What is Wave Steepness?

And why should sailors care about it?

Wave height does not tell you the full story.

Intuitively, a wave 3 m (10 ft) tall is not much of a worry when it’s a gentle ocean swell. But under the right conditions, the same 3 m (10 ft) wave—but this time, steep—may swamp or capsize a small vessel.

Wave steepness refers to the ratio of a wave’s height to its length (or period—more on this below).

NOAA defines steepness as:

Wave Steepness
The ratio of wave height to wavelength and is an indicator of wave stability. When wave steepness exceeds a 1/7 ratio; the wave typically becomes unstable and begins to break.

Glossary – NOAA’s National Weather Service

A general rule of thumb is that when the wave height in feet is greater than the wave period in seconds, it will start to become uncomfortable for some small vessels and potentially dangerous for others.

As waves become steeper, the chances of them breaking increases:

“The ratio of height to wave length will steadily increase until the ratio approaches 1/10. At this ratio, some of the higher waves will be breaking, and theoretically, all should be breaking when the ratio H/L = 1/7.”

G. P. Britton [1]

In other words, some waves will start to break at a height to length ratio of 1:10, while virtually all waves will break at a height to length ratio of 1:7.

“The steepness of the waves is often of far greater interest to the seaman than the mere heights of the waves.”

G. P. Britton [1]

Despite this statement made over 40 years ago—and not least of all the importance of wave steepness and its implications for safe seafaring—today’s sailors will have a difficult time finding weather forecast and data products pertaining to wave steepness.

NOAA’s National Data Buoy Center (NDBC) buoys are one of the few sources that report wave steepness. For example, this NDBC buoy station 41001, 150 NM east of Cape Hatteras, which is showing significant wave height (in feet) close to the period (in seconds):

Did you know? At sea you should expect that waves of double the significant wave height will be a regular occurrence. [2]

Wave period vs. wave length

Wave period and wave length are different, but related, measurements of the spacing between wave crests:

Image: NOAA (link)

As the wave length decreases, so does the wave period—as wave crests get closer together, the time from one crest to the next decreases. And vice versa.

In fact, they’re related by the equation

L = gT2/2π


  • L is the wavelength
  • T is the wave period
  • and g is acceleration due to gravity, i.e., 9.8 m/s2. [3]

At sea, wave period is more easily measured than wave length.

Image: NOAA (link)

What Can Sailors Do to Help Avoid Encountering Steep Waves?

  • Check buoys. Visit the National Data Buoy Center home page to obtain information from buoys for the areas in which you’ll be sailing. These will show you actual conditions now and from the recent past.
  • Check GRiBs. It’s time consuming and tedious, but you can check GRiBs, weather fax, and other sources to manually deduce wave steepness. You will need to check several time steps for the period of time over which you’re interested, but you can mentally compare the significant wave height to the wave period to get a rough sense of when and where waves will be steep.
  • Check the Weathermuffin app, which saves you the trouble of menially scanning GRiBs by monitoring the forecasts continually and warning when the forecasts indicate you might encounter steep waves in the next 72 hours (premium subscription required).



  1. G. P. Britton, Sea State Forecasting (1981)
  2. Ruling the waves: How a simple wave height concept can help you judge the size of the sea, Bureau of Meteorology, Australia (2015)
  3. LAB 6.3 – WAVE DYNAMICS (Rutgers University)
  4. How are significant wave height, dominant period, average period, and wave steepness calculated?, NDBC, NOAA
  5. W. Buckley, Extreme and Climatic Wave Spectra for Use in the Structural Design of Ships, Naval Engineers Journal, September 1988.
  6. D. Gilhousen, Buoy Wave Extremes, Mariners Weather Log Vol. 37 Iss. 4 (1993)
  7. Nondirectional and Directional Wave Data Analysis Procedures, NDBC, NOAA (1996)
  8. Guide to Wave Analysis and Forecasting, WMO (2018)

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