Wave Period and Wavelength Calculator
Ocean waves in deep water follow the deep-water dispersion relation. The wavelength L = (g / 2pi) * T^2, which simplifies to approximately L = 1.56 * T^2 meters for period T in seconds, using g = 9.81 m/s^2. Wave phase speed C = L / T = 1.56 * T m/s. Enter the wave period in seconds to calculate wavelength in meters and feet, wave speed in m/s and knots, and the minimum water depth at which deep-water approximations apply. These formulas describe gravity waves in open ocean; they do not apply to tsunami waves or waves in very shallow water.
Deep-water wave formula
Wavelength L = (g / 2pi) * T^2 = 1.5607 * T^2 (meters)
Wave speed C = L / T = 1.5607 * T (m/s)
Wave speed in knots = C * 1.9438
Minimum deep-water depth = L / 2
g = 9.81 m/s^2. Deep-water approximation valid when depth exceeds L/2. For T = 10 s: L = 156.1 m, C = 15.6 m/s (30.3 kts).
Practical ocean wave information
- NOAA buoy data at ndbc.noaa.gov reports dominant wave period and significant wave height in real time.
- Wave steepness (height / wavelength) greater than 1/7 causes breaking. Steep short-period seas are more uncomfortable than long-period swell of the same height.
- Vessel natural roll period matching wave period causes resonance and excessive rolling.
- Group velocity of deep-water waves is half the phase velocity: wave energy travels at C/2.
Wave period and wavelength: frequently asked questions
What is the deep-water wave formula?
For deep-water gravity waves (where depth exceeds half the wavelength), wavelength L = 1.56 T^2 meters, where T is the wave period in seconds. Wave speed C = 1.56 T meters per second. These are approximations of the full dispersion relation using g = 9.81 m/s^2.
What counts as deep water for wave propagation?
Water is considered deep for wave purposes when depth exceeds half the wavelength (d > L/2). In shallow water, waves slow down and the formula changes. Most open-ocean swell behaves as deep-water waves until it approaches the coast.
What is a typical ocean swell period?
Ocean swell periods typically range from 8 to 20 seconds. Wind chop has shorter periods of 2-6 seconds. A 10-second swell has a wavelength of about 156 m and a wave speed of about 15.6 m/s (30 knots). Longer-period swell travels faster and is typically from distant storms.
How does wave period relate to wave energy?
Wave energy is proportional to the square of wave height. Period affects wave group velocity (how fast wave energy travels), which is half the phase speed for deep-water waves. Long-period swell from distant storms retains energy well because wave groups travel efficiently.
Can I use this formula for tsunami waves?
No. Tsunamis behave as shallow-water waves even in the deep ocean because their wavelengths (hundreds of kilometers) vastly exceed water depth. The shallow-water formula applies: C = sqrt(g * d), giving speeds of 500-900 km/h in the deep ocean.
Official sources
- NOAA National Data Buoy Center: NOAA NDBC Wave Data.
- National Geospatial-Intelligence Agency: Bowditch American Practical Navigator.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.