Boat Speed Calculator
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 (visit the boat loan calculator for more). 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 = √(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 in miles per hour and displacement in pounds.
💡 Our tools can convert units automatically, but if you'd like to learn how to do these conversions yourself, then our speed conversion and torque to hp calculator could come in handy!
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. Fordclass aircraft carrier displaces about 100,000
tons at its full load, whereas a 17thcentury fishing boat displaces only about 13
tons. The tonnage of the ship varies as per its class and purpose.
Keep reading about Archimedes' principle at our Archimedes' principle calculator and find out if an object sinks or floats in a liquid!
Crouch constant
The Crouch constant depends on the type of boat. The constant is applicable to a wide variety of boats, from runabouts to highspeed 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  Cruisers, average runabouts, passenger vessels 
190  Light highspeed cruisers, Highspeed runabouts 
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 = √(P / D) × C = √(3000 / 6800) × 220 = 146.13 mph
i.e., the speed of the hydroplane is about146.13
miles per hour.
Alternatively, you can also run this calculator backward 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:

Divide the power delivered by the boat to the displacement.

Find the square root of the result from step 1.

Multiply by the Crouch constant.
S = √(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 = √(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 highspeed runabouts.