What hull speed actually is
A boat moving through water makes waves, and those waves cost energy. The bow pushes up a crest, the water falls away behind it into a trough, and a train of waves runs aft along the hull. The speed of a deep-water surface wave is fixed by physics: a wave of length λ travels at √(gλ/2π). As the boat goes faster, the waves it generates get longer, and at one particular speed the wavelength equals the boat's own waterline length. That speed is hull speed.
What makes it significant is what happens next. Below hull speed, the hull sits in several of its own wave crests and is broadly level. At hull speed, the boat sits in exactly one wave: a crest at the bow and a crest at the stern, with the hull in the trough between them. To go faster still, the boat must climb its own bow wave, and the power needed to do that rises so steeply that for a heavy hull it is effectively unavailable. That is why a 30-foot cruising sailboat motors at 6.5 knots whether you fit a 20 hp or a 60 hp diesel.
Put g = 32.174 ft/s² and λ = LWL into the wave-speed formula and convert to knots and you get V = 1.34√LWL. The 1.34 is not empirical fudge; it is √(g/2π) expressed in knots per square-root-foot. What is conventional is the assumption that the significant wavelength equals exactly the waterline length, which is why real boats deviate from the rule in both directions.
The metric form is V(kt) = 2.43√LWL(m), which follows directly: 1.34 × √(1 ÷ 0.3048) = 2.426, usually rounded to 2.43.
Speed-length ratio, Froude number, and why they matter more
Hull speed is a single number, but the useful quantity is the speed-length ratio: speed in knots divided by the square root of waterline length in feet. Hull speed is simply the speed at which that ratio equals 1.34, so the ratio tells you where a boat sits relative to its own limit without you having to compute the limit first.
The ratio also sorts boats into regimes. Below about 1.0 a hull is in the friction-dominated range, where resistance climbs roughly with the square of speed and modest power increases still buy real speed. Between 1.0 and 1.34, wave-making resistance rises sharply and each extra tenth of a knot costs disproportionately more. Between 1.34 and about 2.5 a hull is semi-displacement, driveable only with substantial power and a stern shape that lets the flow separate cleanly at the transom. Above 2.5 the boat is planing, supported by dynamic lift rather than buoyancy, and hull speed no longer constrains it — that is the domain of the Crouch's formula calculator.
The Froude number is the same idea made dimensionless and unit-free: Fn = V ÷ √(gL), with V and L in consistent units. Hull speed corresponds to Fn ≈ 0.3987 for any boat of any size in any unit system. Naval architects work in Froude number because model tests scale by it: a 1:16 scale model towed at the same Froude number as the full-size ship produces a geometrically similar wave pattern, which is what makes tank testing possible. Convert between the two with Fn = S/L ratio ÷ 3.3554 for knots and feet.
The coefficient is negotiable. Real hulls do not all break at 1.34. A heavy, full-bodied hull with a wide transom and a shallow buttock line can struggle to reach 1.2. A long, fine-ended hull with low displacement-to-length ratio drives comfortably past 1.5, and a light multihull or a planing dinghy simply ignores the concept. Setting the coefficient input is how you tune the calculation to your actual boat.
Worked example: a 25 ft waterline cruiser at 6 knots
Take a cruising sailboat with a 25 ft waterline, running at 6 knots under power.
- Square root of the length. √25 = 5.000.
- Hull speed. 1.34 × 5.000 = 6.70 kt.
- In other units. Multiply by 1.150779 for statute mph: 6.70 × 1.150779 = 7.71 mph. Multiply by 1.852 for km/h: 6.70 × 1.852 = 12.41 km/h.
- Speed-length ratio at 6 kt. 6 ÷ 5.000 = 1.200. The boat is at the upper end of the displacement range, below its hull speed but into the part of the curve where wave-making dominates.
- As a share of hull speed. 6 ÷ 6.70 = 89.6%.
- Froude number. Convert to feet per second: 6 × 1.68781 = 10.127 ft/s. Then √(32.174 × 25) = √804.35 = 28.361. So Fn = 10.127 ÷ 28.361 = 0.3571. Compare that to 0.3987 at hull speed — the same 89.6% relationship, as it must be, because both quantities are linear in speed.
Now consider what the extra 0.7 knots to reach hull speed would cost. This calculator does not compute resistance, but the shape of the curve is well established: in the range from S/L 1.2 to 1.34, residuary resistance on a typical cruising hull roughly doubles. If the boat needs 12 hp to hold 6 knots, expect something in the region of 20 hp to hold 6.7, and considerably more than that to go beyond. Compare with the friction-dominated part of the curve, where going from 3 to 4 knots costs perhaps 80% more power for a 33% speed gain.
Finally, check the metric route as a cross-check. 25 ft is 7.62 m, and √7.62 = 2.7604, so 2.43 × 2.7604 = 6.708 kt. The two forms agree to within the rounding of the constant, which is the point of quoting 2.43 rather than 2.4.
How to read the result
Hull speed is a soft limit, not a wall. This is the most important thing to understand about the number. Plenty of boats exceed it routinely: light-displacement racing monohulls surfing down a swell, catamarans and trimarans whose slender hulls make very small waves, and any planing craft at all. What hull speed genuinely marks is the speed beyond which a heavy hull's power demand rises faster than almost any owner is willing to pay for.
Use it for passage planning, not for bragging. The practical value is in estimating a day's run. A boat with a 30 ft waterline has a hull speed of 7.34 kt, and a realistic motoring average is 80 to 90% of that — call it 6.0 to 6.6 kt, or 72 to 79 nautical miles in a 12-hour day. Planning at hull speed overstates a passage by a fifth.
Waterline length, not length overall. Overhangs at bow and stern do not count while the boat is upright, which is why classic long-overhang designs are slower than their advertised length suggests. They do have one virtue: when a sailboat heels, the immersed waterline lengthens, and a boat with generous overhangs can gain a foot or more of effective LWL and a few tenths of a knot with it.
A low percentage is not a problem. Running at 60% of hull speed is where most cruisers get their best fuel economy, because resistance in that range is comparatively cheap. Many trawler owners find that dropping from 90% to 70% of hull speed cuts fuel burn by roughly half while costing only a fifth of the speed.
Check the coefficient against your boat. If you know from experience that your hull runs out of steam at 6.2 kt on a 25 ft waterline, your effective coefficient is 6.2 ÷ 5 = 1.24, not 1.34. Enter that and every subsequent estimate for the boat improves.
Hull speed by waterline length
| LWL (ft) | LWL (m) | Hull speed (kt) | Hull speed (mph) | Hull speed (km/h) | Nautical miles in 12 h |
|---|---|---|---|---|---|
| 16 | 4.88 | 5.36 | 6.17 | 9.93 | 64 |
| 20 | 6.10 | 5.99 | 6.90 | 11.10 | 72 |
| 25 | 7.62 | 6.70 | 7.71 | 12.41 | 80 |
| 30 | 9.14 | 7.34 | 8.45 | 13.59 | 88 |
| 36 | 10.97 | 8.04 | 9.25 | 14.89 | 96 |
| 42 | 12.80 | 8.68 | 9.99 | 16.08 | 104 |
| 50 | 15.24 | 9.48 | 10.90 | 17.55 | 114 |
| 64 | 19.51 | 10.72 | 12.34 | 19.85 | 129 |
| 100 | 30.48 | 13.40 | 15.42 | 24.82 | 161 |
The final column is hull speed times 12 hours, an upper bound on a day's run. A realistic passage average is 80 to 90% of it.
Where the hull speed rule breaks down
- Multihulls. A catamaran hull is so slender that it makes very small waves for its length, and the wave-making argument barely binds. Cruising catamarans regularly sail at speed-length ratios well above 2, and racing multihulls far beyond that.
- Light-displacement monohulls. A modern racing hull with a low displacement-to-length ratio and a wide flat run aft can plane or semi-plane downwind, breaking clean through 1.34 whenever the wind allows.
- Surfing. Any hull can exceed hull speed while riding down the face of a wave, because it is being accelerated by gravity rather than by its own propulsion.
- Very short hulls. Below roughly 8 ft of waterline, viscous drag dominates so heavily that wave-making is a minor term and the concept adds little.
- Shallow water. In water shallower than about half the wavelength, wave speed itself is reduced, and the effective hull speed drops. A boat that makes 7 kt offshore can hit a wall at 5 kt in a shallow canal, with a large stern wave and a suction effect known as squat.
- Planing craft. Once dynamic lift supports the boat, the hull is no longer displacing water in the way the rule assumes, and the relevant tool is a planing formula rather than this one.
How this fits with the rest of the powering picture
Hull speed answers the question “how fast can this hull be driven before physics starts charging silly money?” It does not tell you how much power you need to reach any particular speed below that, and it says nothing at all about planing boats. For a planing hull the right tool is Crouch's formula, which relates speed to the power-to-weight ratio directly. For an accurate resistance prediction on a specific displacement hull, the standard approaches are the Holtrop-Mennen statistical method for ships and the Delft series regressions for sailing yachts, both of which take beam, draught, prismatic coefficient and displacement into account rather than length alone.
Displacement-to-length ratio is the natural companion figure: DLR = displacement in long tons ÷ (0.01 × LWL in feet)³. A DLR under 150 marks a light hull that will exceed the classic coefficient; above 300 is a heavy cruiser that will not reach it. Reading hull speed alongside DLR tells you far more than either alone.
Once a passage is planned around a realistic speed, the rest of the navigation follows. How far ahead you will pick up a light or a headland is a matter of geometry and height of eye, handled by the distance to horizon calculator. Waypoints taken off a chart or an almanac often arrive in a coordinate format your plotter does not use, which the GPS coordinate converter resolves. And at the end of the run, how much rode to veer for the depth and tide you find is the job of the anchor scope calculator.
A closing historical note: the constant traces back to William Froude's tank-testing work in the 1860s and 1870s, which established that wave-making resistance scales with the dimensionless ratio now named after him. The 1.34 rule of thumb is simply that scaling law dressed in knots and feet, and the Froude number is how the same insight is written when you want it to hold in any unit system.