# Boat Speed Calculator

By Rahul Dhari
Last updated: May 27, 2021

The boat speed calculator determines the top speed of a boat based on the boat's power and displacement. If you wonder how fast a boat can go, this calculator will help you answer that. The calculator also utilizes a constant known as Crouch constant which differs based on the type of the boat.

The formula for the top speed of a boat is used by designers to perform preliminary design analysis of the hulls. This helps in keeping the cost of building a boat in check. Read on to understand how to calculate the speed of your yacht using Crouch's formula and to know how much horsepower do I need for my boat?

## What is boat speed — Calculating using Crouch's formula?

The speed of the boat, in simple words, is how fast it can go. However, unlike land vehicles this speed is not a ratio of distance and time. The speed of a boat having an engine to deliver P horsepower and displacing D pounds is written as:

S = Speed = sqrt(P / D) * C,

where S is the boat speed and C is the Crouch constant. The above equation is known as Crouch's formula.

Note: The formulation and value for the Crouch constant are specific for units such as the speed is in miles per hour and displacement is in pounds.

## What is displacement?

The displacement for a boat is defined as the volume of water displaced. The volume is then converted to weight. This property of a ship is an application of Archimedes' principle. In other words, the displacement of a boat is its weight. This weight is usually measured in tonnes or pounds. For instance, a modern US navy Gerald R Ford-class aircraft carrier displaces about 100,000 tons at its full load whereas a 17th-century fishing boat displaced only about 13 tons. The tonnage of the ship varies as per its class and purpose.

## Crouch constant

The Crouch constant depends on the *type of boat. The constant is applicable to a wide variety of boats, from runabouts to high-speed racing boats. It does not take the hull length into account. The table below has the value of the Crouch constant for different types.

Constant
Boat types
150
190
210
Racing boats
220
Hydroplanes
230
Racing catamarans, Sea sleds

## How to calculate boat speed using this calculator?

Follow the steps below to calculate boat speed:

• Step 1: Enter the shaft horsepower value, P.
• Step 2: Insert the boat's displacement, D.
• Step 3: Choose the Crouch constant, C from the list of boat types, or you can directly enter the value.
• Step 4: The boat speed calculator will now return the value of boat's top speed.

## Example of using the boat speed calculator

Calculate the speed of a racing hydroplane having an engine that delivers 3000 hp and displaces 6800 pounds of water.

To calculate boat speed:

• Step 1: Enter shaft horsepower value P = 3000 hp.
• Step 2: Insert the boat's displacement, D = 6800 lbs.
• Step 3: Choose the Crouch constant, C from the list for hydroplanes, i.e., C = 220.
• Step 4: Using the Crouch's formula:
S = sqrt(P / D) * C = sqrt(3000 / 6800) * 220 = 146.13 mph,
i.e., the speed of the hydroplane is about 146.13 miles per hour.

Alternatively, you can also run this calculator backwards to know how much horsepower I need for my boat to achieve a certain speed. Say you want a top speed of 150 miles per hour for your 6,000 lb hydroplane. You can then:

• Step 1: Enter top speed value S = 150 mph.
• Step 2: Insert the boat's displacement, D = 6000 lbs.
• Step 3: Choose the Crouch constant, C from the list for hydroplanes i.e C = 220.
• Step 4: The calculator will use Crouch's formula to return the horsepower value as:
Power = (P / C)2 * D = (150 / 220)2 * 6000 = 2789 hp

Therefore, you need an engine to deliver about 2800 hp to take your boat as fast as 150 mph.

## FAQ

### How do I calculate a boat's top speed?

To calculate the boat speed:

1. Divide the power delivered by the boat to the displacement.
2. Find the square root of the result from step 1.
3. Multiply by the Crouch constant.
S = sqrt(P / D) × C

### What is Crouch's formula?

Crouch's formula is the equation to find the top speed of a boat based on its power P and tonnage D. The speed of the boat, S is given by the equation.

S = sqrt(P / D) × C

### What is the value of Crouch's constant for a racing boat?

A racing boat has the value of Crouch constant around 210.

### What is the value of Crouch's constant for runabout boats?

An average runabout has the value of Crouch constant around 150 whereas it can go up to 190 for high-speed runabouts.

Rahul Dhari
Shaft horsepower (P)
hp(l)
Boat displacement (D)
lb
Boat type
Select...
Crouch's constant (C)
Speed (S)
mph
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