Hull Speed Calculator (displacement boat maximum speed from waterline length)

Understanding the hull speed calculator — concept and principle

Sailboats, trawlers and other displacement boats have a practical top speed set by the length of their waterline. This calculator finds that hull speed in knots, km/h and mph and, if you enter your boat's speed, shows your speed-length ratio, Froude number and how close you are to hull speed.

A displacement hull makes a bow wave as long as itself near 7.3 knots.

How it is calculated

Hull speed (knots) ≈ 1.34 × √(LWL in feet) ≈ 2.43 × √(LWL in metres)

Speed-length ratio = V (knots) ÷ √(LWL ft)

Froude number Fn = V ÷ √(g × L), with V in m/s and L in metres

LWL is the length at the waterline; 1 knot = 1.852 km/h; 1 ft = 0.3048 m.

The principle

A boat moving through water makes a bow wave, and deep-water waves travel at a speed set by their wavelength: c = √(g λ ÷ 2π). As the boat speeds up, its bow wave lengthens. When the wavelength equals the waterline length, the stern sits in the trough of its own wave and the boat is effectively trying to climb uphill. Going faster then needs disproportionately more power. Setting λ = LWL in the wave-speed formula gives roughly 1.34 × √LWL in knots for feet, a Froude number of about 0.40. Planing hulls avoid this limit by riding up on top of their bow wave.

Worked example

Default inputs: LWL 30 ft, your speed 6 knots.

Hull speed = 1.34 × √30 = 1.34 × 5.477 = 7.34 knots.
In other units: 7.34 × 1.852 = 13.6 km/h = 8.4 mph; LWL = 9.14 m.
Speed-length ratio = 6 ÷ 5.477 = 1.1.
Froude number = (6 × 0.5144) ÷ √(9.80665 × 9.144) = 3.087 ÷ 9.470 = 0.326.
Your speed is 6 ÷ 7.34 = 82% of hull speed.

Each point is the calculator re-run with only “Length at the waterline (LWL)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Length at the waterline (LWL)	Hull speed (knots)
7.5	3.67
15	5.19
22.5	6.36
30	7.34
37.5	8.21
45	8.99
60	10.38

How to read the result

Cruising sailboats usually spend most of their time well below hull speed. Near hull speed, the stern squats and the wake grows steep, and more power or sail gives little extra speed. Light, narrow boats and multihulls can exceed the traditional figure, and planing boats are not limited by it at all. Hull speed is a guideline, not a hard barrier.

Common mistakes

Using overall length instead of waterline length.
Applying hull speed to planing boats.
Mixing feet and metres in the formula.
Treating 1.34 as a precise physical constant; it is a traditional rounding.

Keep in mind: Real boat performance depends on hull shape, weight, sea state and power. Use manufacturer data and sea trials for planning passages.

Frequently asked questions

Why can't a sailboat go faster than hull speed?

It can, but beyond about hull speed it must climb its own bow wave, so the power needed rises steeply.

How does waterline length change hull speed?

Hull speed grows with the square root of waterline length; four times the length doubles hull speed.

What is the Froude number?

A dimensionless speed, V ÷ √(gL), used to compare boats of different sizes.

Do catamarans have a hull speed?

Their slender hulls make smaller waves, so they can often exceed the traditional figure.

Sources: Linear deep-water wave theory: phase speed c = √(gλ/2π); traditional hull-speed rounding 1.34 × √LWL (ft)

Checked 9 Nov 2026. Deep-water wave phase speed c = √(gλ/2π) (standard linear wave theory, g = 9.80665 m/s²); the traditional 1.34 × √LWL(ft) rounding. 1 knot = 1.852 km/h, 1 ft = 0.3048 m (standard values).

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