Wave Energy and Power Calculator
Find the energy density and the power per meter of wave crest from height, period and water depth, and see how it compares with wave energy resource levels.
⚡ What is Wave Energy and Power?
Wave energy is the mechanical energy stored in the motion of ocean surface waves, and wave power is the rate at which that energy is carried past a line in the sea. A passing wave stores energy in two equal parts: the potential energy of the raised crests and lowered troughs, and the kinetic energy of the circulating water beneath them. Per square meter of sea surface this adds up to the energy density E = ρgH²/8 for a regular wave of height H. The energy does not stay put. It travels with the wave group at the group speed cg, so the power crossing one meter of crest is P = E cg, measured in watts per meter or, more usually, kilowatts per meter (kW/m).
This number is the standard way to describe a wave energy resource and to size wave energy converters. Developers compare coastlines by their annual mean power in kW/m, coastal and offshore engineers use the extreme values to design moorings and platforms, and forecasters use it to describe how much punch an approaching swell carries. A calm 0.5 m sea might carry under 1 kW/m, a typical North Atlantic swell some 40 kW/m, and a severe storm several hundred kW/m. Because power rises with the square of the height, large waves dominate the energy budget, which is why the resource and the survival loads are so far apart.
Two points are often confused. First, the wave height convention matters. Forecasts and buoys report the significant wave height Hs, and for a random sea the energy density is ρgHs²/16, half of what the regular-wave formula gives with the same number. This calculator lets you choose either. Second, the period that belongs in the power formula is the energy period Te, not the peak period Tp. For typical spectra Te is about 90 percent of Tp, so using Tp overstates the power by about 10 percent.
The calculator solves the full linear dispersion relation for your water depth, so it works from the open ocean to a shallow shelf. It shows the deep-water shortcut next to the exact answer, classifies the energy flux level, and draws two charts so you can see how the power responds to height and period. To explore the underlying wave speeds in more detail, use the ocean wave speed calculator.
📐 Formula
The classification of the resource follows common practice: below 10 kW/m is low, 10 to 30 kW/m is moderate, 30 to 50 kW/m is high, and above 50 kW/m is very high. These are the dashed reference lines on both charts.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — North Atlantic Swell
Hs = 3 m, T = 10 s, h = 1000 m, ρ = 1025 kg/m³
Example 2 — Calm Sea
Hs = 0.5 m, T = 6 s, h = 100 m, ρ = 1025 kg/m³
Example 3 — Severe Storm
Hs = 8 m, T = 14 s, h = 200 m, ρ = 1025 kg/m³
Example 4 — Shallow Coast
Hs = 1.5 m, T = 9 s, h = 8 m, ρ = 1025 kg/m³
Example 5 — Regular Wave Height Convention
H = 2 m (regular), T = 8 s, h = 500 m, ρ = 1025 kg/m³
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate wave power per meter of wave crest?
Compute the energy density E = rho g H^2 / 8 (or rho g Hs^2 / 16 for significant wave height), then multiply by the group speed cg from the linear dispersion relation. P = E cg is in watts per meter of crest. In deep water cg = gT/(4 pi), which gives P = rho g^2 H^2 T / (32 pi).
What is the formula for wave energy density?
For a regular wave of height H, the total energy per unit sea surface area is E = rho g H^2 / 8, in J/m2, half kinetic and half potential. For a random sea described by the significant wave height Hs, E = rho g Hs^2 / 16, because Hs is about twice the amplitude of the typical wave.
Why is wave power measured in kW per meter?
Wave energy travels in a direction, so the natural quantity is the energy flux through a vertical plane one meter wide, parallel to the wave crest. This is power per unit length of crest, in W/m or kW/m. Multiply by the crest length of a device or coastline to get the total power.
What is the deep-water wave power rule of thumb?
For significant wave height Hs in meters and energy period Te in seconds, P is about 0.49 Hs^2 Te kW/m in seawater. For a regular wave height H it is about 0.98 H^2 T kW/m. A 3 m, 10 s sea therefore carries roughly 44 kW/m.
How much wave power is a good wave energy resource?
Annual mean wave power above about 30 kW/m is generally considered a strong resource, and the best coasts, such as western Ireland, Scotland, Chile and southern Australia, average 40 to 70 kW/m. Most sheltered coasts and seas average below 10 kW/m.
What is the difference between Hs and Hrms for wave energy?
Hs is the mean of the highest third of waves, about 4 times the standard deviation of the surface elevation, and Hrms is the root-mean-square wave height. For a Rayleigh distribution Hs = sqrt(2) Hrms. Energy density is rho g Hrms^2 / 8, which equals rho g Hs^2 / 16.
Does water depth change wave power?
Yes, through the group speed. For a given local wave height, cg rises from half the phase speed in deep water toward sqrt(gh) in shallow water, so the energy flux per meter rises as the water shoals. In practice the height also changes by shoaling, refraction and breaking, so power stays roughly constant until dissipation sets in.
Which wave period should I use, peak period or energy period?
The energy period Te, also written Tm-1,0, is the correct period for wave power in a random sea. It is usually 0.85 to 0.95 of the peak period Tp. If you only have Tp, multiplying by 0.9 gives a reasonable estimate of Te.
How much power does a storm wave carry?
A severe North Atlantic storm with Hs of 8 m and a 14 s period carries about 440 kW/m, ten times a typical 3 m, 10 s swell. This extreme power is why wave energy devices must survive loads far above what they are designed to harvest.
Does water density matter for wave power?
Power is directly proportional to density. Seawater at 1025 kg/m3 carries about 2.5 percent more wave power than fresh water at 1000 kg/m3 for the same wave. The default of 1025 kg/m3 suits open ocean water of typical salinity.
Is linear wave theory accurate for wave power?
Linear (Airy) theory is accurate for small to moderate steepness and gives power estimates within a few percent for typical sea states. For very steep or breaking waves, and for the real directional spectrum, nonlinear and spectral methods give somewhat different results.