Wave Steepness & Breaking Limit Calculator
Check waves against the Miche steepness limit and the 0.78 depth-limited breaking criterion.
Last reviewed by the myCalculator Editorial Team
Input Parameters
0.02 is a 1 in 50 dissipative beach; 0.1 is a 1 in 10 steep reflective beach.
Calculation Results
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Formula & How Wave Steepness & Breaking Limit Calculator Works
Waves break by two independent mechanisms. In deep water a wave cannot exceed a steepness of about 1 in 7 before the crest angle reaches 120° and the wave whitecaps — the Miche limit. In shallow water the wave breaks when its height reaches roughly 0.78 times the depth, regardless of steepness. The Iribarren number, combining seabed slope with deep-water steepness, then predicts whether the break is a gentle spilling, a barrelling plunging, or a surging non-break. Worked example: an 8 second wave has a deep-water wavelength of 1.56 × 8² = 99.8 m, so a 2.5 m wave has a steepness of 2.5 ÷ 99.8 = 0.025, well below the 0.142 deep-water limit. With a seabed slope of 0.02 the Iribarren number is 0.02 ÷ √0.025 = 0.13, which is below 0.5 and means a gentle spilling breaker. Steeper beaches produce plunging or surging breakers, which are more powerful and more dangerous for swimmers and vessels.
- Enter Wave Height (m) (m): Input your target parameter value.
- Enter Wave Period (s) (s): Input your target parameter value.
- Enter Water Depth (m) (m): Input your target parameter value.
- Enter Seabed Slope (m/m): Input your target parameter value.
- Apply Formula: Calculate using
Miche: H/L ≤ 0.142 tanh(kh) | McCowan: H/h ≤ 0.78 | Iribarren ξ₀ = slope / √(H₀/L₀). - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
At what depth does a wave break?
Approximately when the water depth falls to 1.28 times the wave height, from the McCowan criterion H/h = 0.78. A 2 m wave therefore breaks in roughly 2.6 m of water.
What makes a wave barrel instead of crumble?
The Iribarren number. Between 0.5 and 3.3 a wave plunges and barrels, which needs a steeper seabed and longer-period low-steepness swell. Below 0.5 the wave spills gently.
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