Crouch's formula (S = √(P/D) × C) is a practical marine engineering equation developed to estimate the maximum speed of planing hull boats. It's widely used in the boating industry because it provides quick, reasonably accurate estimates based on three key parameters: shaft horsepower, displacement, and a constant specific to boat type. The formula accounts for the relationship between available power, boat weight, and hydrodynamic efficiency.

Crouch's constant (C) is a numerical coefficient that varies between 150 and 230 depending on boat type and hull design. It represents the efficiency of the hull in converting available horsepower into forward motion. For example, lightweight planing cruisers use C=150, while high-performance hydroplanes use C=220-230. The constant accounts for differences in hull shape, waterline length, beam, and other factors affecting hydrodynamic performance. Higher constants indicate more efficient hulls capable of higher speeds with the same horsepower.

The calculator typically provides accuracy within 5-15% for planing hulls when using correct input values. Accuracy depends heavily on the accuracy of your input data (particularly displacement and horsepower) and the appropriateness of the Crouch constant for your specific boat. For displacement hulls, accuracy is lower. Actual performance varies due to water conditions, propeller matching, hull fouling, trim, weight distribution, and numerous other factors. Use results as estimates and benchmarks rather than absolute values. Always conduct actual speed trials for precise performance data.

Yes! Use the reverse formula: P = (S/C)² × D. Simply rearrange the original Crouch formula when you know your target speed (S), displacement (D), and boat type (C). For example, if you want a 50 mph speed with a 5,000 lb runabout (C=180): P = (50/180)² × 5,000 ≈ 386 hp required. This helps determine the engine size needed for your desired performance level. Remember that engine selection also depends on available space, fuel efficiency, and other practical considerations.

The calculator supports comprehensive unit options: Horsepower (HP) or kilowatts (kW) for engine power, kilograms (kg), pounds (lb), or metric tons (t) for displacement, and miles per hour (mph), kilometers per hour (km/h), knots (kn), or meters per second (m/s) for speed. Simply select your preferred units from the dropdown menus before entering values. The calculator automatically converts between units for internal calculations and displays results in your chosen format.

Boat displacement is the weight of water that your boat displaces when floating. By Archimedes' principle, this equals your boat's total weight, including the hull, engine, fuel, cargo, passengers, and all equipment. For a boat to float, it must displace a weight of water equal to its own weight. Displacement is critical for speed calculations because heavier boats require more power to achieve the same speed as lighter boats. You'll typically find displacement specifications in your boat's manual or technical specifications. If unavailable, you can estimate it from the boat's dimensions and construction materials.

Planing hulls rise onto the water surface at speed, reducing drag and enabling high speeds. They use Crouch's formula effectively and include speedboats, runabouts, and racing boats. Displacement hulls push through water rather than rise on it, limiting speed but offering comfort and fuel efficiency. They include trawlers, cruisers, and sailboats. Crouch's formula works best for planing hulls and gives less accurate results for pure displacement hulls. Semi-displacement hulls blend characteristics of both types.

Multiple factors reduce actual speed below calculated estimates: (1) Water conditions - rough seas and waves increase resistance; (2) Hull fouling - algae and barnacles reduce efficiency by 5-15%; (3) Propeller issues - damaged props or poor pitch matching; (4) Engine wear - aged engines deliver less power; (5) Improper trim - bad weight distribution affects hydrodynamics; (6) Increased load - more fuel, cargo, or passengers increases displacement; (7) Cold water - increases drag; (8) Wind - headwinds create resistance. Regular maintenance maximizes achievable speed.

Shaft horsepower (SHP) is the power delivered to your propeller shaft. It's typically 85-95% of your engine's rated brake horsepower (BHP) due to transmission losses. Check your boat's manual or specifications for SHP. If only BHP is available, multiply by 0.9 for a rough estimate. For older boats, SHP might be listed as "HP at propeller" or similar. If no documentation exists, you can work backward from actual speed trials using Crouch's formula: P = (S/C)² ÷ D. Consult a marine mechanic if unsure about your engine's specifications.

Hull speed is the theoretical maximum speed of displacement hulls calculated by 1.34 × √(waterline length in feet), expressed in knots. It's determined purely by hull geometry and wave-making characteristics. Maximum speed (calculated by Crouch's formula) is the actual achievable speed combining horsepower, displacement, and hull efficiency. For planing hulls, actual maximum speed can far exceed hull speed because they rise on the water surface. For displacement hulls, actual speeds rarely exceed 10% above theoretical hull speed regardless of added power, making it a hard physical limit for that hull design.

Select the boat type from the dropdown menu that best matches your vessel: lightweight cruisers (150), typical runabouts (160), high-speed runabouts (180), racing boats (210), or hydroplanes (220). If your boat doesn't fit these categories, research your specific hull type or check your boat's documentation. For custom boats, naval architects can recommend appropriate values. When in doubt, select "Custom Value" and enter the constant. You can verify by comparing calculated speeds against actual speed trials—if results are consistently off, try adjacent constant values (vary by ±10-20) to fine-tune accuracy for your specific hull.