ONE FORMULA, ONE ANSWER
Finite-Depth Gravity Wave Wavelength Calculator
Solve the finite-depth linear gravity-wave dispersion equation for positive wavenumber to obtain wavelength, continuously spanning shallow and deep water. Choose input units and calculate one value within the stated conditions.
Inputs
Calculations run in this browser. Scientific notation such as 1.2e-3 is supported. Do not group thousands.
Result
Linear gravity-wave wavelength λ
Enter values and select Calculate.
(2π/T)² = gk tanh(kh), λ = 2π/k
Assumptions
Required: small-amplitude linear gravity waves over a flat bottom with uniform depth, incompressible inviscid irrotational flow and no mean current. Excluded: surface tension, breaking, strong nonlinearity, capillary waves and rapidly varying depth.
Displayed values are floating-point approximations. Design safety factors and unprovided error contributions are not calculated.
Formula references and credits
NaNa Lab created the code, descriptions, icons and preview images. Text, figures and code from the linked references have not been reproduced.
Physical constants: NIST / CODATA 2022. The values of μ₀ and ε₀ are measured recommendations, not exact defining constants. Values and precision notes are in the source record.
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