What is boat speed — Calculating using Crouch's formula?
The Boat Speed Calculator determines the top speed of a boat based on its engine power and displacement. The formula used is known as Crouch's formula:
S = √(P / D) × C
Where:
- S — Boat speed (miles per hour, mph)
- P — Shaft horsepower (hp)
- D — Displacement in pounds (lbs)
- C — Crouch constant (depends on boat type)
This formula is widely used by naval designers to perform preliminary design analysis of hulls and estimate the top speed of a vessel before construction.
What is displacement?
The displacement of a boat is defined as the volume of water it displaces, converted to weight. By Archimedes' principle, a floating object displaces water equal to its own weight — so the displacement essentially equals the weight of the boat.
Displacement is typically measured in tonnes or pounds. For example:
- A modern US Navy Gerald R. Ford-class aircraft carrier displaces about 100,000 tons
- A 17th-century fishing boat displaces only about 13 tons
Crouch constant
The Crouch constant C depends on the type of boat. The table below shows the values for different vessel categories:
| Constant (C) | Boat Type |
|---|---|
| 150 | Cruisers, average runabouts, passenger vessels |
| 190 | Light high-speed cruisers, high-speed runabouts |
| 210 | Racing boats |
| 220 | Hydroplanes |
| 230 | Racing catamarans, sea sleds |
How to calculate boat speed using this calculator?
Follow these steps to calculate boat speed:
- Select Calculate Speed mode.
- Enter the shaft horsepower value (P).
- Enter the boat's displacement in pounds (D).
- Choose the Crouch constant from the boat type dropdown, or enter a custom value.
- The calculator will instantly return the boat's top speed in mph.
You can also run the calculator in reverse (select Calculate Power mode): enter the desired speed, displacement, and Crouch constant to find out how much horsepower your engine needs to deliver.
Example of using the boat speed calculator
Calculate the speed of a racing hydroplane with an engine delivering 3,000 hp and a displacement of 6,800 lbs.
- Enter shaft horsepower: P = 3,000 hp
- Enter boat displacement: D = 6,800 lbs
- Select Crouch constant for hydroplanes: C = 220
- Result: S = √(3000 / 6800) × 220 ≈ 146.13 mph
Reverse example: To achieve 150 mph with a 6,000 lb hydroplane (C = 220):
- Enter target speed: S = 150 mph
- Enter boat displacement: D = 6,000 lbs
- Select Crouch constant: C = 220
- Result: P = (150 / 220)² × 6,000 ≈ 2,789 hp
FAQs
How do I calculate a boat's top speed?
Use Crouch's formula: divide the power by the displacement, take the square root, then multiply by the Crouch constant:
S = √(P / D) × C
What is Crouch's formula?
Crouch's formula calculates the top speed of a boat based on its engine power P and displacement D. The Crouch constant C varies by boat type and accounts for hull design characteristics.
What is the Crouch constant for a racing boat?
A racing boat has a Crouch constant of approximately 210.
What is the Crouch constant for runabout boats?
An average runabout has a Crouch constant of 150, while a high-speed runabout can reach up to 190.