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Boat Speed Calculator

Calculate hull speed, maximum velocity, and Froude number for displacement and planing boats using waterline length, power, and displacement.

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Category Water Transport
Quick Presets:
Length at water surface when floating level
Total weight of boat including fuel, gear, passengers
Total shaft horsepower (0 for sail only)
Determines Crouch's constant for speed calculation
Enter boat specifications and click Calculate
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About

Hull speed represents the theoretical maximum velocity a displacement vessel can achieve before wave-making resistance increases exponentially. The formula V = 1.34 × √LWL derives from the Froude number Fr = 0.4, where wave crests align with bow and stern. Exceeding this threshold without planing capability wastes fuel and stresses the hull structure. Underestimating displacement or miscalculating waterline length leads to incorrect speed predictions, poor voyage planning, and potential engine overwork.

This calculator computes theoretical hull speed for displacement vessels, estimates planing speed using Crouch's constant C, and determines the Froude number to classify your hull's operating regime. Results assume calm water, clean hull, and optimal trim. Real-world performance degrades with fouling, sea state, and loading conditions - expect 10−15% reduction in choppy waters.

boat speed hull speed knots calculator froude number marine calculator waterline length displacement hull planing hull

Formulas

The theoretical hull speed for displacement vessels derives from the Froude number relationship, where wave resistance dominates at the critical threshold.

Vhull = 1.34 × √LWL

Where Vhull is hull speed in knots and LWL is waterline length in feet. The constant 1.34 corresponds to a Froude number of approximately 0.4.

For planing hulls with sufficient power, Crouch's formula estimates maximum speed.

Vmax = C × √HPD

Where C is Crouch's constant (ranges 100−260 based on hull type), HP is engine horsepower, and D is displacement in pounds.

The dimensionless Froude number classifies the operating regime.

Fr = V√g × LWL

Where g = 9.81m/s². At Fr < 0.3 the hull operates in displacement mode. Between 0.3 and 0.5 is semi-displacement. Above 0.5 indicates planing.

Reference Data

Vessel TypeTypical LWLHull SpeedCrouch's CDisplacementOperating Regime
Racing Dinghy12ft4.6kn230200lbPlaning
Day Sailer18ft5.7kn1901,500lbSemi-displacement
Coastal Cruiser28ft7.1kn1508,000lbDisplacement
Motor Yacht45ft9.0kn18035,000lbSemi-displacement
Bass Boat16ft5.4kn2201,200lbPlaning
Center Console22ft6.3kn2103,500lbPlaning
Trawler38ft8.3kn13028,000lbDisplacement
Catamaran35ft7.9kn20012,000lbSemi-displacement
Offshore Racer40ft8.5kn22015,000lbPlaning
Tugboat50ft9.5kn10080,000lbDisplacement
Runabout14ft5.0kn200900lbPlaning
Pocket Cruiser20ft6.0kn1603,000lbDisplacement
Sport Fisher32ft7.6kn19014,000lbSemi-planing
Inflatable RIB10ft4.2kn240400lbPlaning
Classic Wooden25ft6.7kn1406,000lbDisplacement
Express Cruiser30ft7.3kn18510,000lbSemi-planing
Houseboat42ft8.7kn11025,000lbDisplacement
Jet Ski (PWC)8ft3.8kn260600lbPlaning
Mega Yacht120ft14.7kn160400,000lbDisplacement
Fishing Skiff15ft5.2kn180700lbSemi-planing

Frequently Asked Questions

At hull speed, the bow wave and stern wave synchronize with the vessel length, creating a trough the boat cannot climb out of without planing capability. The wave-making resistance increases with the sixth power of speed beyond this point, requiring exponentially more power for marginal gains. A displacement hull trapped in its own wave system would need roughly eight times the power to gain 50% more speed.
Waterline length (LWL) measures only the portion of the hull in contact with water at rest. Overhangs at bow and stern contribute to LOA but not LWL. A 30-foot boat with extended bow pulpit might have only 25 feet of waterline. Using LOA instead of LWL inflates hull speed predictions by approximately 10%, leading to unrealistic voyage time estimates.
Light racing hulls with stepped bottoms use C values of 220-260. Typical recreational planing boats range 180-210. Heavy cruisers and semi-displacement hulls use 140-170. Houseboats and full-displacement vessels use 100-130. When uncertain, use the lower value for conservative estimates. The constant accounts for hull efficiency, trim angle, and hydrodynamic lift characteristics.
Displacement directly impacts planing speed through Crouch's formula. Adding 500 pounds to a 3,000-pound boat increases displacement by 17%, reducing planing speed by approximately 8%. Hull speed remains unaffected since it depends only on waterline length. However, increased displacement may slightly increase waterline length due to deeper immersion, marginally raising hull speed.
Calculated speeds assume flat water and clean hull. Wind chop reduces speed by 5-10%. One-foot seas reduce it by 15-20%. Heavy fouling (barnacles, algae) adds drag equivalent to losing 10-25% of propulsive power. Head currents directly subtract from ground speed. A boat with 7-knot hull speed making way against a 2-knot current achieves only 5 knots over ground.
Modern racing sailboats with planing hulls (like dinghies and sport boats) regularly exceed hull speed when surfing downwind. Traditional cruising sailboats with heavy displacement cannot. Catamarans effectively double waterline length by using two narrow hulls, achieving higher speeds without planing. A 40-foot catamaran might sustain 12+ knots where a monohull is limited to 8.5 knots.