Hull Speed Calculator
Enter your boat's waterline length to find its theoretical hull speed, the practical upper limit for any displacement hull before wave-making resistance rises steeply. You get the result in knots, mph, and km/h, along with the Froude number, the speed-length ratio, and a worked breakdown showing every step. Switch freely between feet and metres - the result updates instantly.
Formula
Worked example
A cruising sailboat with a 36 ft waterline: hull speed = 1.34 x sqrt(36) = 1.34 x 6 = 8.04 knots. In metric: 10.97 m waterline gives 2.43 x sqrt(10.97) = 2.43 x 3.31 = 8.05 knots. Froude number = (8.04 x 1852/3600) / sqrt(9.81 x 10.97) = 4.134 / 10.374 = 0.398, very close to the theoretical 0.40 threshold.
What is hull speed?
Hull speed (also called displacement speed) is the theoretical maximum speed at which a displacement hull can travel efficiently through the water. As a vessel accelerates, it creates a bow wave whose length grows with speed. When the bow wave length equals the waterline length of the hull, the boat is effectively trapped in the trough between two wave crests and must climb its own bow wave to go faster. The energy cost of doing so rises so sharply that for practical purposes it defines a speed ceiling. This limit is not absolute - light-displacement or fine-entry hulls can push through it with enough power - but for typical cruising displacement vessels it is the meaningful upper bound. Planing hulls, semi-displacement hulls, catamarans, and hydrofoils all operate on different principles and can exceed it substantially.
The hull speed formula and its variants
The standard formula is: hull speed (knots) = 1.34 x sqrt(LWL in feet). The coefficient 1.34 is empirical, derived from testing a wide range of displacement hulls. For metric users, the equivalent is hull speed (knots) = 2.43 x sqrt(LWL in metres). Some naval architects use a higher coefficient - up to 1.51 - for fine-entry or light-displacement designs that can exceed the standard limit before peak wave resistance hits. The Froude number at hull speed is approximately 0.40, a dimensionless ratio comparing inertial forces to gravitational forces: Fn = v / sqrt(g x LWL), where v is in m/s and LWL is in metres. The speed-length ratio (SLR), v / sqrt(LWL in feet), numerically equals the coefficient (1.34 for standard hulls) at the theoretical hull speed.
How to use this calculator and what each output means
In forward mode, enter your boat's waterline length to find its hull speed in knots, mph, and km/h. The Froude number and speed-length ratio are also shown so you can compare your boat to hydrodynamic benchmarks. In reverse mode, enter a target speed to find the minimum waterline length that reaches it - useful when designing or comparing vessels. The coefficient selector lets you switch between 1.34 (typical cruising hulls) and 1.51 (fine-entry and light-displacement designs). The "Show your work" panel displays every arithmetic step so you can verify or adapt the calculation for your own purposes.
Practical implications for sailors and powerboaters
Understanding hull speed helps set realistic expectations for passage planning and engine or sail sizing. For sailboats, hull speed under sail is rarely achieved in light conditions; it typically requires 15-20 knots of true wind at a close reach or broad reach. Motor sailors and trawler-style power vessels are routinely operated well below hull speed for fuel efficiency - running at 80-85% of hull speed can dramatically cut fuel consumption compared with pushing hard against the bow wave. Adding waterline length (a longer hull, or pressing deeper into the water with more displacement) is the primary way to raise hull speed on a displacement design. Installing a more powerful engine does not help much once the wave resistance wall is reached.
Typical waterline lengths and hull speeds
| Vessel type | Typical LWL (ft) | Hull speed (knots) | Hull speed (mph) |
|---|---|---|---|
| Dinghy / day sailer | 14 | 5.0 | 5.8 |
| Small cruising sailboat | 22 | 6.3 | 7.2 |
| Mid-size cruiser | 30 | 7.3 | 8.4 |
| Offshore cruising sailboat | 36 | 8.0 | 9.2 |
| Bluewater passage-maker | 44 | 8.9 | 10.2 |
| Sailing yacht / cruiser-racer | 50 | 9.5 | 10.9 |
| Ocean racer / maxi yacht | 65 | 10.8 | 12.4 |
| Coastal trawler / motor cruiser | 35 | 7.9 | 9.1 |
| Long-range motor cruiser | 55 | 9.9 | 11.4 |
Calculated using the standard coefficient of 1.34. Actual performance varies by hull form, loading, and conditions.
Frequently asked questions
What is hull speed and why does it matter?
Hull speed is the theoretical maximum efficient speed for a displacement hull, governed by the bow wave it creates. When the bow wave length equals the waterline length, the boat sits trapped between two crests and speed gains require disproportionate power. For cruising sailors and trawler operators, hull speed is the practical ceiling for planning passages and choosing engines.
Can a boat exceed its hull speed?
Yes, but only under specific conditions. A displacement hull can push through its hull speed with enough power or favourable conditions (surfing down a wave, for example), but the energy cost is extreme. Planing hulls rise up onto the water surface at speed and are not subject to this limit. Semi-displacement and wave-piercing hulls fall in between. Multihulls such as catamarans have much longer effective waterlines relative to their displacement and can exceed their theoretical hull speed more easily.
Why does the formula use 1.34 instead of another number?
The coefficient 1.34 is empirical - it comes from fitting the formula to measured performance data from a large population of displacement hulls. It is not a fundamental physical constant; it represents the typical speed at which wave-making resistance becomes dominant for conventional cruising hulls. Light-displacement or fine-entry designs often use 1.51 because their wave resistance peaks at a higher speed-length ratio.
How does waterline length differ from overall length (LOA)?
Overall length (LOA) measures the hull from the furthest point forward to the furthest point aft, including overhangs, swim platforms, and bow pulpits. Waterline length (LWL) is the length of the hull actually in the water at the designed waterline when floating at rest. For most modern designs these are close, but older boats with pronounced overhangs can have an LWL several feet shorter than their LOA. Hull speed depends on LWL, not LOA.
What is the Froude number and why does the calculator show it?
The Froude number (Fn) is a dimensionless ratio defined as v / sqrt(g x LWL), where v is speed in m/s and LWL is in metres. It is used in naval architecture to compare vessels of different sizes without unit effects. Displacement hulls typically reach peak wave-making resistance around Fn = 0.40, which corresponds to the hull speed formula. Showing the Froude number lets you benchmark your boat against published hydrodynamic data and compare designs of very different sizes on equal terms.
How do I increase my boat's hull speed?
The primary lever is increasing waterline length: a longer hull or loading the boat to float deeper both lengthen the effective wave and raise the limit. Beyond that, switching to a semi-displacement or planing hull form removes the limit entirely, but changes the hydrodynamics of the whole design. Adding engine power alone does not meaningfully raise hull speed on a displacement hull - the boat simply burns more fuel fighting the same wave resistance wall.
Does hull speed apply to catamarans and trimarans?
Multihulls have very low displacement-to-length ratios and slim, fine hulls, which means they generate far less bow wave resistance per unit of speed than monohulls. Their effective Froude number at a given speed is much lower, allowing them to run comfortably at speed-length ratios well above 1.34 without the sharp resistance increase a monohull would experience. The formula gives a rough ballpark for each individual hull, but multihulls routinely achieve sustained speeds well above the theoretical limit.