Horsepower to Knots Calculator

Estimate boat speed in knots from engine horsepower and displacement.

HP to Knots Calculator
RESULT

This calculator estimates a planing boat's speed from its engine horsepower and weight, using Crouch's classic formula. Results are shown in knots and MPH.

Quick answer: Speed (MPH) = C × √(HP ÷ Weight), where C is a hull constant (150–230). Multiply MPH by 0.869 for knots.

Crouch's Planing Formula

Formula
MPH = C × √(HP ÷ Weight)
C ≈ 150 (heavy cruisers) to 230 (race boats). Knots = MPH × 0.869.

The hull constant C reflects how efficiently the boat planes: around 150 for heavy cruisers, 190 for runabouts, and 220+ for light race hulls. Choose the value that matches your boat type for the best estimate.

How to Use This Calculator

  1. Enter boat weight (loaded) in pounds.
  2. Enter engine horsepower.
  3. Set the hull constant for your boat type.

Worked Example

Worked Example
MPH = 190 × √(250 ÷ 5000) = 42.5 MPH
Knots = 42.5 × 0.869 = 36.9 knots

Understanding Crouch's Formula

Crouch's planing-speed formula is the boating world's equivalent of the drag-strip trap-speed equations. It estimates the speed of a planing hull — one that rises up and skims across the water — from horsepower, weight, and a hull-efficiency constant C. It doesn't apply to displacement hulls, which push through the water and are limited by hull speed instead. The result is an estimate; real speed depends on hull condition, load distribution, and water state.

Choosing the Right Hull Constant

The constant C captures how efficiently a hull planes. We use roughly 150 for heavy cruisers and pontoon boats, 190 for typical runabouts and bowriders, 210 for performance V-hulls, and 220–230 for light race boats. Picking the value that matches your boat type is the biggest factor in getting an accurate estimate.

Estimated Speed (5,000 lb boat)

HorsepowerC=150C=190C=220
15026 MPH33 MPH38 MPH
25034 MPH42 MPH49 MPH
40042 MPH54 MPH62 MPH

Electric propulsion is rated in pounds of thrust rather than horsepower, which is a different quantity entirely — thrust to HP explains why a stationary trolling motor produces zero horsepower despite full thrust. For power-to-weight on land, see power-to-weight ratio.

Crouch's Formula Only Works Above Planing Speed

This is the limitation that produces most wrong answers. Crouch's formula describes a hull that has climbed onto the water and is skimming across it, supported by hydrodynamic lift. A hull that's still pushing through the water obeys entirely different physics, and the formula will badly overstate its speed.

A displacement hull is limited by the wave it generates. As it speeds up, the bow and stern waves lengthen. Eventually the boat is trying to climb the back of its own bow wave. Past that point, adding power just makes a bigger wave rather than more speed. That ceiling depends on waterline length alone:

Displacement hull speed
Hull speed (knots) = 1.34 × √(waterline length in feet)
Applies to any hull that can't generate enough lift to plane.
Waterline lengthHull speedWhat extra power achieves
20 ft6.0 knotsAlmost nothing beyond this point
25 ft6.7 knotsSteeply rising fuel burn for marginal gain
30 ft7.3 knotsLarger wake rather than more speed
40 ft8.5 knotsPractical ceiling for most displacement cruisers
50 ft9.5 knotsLonger waterline is the only real answer
Which formula applies to your boat? If it planes — most powerboats, RIBs and sport boats — use Crouch's formula and this calculator. If it doesn't plane, which covers trawlers, sailing yachts under power, narrowboats and most displacement cruisers, hull speed governs and doubling the engine won't meaningfully increase top speed.

The Three Speed Regimes

Boats don't accelerate smoothly from rest to top speed the way a car does. They pass through three distinct regimes with different physics, and the transition between them is why a boat can feel underpowered right up until it suddenly isn't.

RegimeWhat supports the hullSpeed behaviorGoverning rule
DisplacementBuoyancy aloneCapped by waterline length1.34 × √LWL
Semi-displacementPartly buoyancy, partly liftThe hardest, least efficient phaseNeither formula fits well
PlaningHydrodynamic liftRises with power-to-weightCrouch's formula

The middle regime is the one that catches people out. Getting over the hump takes more power than either cruising slowly or running fast on the plane, which is why an underpowered boat can wallow with the bow high and never break through. Once it does plane, the hull is riding on top of the water rather than pushing through it, drag falls sharply, and it'll often cruise comfortably at a throttle setting it could not accelerate through.

The practical consequence: a boat that can't plane with a full load isn't slightly underpowered. It's stuck in the worst part of the curve. Adding people, fuel and gear can be enough to push a marginal setup back over the hump in the wrong direction.

Why Loading Matters More Than It Looks

Crouch's formula uses the square root of power divided by weight, so weight changes hit speed less than proportionally. The effect is still bigger than most owners expect. On a small boat, what you load for a day out is a real fraction of its displacement.

Load conditionTotal weightSpeed vs empty
Empty, minimal fuel3,500 lb100%
Two people, half fuel4,000 lb94%
Four people, full fuel4,600 lb87%
Six people, full fuel and gear5,400 lb80%

A fifth of the top speed disappears with a full load, and manufacturers quote figures for the light condition. That gap isn't a fault; it is the difference between a test-day boat and a working one. The same principle applies to trim and weight distribution: shifting weight aft to help the hull get onto the plane, then trimming the drive out once planing, is worth more real speed than most bolt-on changes.

The Propeller Sits Between Power and Speed

The formula assumes the engine's power actually reaches the water, and the propeller decides how much of it does. Two boats identical in every other respect can differ by several knots on propeller choice alone.

Propeller factorEffect
Pitch too lowEngine hits its rev limit before the boat reaches its speed; power is available but unusable
Pitch too highEngine can't reach rated RPM, so it never makes its rated power; also lugs and runs hot
SlipThe propeller advances less per revolution than its pitch implies, typically 10–20%
Cavitation and ventilationThrust collapses as the blade loses grip on solid water
Blade count and diameterMore blades give smoother thrust and better grip, usually at some cost in top speed

The standard check is whether the engine reaches the top of its manufacturer-specified wide-open-throttle RPM range with a normal load. Falling short means the propeller is over-pitched and the engine isn't producing the horsepower this calculator assumes. Every calculation here depends on the engine actually being able to make its rated output, which the thrust to HP calculator approaches from the force side instead.

How this calculator is checked

We use the empirical cube-law relation between propulsive power and hull speed. Treat it as a planning estimate; hull type dominates real results.

Frequently Asked Questions

Use Crouch's formula: speed in MPH = C × √(HP ÷ weight), where C is a hull constant. Convert to knots by multiplying MPH by 0.869.

It reflects hull efficiency: roughly 150 for heavy displacement cruisers, 190 for typical runabouts, and 220+ for light high-performance race boats.

One knot equals about 1.151 MPH, so to convert MPH to knots you multiply by 0.869.

Crouch's formula is for planing hulls. Pure displacement hulls follow hull-speed limits based on waterline length instead.

Like cars, boats accelerate and plane based on power-to-weight. A heavier boat needs much more horsepower to reach the same speed.

No, and it'll badly overstate the speed. A displacement hull is limited by the wave it makes, capped at roughly 1.34 times the square root of waterline length in feet. A 30-foot waterline gives about 7.3 knots regardless of engine size — extra power just makes a bigger wake.

Getting over the hump takes more power than either slow cruising or running fast on the plane. An underpowered or heavily loaded boat can sit bow-high in that semi-displacement phase and never break through, even though it would cruise comfortably once planing.

More than expected on a small boat. Speed varies with the square root of power over weight, so a 3,500 lb boat loaded to 5,400 lb with six people, full fuel and gear loses about 20% of its top speed. Manufacturer figures are quoted for the light condition.

Yes, because the formula assumes the engine actually makes its rated power. An over-pitched propeller stops the engine reaching rated RPM, so it never produces the horsepower you entered. The check we run first: does the engine reach the top of its specified wide-open-throttle RPM range under a normal load?