parts per thousand), and depths of 0 to 8,000 metres.

What are the validity limits for the Lubbers & Graaff (1998) equation?

Lubbers & Graaff (1998) is formulated as c = 1404.3 + 4.7T − 0.04T² for pure water at atmospheric pressure across 15 to 35 °C, reporting agreement within 0.20 m/s.

What conversion factors are used for velocity units?

Conversions follow NIST Special Publication 811: 1 ft = 0.3048 m (1 m/s = 3.2808399 ft/s), 1 statute mile = 1609.344 m (1 m/s ≈ 2.2369363 mph), 1 knot = 1852/3600 m/s (1 m/s ≈ 1.9438445 kn), and 1 m/s = 3.6 km/h exactly.

Sound Speed in Water Calculator

Calculate the speed of sound in seawater (Mackenzie 1981) or pure water (Lubbers & Graaff 1998) in m/s, ft/s, mph, km/h, and knots.

Acoustic Medium & Parameters

Select an evidence-backed model within its published domain.

Temperature Scale

Depth Scale

Temperature (°C) 2.0 to 30.0 °C

Salinity (ppt) 25.0 to 40.0 ppt

Open-ocean standard: 35.0 ppt (parts per thousand by mass).

Depth (m) 0 to 8,000 m

0 represents atmospheric ocean surface level.

Validated Reference Presets

Calculated Sound Speed Mackenzie (1981)

SI Velocity (m/s)

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Feet / second —

Miles / hour (mph) —

Kilometres / hour —

Knots (nmi/h) —

Model Term Breakdown Δ (m/s)

Factual Model Boundaries & Provenance

Mackenzie (1981): Documented for seawater acoustics over T ∈ [2, 30] °C, S ∈ [25, 40] ppt, and D ∈ [0, 8000] m. Empirical-model uncertainty remains application dependent.

Unit conversions per NIST SP 811: 1 ft = 0.3048 m, 1 mi = 1609.344 m, 1 nmi = 1852 m.

Sources: UK NPL seawater equations, Lubbers & Graaff pure-water study, and NIST conversions.

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Summary

Calculate the speed of sound in seawater (Mackenzie 1981) or pure water (Lubbers & Graaff 1998) in m/s, ft/s, mph, km/h, and knots.

How it works

Select the medium: Seawater (Mackenzie 1981) or Pure Water (Lubbers & Graaff 1998).
Choose preferred input units for temperature (°C or °F) and depth (metres or feet).
Enter water parameters within verified published validity intervals.
Review velocity outputs across m/s, ft/s, mph, km/h, and knots (NIST SP 811 conversion factors).
Inspect individual mathematical term contributions and published model boundaries.

Use cases

Calibrate marine acoustic modems, echo sounders, and hydrophone arrays in verified seawater regimes.
Determine acoustic reference velocity for pure-water laboratory ultrasound and medical transducer calibration.
Convert between metric and imperial acoustic speeds for naval, commercial diving, or bathymetric reports.
Demonstrate the competing effects of thermal expansion, salinity, and hydrostatic compression in physical oceanography.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu