Ocean Wave Calculator (Wavelength, Speed and Power)
Wavelength, speed, group speed and power of ocean waves from their period, the water depth and the wave height, solving the full dispersion relation.
Results
What this tool does
In deep water a wave's length and speed depend only on its period — a 10-second swell is about 156 m long and travels at about 56 km/h — but as the water gets shallower than half a wavelength the bottom slows it down, the wave shortens and steepens, and that is what makes it break. Swell energy travels at the group speed, half the wave speed in deep water, which is why surf forecasts track it. Power is per metre of crest, using linear wave theory, so it is an estimate for steep or breaking waves.
Formula
ω² = g k tanh(k h) · L = 2π ÷ k · c = L ÷ T · c_g = c ÷ 2 × (1 + 2kh ÷ sinh 2kh) · P = ρ g H² ÷ 8 × c_g
Variables
| Symbol | Meaning | Unit |
|---|---|---|
tp | Wave period | s |
hw | Water depth | m |
hh | Wave height (crest to trough) | m |
L | Wavelength | m |
C | Wave speed | m/s |
CG | Group speed (how fast the energy travels) | m/s |
P | Wave power per metre of crest | kW/m |
L0 | Wavelength in deep water | m |
RG | Water depth regime | — |
Worked example
- Wave period10 s
- Water depth20 m
- Wave height (crest to trough)1.5 m
- Wavelength121.2 m
- Wave speed12.12 m/s
- Group speed (how fast the energy travels)9.27 m/s
- Wave power per metre of crest26.2 kW/m
- Wavelength in deep water156.1 m
- Water depth regimeIntermediate depth — the wave feels the bottom
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.