Wave Period Calculator

Wave period is the time between successive crests passing a fixed point, and it is the one wave property that survives propagation almost unchanged. Inverting the dispersion relation for deep water gives T = sqrt(2 pi L / g), so a 100 m wavelength corresponds to an 8.0 s period and a 156 m wavelength to 10.0 s. In shallow water T = L / sqrt(g d) applies instead. The ratio d/L governs the switch: above 0.5 the seabed is out of reach and the deep-water form holds, below 0.05 depth controls everything, and the band between requires the full tanh solution. Frequency f = 1/T and angular frequency omega = 2 pi / T follow directly. Ocean wind seas typically run 3 to 8 s, while long swell from distant storms reaches 14 to 20 s. Steepness H/L sets stability. The theoretical limiting steepness for deep-water waves is about 1/7, or 0.142, derived by John Henry Michell in 1893 from the Stokes condition that the crest angle cannot fall below 120 degrees; real seas break well before this, and steepness above about 0.05 already indicates a rough, whitecapping surface. For wind-generated seas the calculator also applies the fetch-limited JONSWAP growth laws, in which height and period both increase with the product of wind speed and fetch, so a 15 m/s wind over 200 km builds roughly a 3 m sea with a period near 7 s. These relations assume steady wind, unlimited duration and deep water, and a real record holds a spectrum of periods, not one value.

The period-wavelength relationship comes from the linear water wave theory George Biddell Airy set out in his 1841 treatise Tides and Waves, which produced the dispersion relation and its deep and shallow limits. John Henry Michell computed the limiting steepness of the highest progressive gravity wave in 1893, obtaining the familiar one-in-seven ratio consistent with the 120 degree crest angle George Gabriel Stokes had deduced. For most of the nineteenth century, wave period was recorded by eye and stopwatch from piers and ships, and observational catalogues of period and height were compiled by naval hydrographic services. Measurement and forecasting changed during the Second World War, when Harald Sverdrup and Walter Munk at the Scripps Institution of Oceanography developed the first quantitative method for predicting sea and swell from wind speed, fetch and duration, applied to Allied landings and published openly in 1947. Charles Bretschneider refined the curves through the 1950s into what became the Sverdrup-Munk-Bretschneider method. The modern spectral view arrived with Willard Pierson and Lionel Moskowitz, who described the fully developed sea spectrum in 1964, and with the Joint North Sea Wave Project of 1968 and 1969, whose results Klaus Hasselmann and colleagues published in 1973 as the JONSWAP spectrum and its fetch-limited growth laws. Since 1970 NOAA and its counterparts have operated moored buoy networks that report peak and mean periods continuously.