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Hull Speed Calculator

Find your displacement hull speed limit

Units

Full-keel cruisers, trawlers

Theoretical Hull Speed

7.3

knots

km/h

13.6

LWL

30 ft

Speed-to-Length Ratio

1.1

Displacement mode

V / √LWL

6 / √30

Wave Resistance (% of total drag)45%

Moderate wave resistance — near hull speed

Hull Speed by Type

Heavy Displacement7.3 kn
Light Displacement7.3 kn
Semi-Displacement8.2 kn
Planing Hull13.7 kn

Speed-to-Length Ratio Guide

SLR ≤ 0.9

Sub-displacement. Very efficient. Low wake and wave-making resistance.

SLR 0.9–1.34

Normal displacement. Bow wave and stern wave begin to interact.

SLR 1.34–2.0

Semi-planing. Partially climbing over bow wave. High power needed.

SLR > 2.0

Planing. Hull is on top of its bow wave. Requires planing hull design.

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Frequently Asked Questions

Q

What is hull speed and how is it calculated?

Hull speed is the maximum efficient speed for a displacement hull, determined by the formula V = 1.34 × √LWL, where LWL is the waterline length in feet. At this speed, the bow wave and stern wave synchronize, creating a "wall" of water the boat cannot efficiently overcome.

  • Hull speed formula: V(knots) = 1.34 × √LWL(feet)
  • A 30 ft waterline gives hull speed of 1.34 × 5.48 = 7.3 knots
  • A 45 ft waterline gives hull speed of 1.34 × 6.71 = 9.0 knots
  • Above hull speed, wave resistance increases exponentially
  • Only applies to displacement hulls — planing hulls can exceed it
Waterline LengthHull SpeedSpeed at SLR 1.0
20 ft6.0 knots4.5 knots
30 ft7.3 knots5.5 knots
40 ft8.5 knots6.3 knots
50 ft9.5 knots7.1 knots
Q

What is the speed-to-length ratio?

The speed-to-length ratio (SLR) equals boat speed in knots divided by the square root of waterline length in feet. An SLR of 1.34 is hull speed. Below 1.0 is efficient displacement mode; above 2.0 indicates planing.

  • SLR = V(knots) / √LWL(feet)
  • SLR < 0.9: sub-displacement, very efficient, low wake
  • SLR 0.9–1.34: normal displacement mode, bow wave forms
  • SLR 1.34–2.0: semi-planing, fighting the bow wave
  • SLR > 2.0: planing, hull rides on top of its bow wave
Q

Can a boat exceed its hull speed?

Yes, but it requires disproportionately more power. Exceeding hull speed in a displacement hull can require 2–4 times the horsepower for a small speed gain. Planing hulls, multihulls, and ultra-light designs can exceed hull speed more efficiently.

  • Doubling power above hull speed may add only 0.5–1.0 knots
  • Light displacement sailboats can exceed hull speed when surfing waves
  • Planing hulls transition to skim the surface above SLR ~2.0
  • Catamarans have high LWL relative to displacement, enabling faster speeds
  • Semi-displacement hulls are designed to operate above displacement hull speed
Q

Why does waterline length matter more than overall length?

Waterline length (LWL) determines the wavelength of the bow wave. Overall length includes overhangs that do not contact water at rest. A boat heeling or loaded can increase its effective waterline and slightly raise hull speed.

  • LWL is measured at the water surface, not including bow/stern overhangs
  • Modern designs minimize overhangs to maximize LWL for a given LOA
  • When a sailboat heels, effective waterline often increases by 5–10%
  • Loading a boat deeper increases LWL slightly but also increases displacement
  • Measure LWL with the boat in normal cruising trim for accuracy
Q

How does wave resistance work at different speeds?

At low speeds, friction dominates drag. As speed increases, wave-making resistance grows and dominates above SLR 1.0. At hull speed, the boat is trapped between its own bow and stern waves, and further acceleration creates a steep resistance curve.

  • Below SLR 0.5: wave resistance is ~10% of total drag
  • At SLR 1.0: wave resistance is ~35–40% of total drag
  • At SLR 1.34 (hull speed): wave resistance is ~50% of total drag
  • Above hull speed: wave resistance can reach 80–95% of total drag
  • Power required increases roughly with the cube of speed in displacement mode

Example Calculations

130 ft Heavy Displacement Cruiser

Inputs

Waterline Length30 ft
Hull TypeHeavy Displacement
Current Speed6 knots

Result

Hull Speed7.3 knots
Speed-to-Length Ratio1.10
ClassificationDisplacement mode
Wave Resistance~45%

V = 1.34 × √30 = 1.34 × 5.477 = 7.3 knots. At 6 knots, SLR = 6 / 5.477 = 1.10 — normal displacement mode.

245 ft Semi-Displacement Motor Yacht

Inputs

Waterline Length45 ft
Hull TypeSemi-Displacement
Current Speed12 knots

Result

Hull Speed10.1 knots
Speed-to-Length Ratio1.79
ClassificationSemi-planing
Wave Resistance~80%

V = 1.50 × √45 = 1.50 × 6.708 = 10.1 knots. At 12 knots, SLR = 12 / 6.708 = 1.79 — semi-planing mode, high wave resistance.

Formulas Used

Theoretical Hull Speed

V = 1.34 × √LWL

Maximum efficient speed for a displacement hull, where the bow wave wavelength equals the waterline length.

Where:

V= Hull speed in knots
1.34= Froude number constant for hull speed (dimensionless)
LWL= Waterline length in feet

Speed-to-Length Ratio

SLR = V / √LWL

Dimensionless ratio classifying a vessel’s speed regime relative to its waterline length.

Where:

SLR= Speed-to-length ratio (dimensionless)
V= Boat speed in knots
LWL= Waterline length in feet

Understanding Hull Speed and Wave Resistance

Hull speed is a fundamental concept in naval architecture that explains why displacement vessels have a practical maximum speed. The formula V = 1.34 × √LWL was empirically derived from observing that a vessel’s bow wave wavelength equals its waterline length at this critical speed.

When a displacement hull moves through water, it creates a wave train. At low speeds, the bow wave and stern wave are separate. As speed increases, the stern wave moves aft until, at hull speed, the boat sits in a single wave trough with crests at bow and stern. Pushing beyond this speed means climbing uphill on its own bow wave.

Understanding hull speed helps boat owners set realistic expectations for passage times and fuel consumption. For sailboats, it explains why a 40-foot boat is substantially faster than a 25-footer in displacement mode — the hull speed difference is 8.5 vs 6.7 knots.

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Last Updated: Mar 25, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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