Hull speed calculator

What is hull speed?

Hull speed is the speed at which a displacement hull becomes trapped by its own wake. As the boat moves it makes a bow wave, and that wave gets longer as she goes faster. When the wave is as long as the boat’s waterline, the hull sits in a single trough between its own bow and stern crests — and to go faster it has to climb uphill out of the hole it has dug. That is why the last half-knot costs so much more than the first six.

Hull speed (knots) = 1.34 × √LWL(feet)

Hull speed (knots) = 2.43 × √LWL(metres)

The two are the same equation. Most references quote the imperial version because the 1.34 is a tidy number, but if your boat papers are in metres the second form saves a conversion. A 9 m waterline gives 7.3 knots either way.

Where the 1.34 actually comes from

It is not an empirical fudge factor, which is how it is usually presented. It falls straight out of the physics of water waves.

A wave in deep water travels at a speed set only by its own length:

c = √( g λ ÷ 2π )

… where g is gravity and λ is the wavelength. Put λ in feet and convert the answer to knots, and the whole constant collapses to 1.34. Hull speed is then just that same equation with the wavelength set equal to the waterline length — the condition where the boat is stuck in its own trough:

substitute λ = LWL → hull speed = 1.34 × √LWL

Naval architects usually write the same idea as a Froude number of about 0.40 — a dimensionless speed-to-length ratio that lets a 9 m yacht and a 300 m ship be compared on the same scale. Hull speed and Fr ≈ 0.40 are two ways of saying one thing.

Two useful consequences follow. Hull speed depends on length alone — not on displacement, sail area or horsepower. And because it goes as a square root, gains come slowly: doubling the waterline buys about 41 % more speed, not double.

When hull speed misleads you

It is a genuinely useful number, and it is also the most over-quoted figure in boating. Four things it does not mean:

• It is a hump, not a wall. Nothing physical stops you exceeding it. Resistance rises steeply around hull speed and then eases again once a hull is light and powerful enough to climb out. Plenty of boats spend their lives just below it because that is where the fuel or the sail area runs out, not because a barrier exists.
• 1.34 is a convention, not a constant. Real boats sit anywhere from roughly 1.2 for a heavy, full-bodied long-keeler to 1.5 and beyond for a light fin-keeled boat surfing downwind. Treat the calculator output as the centre of a range, not a specification.
• Slenderness matters more than length. Wave-making depends on how much water the hull has to shoulder aside for its length. A narrow hull makes a small bow wave and never really gets trapped by it, which is why catamarans and trimarans routinely sail at twice the figure this calculator gives. For a multihull, hull speed is close to meaningless.
• Planing hulls leave it behind entirely. Given enough power and a flat enough run aft, a hull stops pushing water aside and starts riding on top of it. Once planing, waterline length barely governs speed at all.

And the everyday caveat: hull speed is a flat-water, clean-bottom, lightly-loaded number. A foul bottom, a cruising load, a head sea or a foul tide will all keep you well below it.

Frequently asked questions

Can a boat exceed its hull speed?

Yes — but it requires enormous power. Some beamy motorboats and modern lightweight racing sailboats can "plane" over their bow wave and go considerably faster. Displacement cruisers and most sailing yachts cannot plane and are effectively limited to hull speed in practical terms.

Is hull speed the same as maximum speed?

No. Hull speed is a theoretical limit for displacement hulls. Your actual maximum depends on engine power, sail area, wind strength, sea state and loading. Most cruising sailboats reach hull speed only in ideal downwind conditions.

Why does waterline length matter more than overall length?

The bow wave length is determined by the waterline length — the length of the hull that is actually in the water. Overhangs and bow/stern extensions above the waterline don't count. A boat with a long bowsprit has the same hull speed as one without.

How do I calculate hull speed by hand?

Take the waterline length — not the overall length — and square-root it. In feet, multiply by 1.34; in metres, multiply by 2.43. The answer is in knots. For a 9 m waterline: √9 = 3, and 3 × 2.43 = 7.3 knots. It is the rare bit of naval architecture you can do on your fingers.

Why is it called theoretical hull speed?

Because it describes an idealised displacement hull in deep, flat water, and it is derived from wave physics rather than measured from your boat. Real hulls vary either side of it depending on how heavy and how slender they are, so the honest reading is “the speed around which pushing harder stops paying”, not a maximum your boat cannot pass.

What is a realistic cruising speed?

Most displacement sailboats cruise at 55–75% of their hull speed. For a 9 m waterline boat with 7.3 kn hull speed, expect 4–5.5 knots as a realistic day-passage average, depending on wind and swell.

Typical hull speeds