How do you calculate a boat's top speed?

For planing hulls divide the power by the displacement weight, take the square root and multiply by the Crouch constant. S is equal to C multiplied by the square root of P divided by D. If the power is 300 HP, the displacement weight is 6,000 pounds, and the constant is 150 then the top speed will be about 33.5 knots.

What is the Crouch Formula?

The Crouch formula estimates the maximum speed of a planing boat based on its shaft power P and displacement weight D. S is equal to C times the square root of P divided by D. P is in horsepower, D is in pounds, and the resulting speed will be in knots. C is a constant that depends on the type of hull.

What is the crouch coefficient for each boat?

For typical small powerboats or cruisers it is about 150, for fast small powerboats 190, for racing boats 210, for boats with stepped or trihedral hull shape 220 and for racing catamarans or offshore sailboats 230. A higher coefficient indicates a more slippery hull.

What is hull speed and how is it determined?

Hull speed is the maximum speed that a displacement boat can achieve. This type of boat does not actually "glide" over the surface of the water, but rather displaces the water in front of it. Hull speed depends only on the length of the waterline, and when the length of the waterline is given in feet, hull speed (in knots) is approximately 1.34 times the square root of the length of the waterline. For a boat with a waterline length of 30 feet, the hull speed would be about 7.3 knots.

How can you estimate boat speed from engine rpm?

Divide the engine speed by the gear ratio to obtain the propeller speed. Multiply this by the pitch to obtain the theoretical distance traveled and then subtract about a 10- to 15-percent slip. If using inches and miles per hour, the theoretical speed is the product of the propeller speed and pitch divided by 1056. When calculating in knots use 1215 instead of 1056.

Boat Speed Calculator

Your boat

How do you want to estimate speed?

Power and displacement

Displacement hull speed

Propeller RPM

Hull type (Crouch constant)

Shaft power

Displacement (weight)

Find the power needed for a target speed

Enter a target top speed and read the shaft power Crouch's formula requires.

Estimated top speed

Power-to-weight (hp/tonne)

With about 300 hp(l) of shaft power driving 6000 lb, this planing hull tops out near 33.541 kn.

Crouch's formula is an empirical estimate for planing hulls. Real speed depends on the hull shape, trim, load, and water conditions, so treat the number as a ballpark rather than a guarantee.

Speed in detail

The estimated top speed expressed in common speed units
Unit	Top speed
Knots	33.54
Miles per hour	38.6
Kilometers per hour	62.12
Meters per second	17.25
Feet per second	56.61

The ship speed calculator is used to estimate the speed that a boat can achieve. There is no single formula for all boats as the result varies depending on the type of boat. High-speed planing boats are limited by their power and weight, while heavier displacement hulls are limited by their waterline length. Additionally, all motorized boats are limited by the propeller's rotational speed, which turns underwater to create forward propulsion. This tool covers these three cases.

Three methods to determine your boat speed:

Choose the method that is most appropriate for your boat. The power and displacement method uses the classic Crouch formula to estimate the speed of a planing hull based on engine power and weight. The displacement body method is suitable for sailboats or slow-moving trawlers. These boats do not move over the surface of the water, but displace water, so their length at the waterline determines top speed. The propeller RPM method calculates speed from engine revolutions per minute (RPM), gear ratio, and pitch. This is useful when the propulsion system is known but power output is unknown.

The Crouch formula for planing boats:

The Crouch formula relates the top speed of a planing boat to its shaft power and displacement weight, adjusted by a constant that takes into account the type of ship.

S = C \times \sqrt{\frac{P}{D}}

S is the maximum speed in knots. P is the shaft power in horsepower. D is the displacement weight in pounds. C is the Crouch constant. Let's say a small speedboat has a power of 300 HP, a weight of 6,000 pounds and a constant of 150. In this case:

S = 150 \times \sqrt{\frac{300}{6{,}000}} = 150 \times \sqrt{0.05} \approx 33.5 \text{ knots}

The power output is within the root zone so increasing the power only has a small effect on speed, even doubling the power will only increase top speed by about 41 percent. So even small increases in speed of just a few knots can quickly add up to significant costs.

The constant C comes from the book Propeller Handbook by Dave Gerr and depends on how slippery the hull is. The following table shows typical values:

Hull type	Crouch constant C
Average runabout, cruiser, passenger vessel	150
High-speed runabout, light cruiser	190
Race boat	210
Stepped or three-point hydroplane	220
Racing power catamaran, sea sled	230

The Crouch formula can also be used in reverse. If the "Reverse Calculation" option is enabled and a desired top speed is entered, then the calculator will invert the formula to show the required shaft power.

P = D \left(\frac{S}{C}\right)^2

Displacement hull speed

Displacement hulls cannot plane and are therefore limited by the waves they create as they move through the water. When the bow wave and stern wave have the same length as the hull, the ship is in a trough of its own making which makes further acceleration difficult. This limit is called the hull speed and depends only on the length of the waterline.

\text{hull speed} = 1.34 \times \sqrt{\text{LWL}}

The length of the waterline is given in feet while the calculated hull speed is given in knots. A sailboat with a 30-foot waterline has a hull speed of about 7.3 knots. This factor typically ranges from 1.34 to 1.51. Heavier and slimmer hulls tend toward the lower end, while lighter and more efficient hulls can exceed this value. This is similar to the physical principle described by the Froude number, which is a ratio that determines when a ship begins to plane.

Calculation of ship speed based on propeller revolutions.

If the gear ratios are known there is a way to estimate speed using the propeller. The propeller revolutions are usually below engine rpm and the difference is determined by the transmission. If water was a solid then each revolution of the propeller would move the ship forward an amount equal to the pitch.

\text{prop rpm} = \frac{\text{engine rpm}}{\text{gear ratio}}

If you multiply the propeller revolutions by the pitch, you get the theoretical distance traveled per minute. You then need to subtract slippage, which is the amount lost due to water being a liquid. In everyday units, if the pitch is given in inches, the theoretical top speed would be:

\text{mph} = \frac{\text{pitch} \times \text{prop rpm}}{1056}, \qquad \text{knots} = \frac{\text{pitch} \times \text{prop rpm}}{1215}

1056 converts revolutions per minute to miles per hour and 1215 converts it to knots. Sometimes you'll see a conversion constant of 1056 for knots, but that constant is only correct for miles per hour. The corresponding value for nautical units is about 1215. This tool internally calculates in metric units then converts so you can read the results in your preferred units. If the engine is running at 4,000 revolutions per minute and drives a propeller through a gearbox with a ratio of 1.5 to 1, the propeller will be turning about 2,667 revolutions per minute. A propeller with a pitch of 19 inches will slip by 12 percent, which is equivalent to a speed of about 42 miles per hour or about 37 knots.

Slip is the reason actual speed falls short of theoretical speed. Most recreational boats experience a 10 to 15 percent loss, while heavier boats, overloaded boats or improperly sized propellers can result in even greater losses. Hull fouling, improper trim and waves on the water surface can also reduce speed.

What method should be used?

Please select the method that is appropriate for your boat. For motor boats that can plane use the Crouch formula based on power and weight. For sailboats, trawlers or canoes that do not plane use the displacement hull form speed. If you have detailed information about the engine and propeller then using the propeller revs method will give a practical comparison option. All three methods are estimates so it is common to compare them. If the results of the propeller calculations and Crouch formula differ significantly this usually indicates that the propeller is not optimally sized or that the boat is overloaded.

This calculator is for general educational and planning purposes only. Any method described herein is an empirical estimate, and the actual boat speed will depend on hull shape, load, trim, fouling, and water conditions. Check values against sea trials or GPS before relying upon them.

Frequently asked questions

How do you calculate a boat's top speed?: For planing hulls divide the power by the displacement weight, take the square root and multiply by the Crouch constant. S is equal to C multiplied by the square root of P divided by D. If the power is 300 HP, the displacement weight is 6,000 pounds, and the constant is 150 then the top speed will be about 33.5 knots.
What is the Crouch Formula?: The Crouch formula estimates the maximum speed of a planing boat based on its shaft power P and displacement weight D. S is equal to C times the square root of P divided by D. P is in horsepower, D is in pounds, and the resulting speed will be in knots. C is a constant that depends on the type of hull.
What is the crouch coefficient for each boat?: For typical small powerboats or cruisers it is about 150, for fast small powerboats 190, for racing boats 210, for boats with stepped or trihedral hull shape 220 and for racing catamarans or offshore sailboats 230. A higher coefficient indicates a more slippery hull.
What is hull speed and how is it determined?: Hull speed is the maximum speed that a displacement boat can achieve. This type of boat does not actually "glide" over the surface of the water, but rather displaces the water in front of it. Hull speed depends only on the length of the waterline, and when the length of the waterline is given in feet, hull speed (in knots) is approximately 1.34 times the square root of the length of the waterline. For a boat with a waterline length of 30 feet, the hull speed would be about 7.3 knots.
How can you estimate boat speed from engine rpm?: Divide the engine speed by the gear ratio to obtain the propeller speed. Multiply this by the pitch to obtain the theoretical distance traveled and then subtract about a 10- to 15-percent slip. If using inches and miles per hour, the theoretical speed is the product of the propeller speed and pitch divided by 1056. When calculating in knots use 1215 instead of 1056.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Hull speed
Displacement hull speed and the 1.34 x sqrt(LWL) relationship.
Wikipedia: Froude number
The speed-length ratio that governs planing and hull speed.
Gerr, Dave. The Propeller Handbook (International Marine / McGraw-Hill)
Origin of Crouch's planing-speed constants and propeller pitch and slip.