The boat speed calculator above estimates how fast a planing or semi-displacement boat will go from the power driving it and the weight it has to lift. It uses Crouch's formula, the rule of thumb yacht designers have used for this for the best part of a century, and it shows you the constant it is using rather than hiding it, because that constant is where all the argument is.
Arb Digital builds free calculators that cite the relation they implement and are honest about its limits. This one is a rule of thumb, and it should be read as one: it will get you within a few knots for a conventional planing hull with a reasonable propeller, and it can be badly wrong for anything unusual.
This Is Not a Hull Speed Calculator
The distinction matters, so it comes first. Our separate hull speed calculator computes theoretical hull speed from waterline length and a speed-length coefficient, and reports the Froude number alongside it. That is the right tool for a displacement boat — a sailing yacht, a trawler, a canal boat — where the hull cannot climb over its own bow wave and speed is limited by length.
This page does the opposite job. It is for boats with enough power to climb out of that trap and plane, where waterline length is largely irrelevant and power-to-weight decides everything. Crouch's formula does not contain length at all, which is exactly why it works for planing craft and fails for displacement ones.
The boundary between them is the speed-length ratio, which this page reports so you can see which side of the line your boat is on. If yours comes out below about 1.5, you are looking at a displacement boat and the hull speed page is the one you want.
The Formula: How It's Calculated
Crouch's formula, as set out in the naval architecture boat design FAQ hosted at Brown University, is:
V = C ÷ √(displacement ÷ horsepower), which is the same as V = C × √(hp ÷ displacement)
V is speed in knots, displacement is in pounds, and the horsepower is measured at the propeller. That reference gives C as 150 for a lightweight planing cruiser, 180 for a high speed runabout and 200 to 230 for race boats and hydroplanes, and notes that the formula assumes a propeller in the region of 50% to 60% efficient. It also observes that manufacturers routinely understate displacement, which biases the answer optimistically.
Work the defaults through. A 300 hp engine losing 5% to the gearbox and shaft delivers 285 hp at the propeller. With a loaded displacement of 6,000 lb, the ratio is 285 ÷ 6,000 = 0.0475, whose square root is 0.2179. At C = 150 the estimate is 150 × 0.2179 = 32.7 knots, which is about 37.6 mph or 60.5 km/h.
The power-to-weight figure behind that is 6,000 ÷ 285 = 21.1 pounds per horsepower. On a 24 foot waterline, √24 is 4.90, so the speed-length ratio is 32.7 ÷ 4.90 = 6.7 — firmly planing, and comfortably inside the range where the formula is meant to be used.
What the Constant Actually Represents
C is not a physical property. It is a lumped fudge factor that absorbs hull efficiency, running trim, wetted surface, appendage drag and propeller efficiency into a single number, calibrated against boats that already existed.
That has two consequences. The first is that the result is directly proportional to C, so a 15% disagreement about which constant applies is a 15% disagreement about the answer. Moving from 150 to 180 raises the default estimate from 32.7 to 39.2 knots without changing anything about the boat.
The second is that C is only meaningful for a hull broadly like the ones it was calibrated on. A modern stepped hull, a deep-vee with a very high deadrise, a catamaran or a heavily loaded pontoon will all sit somewhere the published constants do not describe well. If you have a measured speed for your own boat at a known load and power, the honest move is to solve for C from that measurement and then use your own figure — that is what the custom option is for, and it turns a generic rule of thumb into a useful predictor for your specific boat.
Why the Displacement Field Deserves More Care Than the Power One
People agonise over horsepower and enter displacement from memory. That is backwards, because the two do not carry equal weight in the arithmetic, and the weight figure is far less reliable.
Both appear under a square root, so a 10% error in either moves the answer by about 5%. But engine power is a published, tested number that varies by a few per cent, while displacement as actually run can be 20% or more above a builder's dry figure once fuel, water, batteries, an outboard bracket, safety gear, a cooler and four adults are aboard.
A worked illustration: at 285 shaft horsepower and C = 150, a 6,000 lb boat estimates 32.7 knots and a 7,500 lb boat estimates 29.2 knots. That 1,500 lb — roughly 100 gallons of fuel plus six people and their gear — costs three and a half knots. This is why the same boat feels transformed when it runs light, and why comparing a magazine test figure against your own loaded experience is comparing two different boats. Our weight converter handles the unit side if your figures are in kilograms or metric tonnes.
Speed-Length Ratio and the Three Regimes
The speed-length ratio, speed in knots divided by the square root of waterline length in feet, is the conventional way to say which regime a boat is operating in. Naval architecture practice broadly treats a ratio below about 1.34 as displacement, roughly 1.34 to 2.5 as semi-displacement or transitional, and above about 2.5 as planing.
Those boundaries are conventions rather than physical constants, and the transitional band is genuinely awkward. As a hull is driven past its displacement speed, resistance rises steeply while the hull is climbing its own bow wave; only once hydrodynamic lift takes over does the picture improve. Wikipedia's overview of planing describes that transition, where a craft's weight shifts from being supported by buoyancy to being supported by hydrodynamic lift.
The practical point is that Crouch's formula assumes you are through that transition. Applied to a boat that never planes, it will confidently report a speed the boat cannot reach, because the formula has power proportional to the square of speed while a displacement hull needs power closer to the cube. The calculator flags this rather than staying silent, and directs you to the hull speed page when the ratio falls short.
What This Estimate Leaves Out
Several real effects are simply absent from the formula and will move your actual speed.
Propeller match is the largest. A boat with the wrong pitch will either fail to reach rated rpm, and so never make rated power, or over-rev and be limited by the governor. Neither shows up in an estimate that assumes a generic 50% to 60% efficient prop.
Running trim is next. A planing hull's drag depends strongly on its angle of attack, and trim tabs, drive angle, and where the load sits fore and aft all change it. A bow-heavy boat and a stern-heavy one at identical weight and power will not do the same speed.
Then there are conditions: sea state, wind, current, a fouled bottom, and air temperature and altitude affecting engine output. And finally the difference between a measured speed and a speed over the ground — a GPS reading in a two knot current is not a hull performance figure. The speed converter handles knots, mph and km/h, and the speed distance time calculator turns a run over a measured course into a speed you can check against this estimate.
Arb Digital designs and builds free interactive calculators that cite the relation they implement, state its limits, and earn links because they are genuinely useful. Browse what we have already published, or tell us what your audience keeps searching for.
Browse the Free Tools Hub Talk to Arb DigitalCommon Mistakes to Avoid
- Using dry displacement. Fuel, water, gear and people commonly add twenty per cent or more, and every pound of it costs speed.
- Entering brochure horsepower as shaft horsepower. The formula wants power at the propeller. Gearbox and shaft losses come off first.
- Applying it to a displacement boat. Crouch's formula has no length term and assumes planing. On a trawler or a sailing yacht it will report a speed the hull cannot reach.
- Treating C as a property of the boat. It is a calibration constant that absorbs hull, trim and propeller efficiency together, and the answer is directly proportional to it.
- Comparing against a GPS speed in a current. Speed over ground is not speed through the water, and a couple of knots of current will flatter or ruin any comparison.
Related Free Tools From Arb Digital
For displacement boats, the hull speed calculator is the correct tool, working from waterline length and a speed-length coefficient with the Froude number alongside. Convert units with the speed converter and the weight converter, check a timed run with the speed distance time calculator, and cross-check engine output with the horsepower calculator. On the running-cost side, the fuel cost calculator and the boat loan calculator cover the parts that are not physics. Everything else is on the free online tools hub.
Frequently Asked Questions
It is a rule of thumb for the top speed of a planing boat: speed in knots equals a hull-type constant divided by the square root of displacement in pounds over horsepower at the propeller. Equivalently, it is the constant multiplied by the square root of horsepower over displacement. It contains no length term at all.
The reference this page cites gives 150 for a lightweight planing cruiser, 180 for a high speed runabout and 200 to 230 for race boats and hydroplanes. If you have a measured speed for your own boat at a known load and power, solving for your own constant from that measurement is far better than picking from a list.
Because a planing hull is supported by hydrodynamic lift rather than buoyancy, so its speed is governed by power-to-weight rather than by length. Length limits a displacement hull, which is why the hull speed calculator uses it and this page does not.
No. Those are displacement hulls, and applying a planing formula to them will report a speed they cannot reach, because power rises roughly with the cube of speed for a displacement hull rather than the square. Use the hull speed calculator instead; this page flags the case when the speed-length ratio comes out low.
Loaded weight, as the boat will actually run, including fuel, water, batteries, gear and people. Builders' dry figures are routinely optimistic, and adding 1,500 lb to the default example costs about three and a half knots.
It is a rule of thumb, not a prediction. For a conventional planing hull with a well-matched propeller it will usually land within a few knots. It says nothing about propeller pitch, running trim, sea state, bottom fouling or a fouled or mismatched drive, any of which can move the real number substantially.
Speed in knots divided by the square root of waterline length in feet. Naval architecture practice broadly treats below about 1.34 as displacement, 1.34 to 2.5 as semi-displacement or transitional, and above about 2.5 as planing. Those boundaries are conventions rather than physical constants.
This page implements a published rule of thumb and reports an estimate, not a performance guarantee. Repowering, reloading or modifying a boat affects stability, structure and safe operation, and those are matters for the builder's specifications and a qualified marine professional rather than for arithmetic.
