# 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. 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.

## 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:
i.e., the speed of the hydroplane is about`S = sqrt(P / D) * C = sqrt(3000 / 6800) * 220 = 146.13 mph`

,`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:

**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 = 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**.