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What is your boat's hull speed?

Calculate the theoretical maximum speed of a displacement hull from its waterline length, your speed-length ratio and Froude number, and passage time.

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Hull speed

7.34

Comfortably below hull speed: efficient cruising
Speed-length ratio of your speed
1.1
Froude number
0.326
Passage time at your speed
6.67 h

Why displacement boats have a speed limit

A displacement hull moves through the water by pushing it aside, unlike a planing hull that rises and skims over the surface. As it moves, it makes a wave system whose wavelength grows with speed. When the wavelength of the bow wave equals the waterline length, the stern settles into the trough and the boat is effectively climbing its own bow wave. Wave-making resistance then rises sharply: doubling the engine power may add only a fraction of a knot. This speed is called hull speed.

The formula

Deep-water waves travel at a speed linked to their length, which gives:

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

or, with the waterline length in meters, about 2.43 × √LWL.

Waterline length Hull speed
20 ft (6.1 m) 6.0 knots
25 ft (7.6 m) 6.7 knots
30 ft (9.1 m) 7.3 knots
40 ft (12.2 m) 8.5 knots
60 ft (18.3 m) 10.4 knots

Note that the waterline length, not the length overall, is what counts. Heeling can lengthen the waterline of a sailboat with long overhangs and slightly raise its hull speed.

The speed-length ratio and Froude number

The calculator also gives two dimensionless measures of your own speed:

  • the speed-length ratio, speed in knots ÷ √(LWL in feet), equal to 1.34 at hull speed;
  • the Froude number, v ÷ √(g × L) in SI units, about 0.40 at hull speed.

Below a speed-length ratio of about 1, resistance is modest and fuel use low. Between 1.1 and 1.34, it climbs steeply. Above 1.34, only semi-displacement or planing hulls continue efficiently.

Example

A boat with a 30-foot waterline has a hull speed of 7.3 knots. Cruising at 6 knots, its speed-length ratio is 1.1, an efficient pace, and a 40-nautical-mile passage takes about 6 hours 40 minutes.

Limits

The 1.34 constant is a rule of thumb. Light, narrow boats with flat sterns, catamarans and racing dinghies can exceed it, and surfing on a wave can carry any boat beyond it briefly. Heavy, full-bodied boats may struggle to reach it. For planing boats, power-to-weight ratio matters more than waterline length.

Frequently asked questions

What is hull speed?

The speed at which the bow wave created by a displacement hull has a wavelength equal to the waterline length. The boat then sits in the trough between its own bow and stern waves, and going faster takes a steep increase in power. In knots, it is about 1.34 × √(waterline length in feet).

Can a boat go faster than hull speed?

Planing hulls, which rise onto the water, and very slender hulls such as racing multihulls and kayaks can go well beyond it. Light sailboats can briefly exceed it when surfing down waves. Heavy displacement boats rarely do so efficiently.

What is the speed-length ratio?

Your speed in knots divided by the square root of the waterline length in feet. A ratio of 1.34 corresponds to hull speed. Many motor cruisers run at a ratio of 1.1 to 1.2 to save fuel, since resistance rises sharply near 1.34.

What is the Froude number?

A dimensionless number that compares speed with the square root of gravity times length. Naval architects use it to compare hulls of different sizes. Hull speed corresponds to a Froude number of about 0.4.

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Results are estimates provided for information purposes. They do not replace professional advice.

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