Estimate your new top speed
Starting from a GPS top speed gives the best estimate. Without one, the rough mode uses published constants.
Calculators
Boat Speed Calculator
Thinking about a bigger motor, or carrying more weight? Start from the top speed your boat runs today, and Crouch's formula estimates the new one. No speed yet? A second mode gives a rough figure.
Free tool · no signup
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How to estimate your boat's new top speed
Measure today's top speed
Run at full throttle on calm water with your usual load and read the speed on a GPS.
Add up the weight on the water
Count everything aboard: the boat, motor, fuel, water, gear and people. Naval architect Lorne Campbell stresses that the weight in Crouch's formula is everything the boat carries.
Use the motor's rated horsepower
Campbell notes that the quoted power of an outboard is usually measured at the prop, which is the power the formula wants.
Enter the new horsepower or weight
Leave a box blank if that number won't change. Before a repower, check the maximum horsepower on your boat's capacity plate.
Check the result on the water
Treat the answer as an estimate, then test with GPS. Prop the new motor so it reaches its rated full-throttle RPM range.
Crouch's formula
Crouch's formula estimates a planing boat's speed from its weight and the horsepower at the prop: speed equals a constant divided by the square root of weight over horsepower. The rec.boats FAQ says it assumes a prop that is 50% to 60% efficient. George Crouch was a Webb Institute mathematics professor and fast-boat designer between the world wars.
The constant depends on the boat, and its number depends on the units. Campbell points out that Crouch worked in mph, feet and pounds, while other versions use knots, so published constants don't carry over from one to the other. This calculator avoids the problem by starting from your own boat. Compared with itself, the constant cancels out, and speed changes with the square root of power to weight.
- New speed = today's speed × √((new hp ÷ new weight) ÷ (today's hp ÷ today's weight))
- It works in mph, knots or km/h, as long as both speeds use the same unit.
No speed to start from?
Then Crouch's formula needs a constant for your kind of boat, and the calculator's rough mode uses the ones in the rec.boats FAQ, which give the answer in knots. The same 3,000-pound, 115 hp boat comes out at about 29 knots (34 mph) with the lightweight planing cruiser's 150, and about 35 knots (41 mph) with the high-speed runabout's 180. That spread is why a measured speed gives a better estimate.
Crouch constants in the rec.boats FAQ
For speed in knots, with weight in pounds and horsepower at the prop.
| Boat type | Constant (C) |
|---|---|
| Typical lightweight planing cruiser | 150 |
| High-speed runabout | 180 |
| Race boats, hydroplanes | 200 to 230 |
How much faster with more horsepower
Crouch's formula for the same boat, with everything else unchanged.
| Change | Top speed |
|---|---|
| 10% more horsepower | +4.9% |
| 20% more horsepower | +9.5% |
| 25% more horsepower | +11.8% |
| 30% more horsepower | +14.0% |
| 50% more horsepower | +22.5% |
| Twice the horsepower | +41.4% |
| 5% more weight | −2.4% |
| 10% more weight | −4.7% |
| 20% more weight | −8.7% |
A worked example
A boat that weighs 3,000 pounds on the water runs 40 mph with a 115 hp outboard. Repowered to 150 hp with no change in weight, Crouch's formula gives 40 × √(150 ÷ 115), or about 45.7 mph. If the bigger motor adds 50 pounds, the estimate drops to about 45.3 mph. Loading 400 pounds of people and gear into the original boat instead brings 40 mph down to about 37.6.
When the estimate is off
Campbell calls Crouch's formula a tool for quick, preliminary estimates and warns to compare like with like. Even on the same hull, he says, the result shifts with the drive type, the outboard's mounting height, the prop's type and condition, where the weight sits and the boat's aerodynamics. A repower that changes any of those changes the real speed too.
Re-prop after a repower so the new motor reaches its rated full-throttle range with the prop pitch calculator, and compare the GPS result with the theoretical speed in the prop slip calculator.
Check the capacity plate first
Under the U.S. Coast Guard's rules (33 CFR 183), monohull boats under 20 feet, other than sailboats, canoes, kayaks and inflatables, must be marked with a maximum persons capacity, a maximum weight capacity and a maximum horsepower. The plate has to sit where the operator can see it when getting underway. Check that horsepower figure before you shop for a bigger motor.
Common questions
By Crouch's formula, top speed rises with the square root of the horsepower increase. A boat that runs 40 mph with 115 hp would run about 45.7 mph with 150 hp at the same weight.
Speed falls with the square root of the weight increase. Adding 10% to the weight on the water costs about 4.7% of top speed, everything else equal.
Roughly. The rough mode uses the rec.boats FAQ's constants, such as 150 for a lightweight planing cruiser and 180 for a high-speed runabout, with speed in knots. Other sources give different values, so a measured GPS speed gives a better estimate.
Campbell notes that the result shifts with the prop, the outboard's mounting height, the drive type, the weight's position and aerodynamics, none of which the formula includes.
Crouch's formula is meant for planing boats, so treat the estimate as rough for a pontoon or any boat that doesn't get on plane.
Look at its capacity plate. U.S. Coast Guard rules require monohull boats under 20 feet, other than sailboats, canoes, kayaks and inflatables, to show a maximum horsepower.
Sources
Lorne Campbell, The Crouch Formula: Quick preliminary performance estimates for fast planing craft (HSBO, 2016); rec.boats FAQ, What's a formula for top speed?; 33 CFR Part 183, Subpart B.