Deep Water Wave Speed Calculator

About this calculator

For ocean or lake waves traveling in water deeper than about half their wavelength — the “deep water” regime — the seafloor has no effect on wave motion, and the wave’s phase speed depends only on gravity and wavelength: c = √(gL/2π), with the period following as T = c/L = √(2πL/g). This is the linear (Airy) wave theory result for gravity waves, the dominant restoring force at these scales (surface tension only matters for much shorter ripples).

Oceanographers and coastal engineers use this relationship to predict how swell generated far offshore will arrive at a coastline, and it’s the same physics behind surf forecasting models that translate open-ocean wavelength and period into expected wave speed. Naval architects also rely on it when estimating how a vessel’s wake or a storm swell’s energy will propagate — enter a wavelength in metres and the calculator returns both the phase speed and period.