Hull Speed Calculator

What the hull speed calculator does

A displacement boat, the kind that pushes through the water rather than skimming over it, has a natural speed limit set by its length, and this tool works it out. You enter the boat's waterline length and pick the speed unit you want, and it returns the hull speed, the efficient top speed the hull is built to reach.

It uses the classic rule of thumb that naval architects have leaned on for generations, and the physics behind that rule is genuinely interesting, so the page walks through it.

How to use it

1. Enter the waterline length. That is the length of the boat actually in contact with the water, not the full length of the deck, which usually overhangs at the bow and stern.
2. Choose your speed unit, from knots to kilometers per hour and others.

Press Calculate for the hull speed, or Reset to clear the fields.

How hull speed is worked out

The rule is short and old:

Hull speed (knots) = 1.34 × √(waterline length in feet)

You take the square root of the waterline length in feet and multiply by 1.34 to get the hull speed in knots, which the calculator then converts to whatever unit you chose. The square root is the heart of it: because speed depends on the root of the length, a boat has to get a lot longer to gain a little speed, which is why length is so prized in fast displacement boats.

Why a hull has a speed limit

Here is the part worth understanding. As a boat moves, it pushes water aside and creates a wave at the bow, and this bow wave gets longer as the boat goes faster. At low speed the boat rides over several small waves of its own making. But as it speeds up, the wave stretches out until its length matches the boat's waterline, and now the boat is sitting in a trough between its own bow wave and the wave at its stern. To go any faster, the boat would have to climb up the back of its own bow wave, which takes a huge and rapidly rising amount of power for almost no extra speed. That wall of resistance is hull speed. The effect comes from the wave-making resistance studied by the naval architect William Froude in the nineteenth century, and it is why the limit scales with the square root of the waterline length: a longer boat can ride a longer, faster wave before it gets trapped in the trough.

An example with real numbers

Say a sailboat has a waterline length of 25 feet.

• Hull speed = 1.34 × √25 = 1.34 × 5 = 6.7 knots

So this boat will cruise efficiently up to about 6.7 knots, and pushing past that takes a steep jump in power for very little gain. A boat with a 36-foot waterline, by contrast, has a hull speed of about 8 knots, the longer waterline buying the extra speed.

What it means, and when it does not apply

For a displacement hull, this is the speed to design and cruise around. Longer boats are faster, which is the single biggest reason waterline length matters to sailors and to anyone choosing a trawler or a sea kayak. But the rule has an important boundary: it only governs hulls that stay down in the water. A planing hull, like a speedboat or a planing dinghy, is shaped to climb up and skim across the surface of the water rather than plough through it, and once it is up on the plane it has escaped the bow-wave trap entirely, so it is not bound by hull speed at all. Even a displacement boat can be forced past its hull speed with enough power, it just does so inefficiently, burning fuel or straining sails to claw up that bow wave. So treat hull speed as the natural, efficient ceiling for a displacement hull, not an unbreakable wall.

Questions people ask

How do you calculate hull speed?

Multiply the square root of the waterline length in feet by 1.34 to get hull speed in knots. A 25-foot waterline gives about 6.7 knots.

Why waterline length and not overall length?

Because it is the part of the hull in the water that makes the bow wave, and the wave sets the speed limit. The deck usually overhangs the water at the bow and stern, so it does not count.

Why can't a displacement boat just go faster?

At hull speed the boat sits in the trough of its own bow wave, and going faster means trying to climb that wave, which takes enormous extra power for almost no gain.

Do all boats obey hull speed?

No. Planing hulls, like speedboats, are designed to rise up and skim across the surface, which escapes the bow-wave limit entirely. Hull speed governs displacement hulls that push through the water.