Significant Wave Height (Hs) & Wave Period Statistics Calculator
Convert Hs and Tz into the full Rayleigh wave height distribution and expected maximum wave.
Last reviewed by the myCalculator Editorial Team
Input Parameters
The mean height of the highest one-third of waves, equal to 4√m₀.
Standard wave buoy records are 20 or 30 minutes long.
Calculation Results
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Formula & How Significant Wave Height (Hs) & Wave Period Statistics Calculator Works
Significant wave height originated as the height a trained observer would report by eye, and was later formalised as the mean of the highest one-third of waves. For a narrow-banded sea the wave heights follow a Rayleigh distribution, which lets every other statistic be derived from Hs alone. The expected maximum wave grows with the number of waves in the record, so a longer record reliably contains a larger maximum — roughly 1.86 × Hs over a standard three-hour sea state.
- Enter Significant Wave Height Hs (m) (m): Input your target parameter value.
- Enter Zero-Crossing Period Tz (s) (s): Input your target parameter value.
- Enter Record Length (minutes) (min): Input your target parameter value.
- Enter Water Depth (m) (m): Input your target parameter value.
- Apply Formula: Calculate using
Hs = 4√m₀ | Hrms = Hs/√2 | H1/10 = 1.27 Hs | Hmax/Hs = √(ln N / 2). - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
Why is the maximum wave so much bigger than Hs?
Hs is the average of the highest third of waves, not a cap. Under Rayleigh statistics the expected maximum over 1,000 waves is about 1.86 times Hs, so a 3 m sea routinely produces 5.5 m waves.
What is the difference between Tz and Tp?
Tz is the mean zero-crossing period measured in the time domain; Tp is the period of the most energetic frequency in the spectrum. For a JONSWAP sea, Tp is roughly 1.28 times Tz.
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