What this calculator does
A displacement hull pushes through the water rather than over it, and it makes its own wave as it goes. When the boat speed matches the speed of that wave, the hull sits in its own trough and going faster requires climbing its own bow wave, which takes disproportionate power.
That point is the hull speed, about 1.34 times the square root of the waterline length in feet, giving knots. A 30 foot waterline gives 7.34 knots. Because it goes with the square root, doubling the waterline length only raises hull speed by about 41%, which is why long boats are fast and why the gains from length come slowly.
The formula
Hull speed in knots is 1.34 multiplied by the square root of the waterline length in feet. The result converts to mph and km/h. The 1.34 constant comes from the physics of deep-water wave speed, and the relationship applies to displacement hulls. Planing hulls and multihulls escape the limit by different means and are not described by it.
| Term | Meaning |
|---|---|
| Waterline length | The length of hull actually in the water, which is less than the overall length on most boats. |
| Displacement hull | A hull that pushes water aside rather than riding on top of it, which is what this limit applies to. |
| Planing hull | A hull shaped to lift onto the surface at speed, escaping the hull speed limit at the cost of much more power. |
| 1.34 | The constant relating wave speed to wavelength in deep water, in knots per root foot. |
The inputs explained
| Field | What to enter |
|---|---|
| Waterline length (ft) | Waterline length in feet. Use the waterline length rather than the overall length, which can be several feet longer on a boat with overhangs. |
When to use it
Estimating passage time
Hull speed sets a realistic ceiling for a displacement boat, and passage planning at somewhere below it is more honest than planning at the maximum.
Comparing two boats
Waterline length is the dominant factor in displacement boat speed, and comparing hull speeds shows what the length difference is actually worth.
Understanding why more power does not help
Past hull speed, additional engine power buys very little for a displacement hull, which is why they are not fitted with large engines.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What hull speed does each waterline length give?
A range of waterline lengths with the resulting hull speed.
| Waterline length | Hull speed | In mph | In km/h |
|---|---|---|---|
| 20 ft | 5.99 knots | 6.90 mph | 11.10 km/h |
| 25 ft | 6.70 knots | 7.71 mph | 12.41 km/h |
| 30 ft | 7.34 knots | 8.45 mph | 13.59 km/h |
| 40 ft | 8.47 knots | 9.75 mph | 15.70 km/h |
| 50 ft | 9.48 knots | 10.90 mph | 17.55 km/h |
Questions
Can a boat exceed hull speed?
Yes, but not efficiently as a displacement hull. Light displacement boats and those with fine sterns can exceed it somewhat, and surfing down a wave does so temporarily. Genuinely sustained higher speed requires planing or a multihull, both of which work differently.
Why 1.34?
It comes from the speed of a deep-water wave whose wavelength equals the waterline length. At that point the boat is trapped between its own bow and stern waves, and further speed means climbing the bow wave, which is where the power requirement rises sharply.
Should I use waterline or overall length?
Waterline. It is the length actually generating the wave. Classic designs with long overhangs can have a waterline several feet shorter than the overall length, and using the wrong one overstates the hull speed noticeably.
Does hull speed apply to multihulls?
Not usefully. Catamarans and trimarans have very narrow hulls that make comparatively small waves, so they are not trapped by the wave-making limit the same way. They routinely exceed the formula figure, which is a large part of why they are fast.
For boat speed in other terms, see the boat speed calculator. For average speed over a distance, see the average speed calculator.