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Calcimator

Wave Height & Period Calculator

Calculate significant wave height, period, and wavelength from wind speed, fetch distance, and duration using the SMB method.

About this calculator

The Sverdrup-Munk-Bretschneider (SMB) method is a widely used empirical technique from the U.S. Army Corps of Engineers' Shore Protection Manual for estimating how large wind waves grow on open water. Wave growth in nature is capped by two independent limits: fetch (how far the wind blows unobstructed over water) and duration (how long it has been blowing). A short, gusty squall over a huge lake produces small waves even with unlimited fetch, because duration limits growth; a long-blowing wind over a narrow bay is capped by fetch instead.

This calculator computes both non-dimensional growth curves from your wind speed, fetch distance, and duration, converts the duration into an "equivalent fetch" -- the fetch that would take exactly that long to fully develop -- and uses whichever of the two is more restrictive to compute significant wave height (Hs, the average height of the highest one-third of waves) and wave period. From those it derives wavelength using the standard deep-water relationship L = gT²/2π, an estimated maximum wave height (roughly 1.86 times Hs, a commonly cited ratio for a fully developed sea state), wave steepness (height divided by wavelength, a rough indicator of how likely waves are to break), and the equivalent Beaufort wind force scale. This is an open-water, deep-water, idealized-fetch model -- it does not account for shoreline shape, variable water depth, or shifting wind direction, so treat results as planning estimates rather than a precise sea-state forecast.

Inputs

knots
mi
hours

Results

Significant Wave Height (Hs)

1.3 m

≈ 9 smartphones

Wave Period4.5 s
Wavelength32.1 m
Max Wave Height (Hmax)2.41 m
Wave Steepness (H/L)0.04
Beaufort Scale5
How to Use This Calculator
  1. Enter Wind Speed, Fetch Distance, and Wind Duration.
  2. Review the Significant Wave Height (Hs) (m) result.
  3. Use Wave Period (s) and Wavelength (m) to inform your decision.

How the result changes with Wind Speed

Wind SpeedSignificant Wave Height (Hs)
100.46 m
150.85 m
302.32 m
504.76 m

What each input means

Wind Speed
Sustained wind speed in knots measured at 10 m above sea surface.
Fetch Distance
Unobstructed distance over water that the wind blows in a constant direction.
Wind Duration
How long the wind has been blowing at the given speed. Shorter durations limit wave development.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Wind Speed = 20, Fetch Distance = 200, Wind Duration = 6 = 3 input(s) provided
  2. Calculate Significant Wave Height
    Significant Wave Height
    1.3 = 1.3
  3. Calculate Wave Period
    Wave Period
    4.5 = 4.5
  4. Calculate Wavelength
    Wavelength
    32.1 = 32.1

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

What does it mean for wave growth to be duration-limited versus fetch-limited?

Fetch-limited means the wind has blown long enough that waves would keep growing if there were more open water to blow across, but the shoreline or an opposing coast cuts the fetch short first. Duration-limited means the opposite -- there is plenty of open water available, but the wind simply hasn't been blowing long enough yet to develop the waves that fetch alone would allow. The calculator checks both limits and reports whichever produces the smaller (more restrictive) wave height.

Why does increasing wind duration eventually stop increasing wave height?

Once the wind has blown long enough for a given fetch to become the binding constraint, the sea state becomes "fully developed" for that fetch -- waves have extracted about as much energy from the wind as that stretch of open water allows, and further duration no longer matters because fetch, not time, is now what's limiting growth. This mirrors real ocean behavior, where a fully developed sea stops growing regardless of how much longer a steady wind continues.

How reliable is the estimated maximum wave height compared to significant wave height?

Significant wave height (Hs) is a statistical average of the highest third of waves in a sea state, not the single largest wave you might encounter. The roughly 1.86x multiplier used here for maximum wave height is a commonly cited estimate for the largest wave in a fully developed sea over a typical observation period, but individual freak waves can exceed it -- mariners and coastal engineers generally treat it as a planning figure, not a hard ceiling.

Does this calculator account for water depth or shoreline effects?

No -- it uses the deep-water SMB formulation, which assumes open water far from shore with no depth-limited wave breaking or shoaling. Coastal areas, shallow bays, and variable bathymetry all modify real wave growth in ways this idealized fetch-and-duration model does not capture, so results near a shoreline should be treated as a rough starting estimate rather than a site-specific forecast.

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