Boat Speed Calculator
Enter your engine horsepower, boat displacement, and boat type to estimate top speed with Crouch's formula. Switch to the propeller mode to solve from RPM, pitch, gear ratio, and slip. Or use the hull speed mode to find the theoretical maximum for a displacement hull from its waterline length. Results update instantly in mph, knots, or km/h.
Crouch's formula: estimating top speed from horsepower
George Crouch's empirical formula -- S = C x sqrt(P / D) -- has been used by naval architects and boating enthusiasts since the early 20th century to estimate the top speed of planing hulls. P is shaft horsepower, D is displacement in pounds, and C is a constant that reflects hull efficiency. Shaft horsepower is the power delivered to the propeller shaft, which is typically 85-90% of rated engine horsepower for outboard motors after accounting for drivetrain losses. Displacement equals the total weight of the loaded boat, including fuel, passengers, and gear, because Archimedes' principle tells us a floating object displaces its own weight in water. Heavier boats need more horsepower to reach the same speed.
Propeller pitch, RPM, and slip
In an ideal world a propeller with 19 inches of pitch would advance exactly 19 inches through the water with every revolution. In practice, the blades slip through the water: a well-trimmed planing hull running in calm water at optimal load typically experiences 10-20% slip, meaning the boat travels only 80-90% of the theoretical pitch distance per revolution. To estimate actual speed from propeller geometry: first divide engine RPM by the gear ratio to get propeller RPM, then multiply by pitch to get theoretical advance per minute, convert to mph (multiply by 60 and divide by 63360 inches per mile), and finally reduce by the slip percentage. Prop slip can be measured by comparing theoretical speed with GPS speed at wide-open throttle on flat water.
Hull speed and displacement hulls
Hull speed, sometimes called wave-making speed, is the theoretical maximum efficient speed for a displacement hull. When a boat reaches this speed the hull length matches its bow wave, creating a trough at the stern that the boat cannot climb out of without dramatically more power. The formula, derived from Froude number theory, is V = 1.34 x sqrt(LWL), where LWL is the waterline length in feet and V is speed in knots. The constant 1.34 corresponds to a Froude number of 0.4. Beyond hull speed, power requirements increase sharply and fuel economy collapses for traditional displacement hulls. Modern semi-displacement and planing designs get around this by lifting the hull clear of the water at higher speeds.
Converting between mph, knots, and km/h
Boat speed is measured in different units depending on context. Knots (nautical miles per hour) are the international standard for marine navigation: one knot equals 1.15078 mph or 1.852 km/h exactly. Racing and recreational boating in the United States typically uses mph. European and international regulations often use km/h. This calculator lets you read results in whichever unit you use. One knot = 1.15 mph = 1.852 km/h. To convert mph to knots, multiply by 0.869. To convert knots to km/h, multiply by 1.852.
Crouch's constants by boat type
| Boat type | Crouch's constant (C) | Typical speed range |
|---|---|---|
| Cruisers, average runabouts, passenger vessels | 150 | 20-40 mph |
| Light high-speed cruisers, high-speed runabouts | 190 | 35-60 mph |
| Racing boats | 210 | 50-80 mph |
| Hydroplanes | 220 | 60-100 mph |
| Racing catamarans, sea sleds | 230 | 70-120 mph |
These hull-type constants were defined by George Crouch and are used worldwide to estimate planing-hull top speed. Higher constants reflect more efficient hull designs.
Frequently asked questions
What is Crouch's formula and is it accurate?
Crouch's formula -- S = C x sqrt(P / D) -- is an empirical rule of thumb published by naval architect George Crouch. It gives a useful ballpark for planing-hull top speed but makes several simplifying assumptions: that the propeller is correctly pitched for that speed, that hull drag follows a predictable curve, and that the hull is in good condition. Real-world speed can vary 10-20% from the estimate. For best results, use actual shaft horsepower (not rated engine horsepower), include the full loaded weight in displacement, and choose the boat-type constant that best matches your hull.
How do I find my boat displacement?
Displacement is the total weight of your loaded boat. Start with the dry hull weight from the manufacturer specification, then add the weight of the outboard or inboard engine if not included, full fuel load (gasoline weighs about 6.1 lb per US gallon), gear, passengers, and anything else on board. Boating magazines sometimes use half-load estimates for comparisons. For Crouch calculations, use the weight you actually run at, since extra weight lowers your speed noticeably.
What is propeller slip and what causes it?
Propeller slip is the difference between the theoretical advance from pitch and the actual distance traveled. It occurs because water is not a solid medium -- the blades push against fluid that has some give, creating turbulence and cavitation. Typical slip ranges from 10% for a well-optimized planing hull in good conditions to 25% or more for an underpowered boat, a fouled bottom, or a badly pitched prop. You can measure your actual slip by running at wide-open throttle on flat water with a GPS and comparing recorded speed to the theoretical pitch speed.
Can I use this calculator for sailboats?
The hull speed mode is well-suited for monohull sailboats and traditional displacement motorboats. Enter the waterline length (not overall length) to get the theoretical hull speed in your chosen unit. Most cruising sailboats are designed to sail comfortably at 90-100% of hull speed under sail. The Crouch and propeller modes are designed for planing powerboats and are not applicable to sailing performance.
What is the speed-to-length ratio?
The speed-to-length ratio (SLR) is boat speed in knots divided by the square root of the waterline length in feet. For a displacement hull, the practical maximum is around 1.34, which is the basis of the hull speed formula. An SLR of 1.0 is comfortable cruising for most displacement designs. Semi-displacement hulls can push to 2.0 or beyond with sufficient power. Planing hulls running at planing speed have SLRs of 3 or higher.
How does gear ratio affect boat speed?
The gear ratio is the number of engine revolutions for each propeller revolution. A 2:1 ratio means the engine turns twice for every propeller turn. A lower gear ratio (closer to 1:1) makes the propeller spin faster relative to the engine, which suits higher-pitch props. A higher ratio slows the prop relative to the engine, suiting lower-pitch props for more torque. The gear ratio multiplied by the pitch and divided by 63360 (inches per mile) gives you the speed-per-engine-RPM before slip -- so you can use it to choose which pitch prop to run at a target RPM.