The hull speed calculator above applies the classic displacement-hull relationship: speed in knots equals a coefficient multiplied by the square root of waterline length in feet. With the traditional coefficient of 1.34, a 30-foot waterline gives a hull speed of about 7.34 knots. The calculator also reports the speed-length ratio you are actually sailing at and the Froude number the result corresponds to.
Arb Digital publishes this with a caveat that belongs in the first paragraph rather than a footnote. Hull speed is a rule of thumb inherited from an era of heavy displacement hulls, and modern naval architecture prefers the dimensionless speed-length ratio or Froude number precisely because those scale properly across boats of any size. The calculator gives you all three, because the classic figure is what people search for and the dimensionless ones are what actually generalise.
What This Hull Speed Calculator Does
It converts waterline length into a theoretical hull speed in knots, miles per hour and kilometres per hour. It lets you change the coefficient, because 1.34 is a convention rather than a constant and different hull types are routinely worked at different values. And it computes two dimensionless figures: the speed-length ratio at whatever speed you actually make, and the Froude number that the hull speed corresponds to.
The dimensionless numbers are the ones worth understanding, because they are what let a towing-tank model tell you something about a full-size vessel. A ratio is comparable between a dinghy and a ship; a speed in knots is not. For plain unit work alongside this, our speed converter handles knots, mph and km/h, the length converter handles feet and metres, and the speed, distance and time calculator handles passage planning arithmetic.
How to Use It
- Enter the waterline length. This is the horizontal length of the hull where it meets the water at normal load — not the overall length quoted in a brochure.
- Choose feet or metres. The formula is defined in feet, so metric input is converted before the square root is taken.
- Adjust the coefficient if you want to. 1.34 is the classic value; long, light or slender hulls are commonly worked higher.
- Enter your actual speed to see the speed-length ratio and Froude number you are operating at rather than the theoretical ones.
- Read the dimensionless figures if you are comparing boats of different sizes, because those are the numbers that compare.
The Formula and Where It Comes From
Hull speed in knots is coefficient × √(waterline length in feet), with 1.34 as the traditional coefficient. Equivalently, the speed-length ratio is speed in knots ÷ √(waterline length in feet), and hull speed is defined as the point where that ratio reaches the coefficient.
The underlying physics is wave mechanics rather than boat design. A hull moving through water generates a wave system, and the speed of a deep-water surface wave depends on its wavelength. The phase velocity of gravity waves in deep water, as set out in a University of Texas fluid mechanics course covering gravity waves in deep water, is proportional to the square root of the wavelength — longer waves travel faster. Hull speed is the speed at which the boat's own bow wave has a wavelength equal to the waterline length, so the hull sits in a trough between its own bow and stern wave crests.
Ship wave systems and the resistance they produce are standard course material in naval architecture. MIT OpenCourseWare's Marine Hydrodynamics lecture notes cover steady ship waves and wave resistance in the lecture on superposition of linear plane progressive waves, alongside wave energy and group velocity — which is the machinery this rule of thumb is a simplification of.
Why 1.34 and Why It Is Not Universal
The coefficient falls out of the physics for one specific case: a heavy displacement hull that has to push its way through its own wave system. Light, slender or long hulls behave differently, because the wave-making resistance they generate at a given speed-length ratio is smaller relative to the power available. In practice, designers and sailors regularly work multihulls, racing hulls and long slender vessels at ratios well above 1.34.
The calculator therefore treats the coefficient as an input rather than a constant. If you are looking at a heavy cruising boat, 1.34 is the sensible figure. If you are looking at something long and light, using 1.34 will understate what it does. That variability is a large part of why modern practice moved away from a single quoted hull speed toward the dimensionless numbers, which describe the regime rather than asserting a limit.
Froude Number, and Why Naval Architects Prefer It
The Froude number is speed divided by the square root of gravitational acceleration multiplied by length, using consistent units. It is dimensionless, which is exactly the point: two hulls of different sizes at the same Froude number are in the same wave-making regime, so a scale model in a towing tank predicts the behaviour of the full-size vessel.
A speed-length ratio of 1.34 knots per square-root-foot corresponds to a Froude number of about 0.40, which the calculator reports. This is the same information in a form that travels between unit systems and between vessel sizes. The classic hull speed figure is the ratio dressed up in knots and feet, which is why it feels like a property of the boat rather than a description of a flow regime.
Boats That Exceed Hull Speed Every Day
Nothing physical prevents a boat exceeding its hull speed, and treating the number as a wall is the most common misreading. What actually happens as a displacement hull approaches the figure is that wave-making resistance climbs steeply, so each additional knot costs disproportionately more power. For a heavy hull with limited power, that increase is enough to feel like a limit; for a boat with power in reserve it is simply expensive.
Planing hulls escape the regime altogether. Above a certain speed the boat lifts and rides on top of its bow wave rather than through the water, and the wave-making relationship that produced the hull speed figure no longer describes what is happening. Surfing does something similar temporarily: a boat running down the face of a wave is being carried by water that is itself moving, and it can hold speeds well above its calculated hull speed for as long as the wave lasts.
Waterline Length Is Not Length Overall
The most consequential input error here is using the wrong length. Length overall includes bowsprits, anchor rollers, sterndrives and overhangs that never touch the water. Only the wetted waterline length generates the wave system the formula describes, and on a traditionally styled boat with long overhangs the difference can be several feet.
There is a real sailing consequence, and it is one of the reasons classic hull shapes behave the way they do. Heeled over, a boat with long overhangs immerses more of its bow and stern, lengthening the effective waterline and raising its hull speed while it is sailing hard. The number is not fixed by the hull; it is fixed by the shape of the hull that is actually in the water at that moment. Loading the boat down does the same thing to a smaller degree, which is one of the rare cases where added weight lengthens the waterline.
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Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using length overall. Only the waterline length generates the wave system, and overhangs can put the two several feet apart.
- Treating hull speed as a hard limit. It marks a steep rise in wave-making resistance, not a speed a boat physically cannot pass.
- Applying 1.34 to every hull. The coefficient suits heavy displacement shapes; long, light and slender hulls routinely work above it.
- Applying it to a planing hull at speed. Once a boat is up and planing, the wave-making relationship behind the formula no longer describes what it is doing.
- Forgetting that waterline length changes. Heel and load both immerse more hull, which lengthens the waterline and moves the figure.
Related Free Tools From Arb Digital
For units, use the speed converter and the length converter. For passage planning, the speed, distance and time calculator and the velocity calculator. For wave physics more generally, the wave equation calculator, and for anglers on the water, the fish weight calculator. Everything else is in the free online tools hub.
Frequently Asked Questions
Multiply 1.34 by the square root of the waterline length in feet to get hull speed in knots. A 30-foot waterline gives about 7.34 knots. The calculator lets you change the 1.34 coefficient because it suits heavy displacement hulls better than light or slender ones.
No. It marks the point where wave-making resistance rises steeply, so each extra knot costs disproportionately more power. Boats with power in reserve exceed it routinely, and planing hulls leave the regime entirely.
Waterline length, always. Overhangs, bowsprits and anchor rollers add to length overall without generating any of the wave system the formula describes, and on classic hull shapes the two figures can differ by several feet.
Speed in knots divided by the square root of waterline length in feet. It is dimensionless in practice, so it compares boats of different sizes, and hull speed is simply the point at which the ratio reaches the chosen coefficient.
It is speed divided by the square root of gravity times length, in consistent units. Being dimensionless, it means two hulls of different sizes at the same value are in the same wave-making regime, which is what makes towing-tank model testing possible.
Because a hull's bow wave is a deep-water gravity wave, and the phase velocity of such a wave is proportional to the square root of its wavelength. Hull speed is the speed at which that wavelength matches the waterline length.
Yes, slightly. Heeling immerses more of the bow and stern on a boat with overhangs, which lengthens the effective waterline and therefore raises the calculated figure while the boat is sailing hard.
Figures produced by this tool are theoretical estimates from a simplified relationship. Real vessel performance depends on hull form, displacement, sea state, loading and power available, and vessel design and safe operation are matters for a qualified naval architect and the vessel's own documentation.
