What does wave energy density mean?

Energy density E (in J/m²) is the total mechanical energy — potential plus kinetic — stored in the wave per unit horizontal area of the sea surface. For a regular sinusoidal wave E = ρgH²/8. It is also called specific energy or energy per unit plan area.

What is wave power per meter of crest?

Wave power P (in W/m) is the rate at which energy passes through a vertical plane of unit width aligned with the wave crest. It equals E × cg, where cg is the group velocity. Real sea states use the significant wave height Hs and energy period Te: P = ρg²Hs²Te / (64π).

What is the difference between phase speed and group velocity?

Phase speed c = λ/T is the speed at which individual wave crests travel. Group velocity cg is the speed at which wave energy (and a wave packet envelope) propagates. In deep water cg = c/2; in very shallow water cg = c (they are equal). This calculator uses the exact linear-theory formula for intermediate depths.

How accurate is this calculator for real ocean waves?

The formulas assume linear (small-amplitude) regular sinusoidal waves. Real ocean waves are irregular and slightly nonlinear. For resource assessment, replace H with the significant wave height Hs and use the energy period Te as the period input — the result then approximates the mean power of the sea state.

What water density should I use?

Use 1025 kg/m³ for typical seawater (salinity ~35 ppt at 15 °C). Use 1000 kg/m³ for fresh water (lakes, rivers). Density varies slightly with temperature and salinity but 1025 is the standard ocean engineering default.

What is the deep-water approximation?

When depth d > λ/2 (roughly), water depth does not affect wave behavior. The dispersion relation simplifies to ω² = gk, giving c = gT/(2π) and cg = gT/(4π). This calculator uses the exact dispersion relation, so entering a large depth gives the deep-water result automatically.

Wave Energy Calculator

Enter wave height, period, and water density to compute wave energy density and wave power per meter of wave crest.

Wave Parameters

Wave Height, H (m) crest-to-trough

Presets:

Wave Period, T (s) time between crests

Presets:

Water Depth, d (m) use ≥ 200 for deep water

Presets:

Water Density, ρ (kg/m³)

Results

Enter values and click Calculate

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Summary

Enter wave height, period, and water density to compute wave energy density and wave power per meter of wave crest.

How it works

Enter the significant wave height H in meters (crest-to-trough height).
Enter the wave period T in seconds (time between successive crests).
Enter the water depth d in meters (use a large value, e.g. 1000 m, for deep-water approximation).
Optionally adjust water density (default 1025 kg/m³ for seawater, 1000 for fresh water).
Click Calculate to get energy density (J/m²) and wave power per meter of crest (W/m or kW/m).
The calculator also displays wavelength, phase speed, and group velocity for reference.

Use cases

Estimate harvestable power from ocean waves for a wave energy converter (WEC).
Compare energy potential between different sea states in coastal engineering.
Verify physics homework or exam problems on wave mechanics.
Assess wave load on offshore structures by understanding energy flux.
Evaluate wave resource maps against first-principles calculations.
Teach linear wave theory in oceanography or coastal engineering courses.
Convert buoy-measured wave data (Hs, Tp) into power estimates.

Frequently Asked Questions

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

Wave Energy Calculator

Use the Wave Energy Calculator

Wave Parameters

Results

Formula Reference

Summary

How it works

Use cases

Frequently Asked Questions