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?

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.

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 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!

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.

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.

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 about 146.13 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.