Maritime ToolNew

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

m

The mean height of the highest one-third of waves, equal to 4√m₀.

s
min

Standard wave buoy records are 20 or 30 minutes long.

m

Calculation Results

Significant Wave Height (Hs)
2.5 m
Expected Maximum Wave (Hmax)
4.41 m over 30 min
WMO Sea State
5 — Rough
Peak Period (Tp)
8.32 s
Zero-Crossing Period (Tz)
6.5 s
Spectral Moment m₀
0.3906 m²
RMS Wave Height (Hrms)
1.77 m
Mean Wave Height (Hmean)
1.56 m
Mean of Highest 10% (H1/10)
3.18 m
Mean of Highest 1% (H1/100)
4.18 m
Rayleigh Expected Hmax
4.19 m
Waves in Record
277 waves
Wavelength at Tp
107.5 m
Water Depth Regime
Intermediate water (0.05 < h/L < 0.5) — partial seabed influence
Summary: An Hs of 2.5 m with Tz of 6.5 s is WMO sea state 5 — Rough. Over a 30-minute record of about 277 waves, the most probable maximum wave is 4.41 m. Hs is the mean of the highest third of waves, so individual waves routinely exceed it.
Step-by-Step Calculation Solution
1.Hs = 4 x sqrt(m₀), so m₀ = (Hs/4)² = (2.5/4)² = 0.3906 m²
2.Hrms = Hs / sqrt(2) = 1.77 m
3.Hmean = Hs / 1.6 = 1.56 m
4.H1/10 = 1.27 x Hs = 3.18 m | H1/100 = 1.67 x Hs = 4.18 m
5.Tp ≈ 1.28 x Tz = 1.28 x 6.5 = 8.32 s (JONSWAP-type spectrum)
6.N = Record / Tz = 1800 s / 6.5 s = 277 waves
7.Rayleigh: Hmax/Hs = sqrt(ln(N)/2) = 1.677
8.Most probable Hmax = 4.41 m
9.Wavelength from dispersion sigma² = gk·tanh(kh): L = 107.5 m

Formula & How Significant Wave Height (Hs) & Wave Period Statistics Calculator Works

Mathematical Formula
Hs = 4√m₀ | Hrms = Hs/√2 | H1/10 = 1.27 Hs | Hmax/Hs = √(ln N / 2)

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.

How to Calculate Significant Wave Height (Hs) & Wave Period Statistics Calculator (Step-by-Step)
  1. Enter Significant Wave Height Hs (m) (m): Input your target parameter value.
  2. Enter Zero-Crossing Period Tz (s) (s): Input your target parameter value.
  3. Enter Record Length (minutes) (min): Input your target parameter value.
  4. Enter Water Depth (m) (m): Input your target parameter value.
  5. Apply Formula: Calculate using Hs = 4√m₀ | Hrms = Hs/√2 | H1/10 = 1.27 Hs | Hmax/Hs = √(ln N / 2).
  6. Review Results: View exact computed answers, metrics, and worked mathematical proofs.
Free Publisher & Webmaster Asset

Need this calculator for your blog, publication, or client portal?

Get pre-formatted embed codes, Markdown citations for forums (Reddit/Whirlpool), or HTML anchor tags free.

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.

Free Embed Generator & Publisher Widget

Embed Significant Wave Height (Hs) & Wave Period Statistics Calculator on Your Site

Offer your readers, students, or clients interactive calculations. Fast, responsive, and 100% free with no login required.

Widget Customizer

650px

Recommended for publishers & educational portals to provide source citation.

Live Embed PreviewAspect Ratio: Responsive (100% × 650px)
Calculated via mycalculator.com.au — Free Australian Calculator Hub
Official Regulatory & Government Data Sources

Authoritative Standards & Verified Reference Citations

Independent & Verified

Calculations and mathematical logic on this page are grounded in published statutory rules, regulatory standards, and official government data published by the following bodies:

SponsoredMortgage Hub

Dedicated Australian home loans, borrowing capacity, mortgage repayments & refinance modeling.

Advertise here →