Boat Planing Speed and Froude Number Calculator

Calculate length-based Froude number from boat speed and loaded waterline length, then find the speed at a selected transition or planing comparison value. Everything runs locally in this browser tab.

A Froude-number threshold does not prove that a boat is planingPlaning is a physical condition involving dynamic lift. Hull geometry, loading, trim, wetted area, power, water depth, waves, and controls determine when and whether a specific boat planes safely. Treat calculated speeds as comparison markers only.

Boat length and speed

Waterline length

Use loaded waterline length, not length overall.

Speed comparison

Optional. Prefer steady speed through the water.

Inputs are processed only in your browser and are not sent, saved, or added to analytics events.

Froude and target-speed result

Enter the loaded waterline length and calculate.

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Length Froude number formula

The International Towing Tank Conference defines Froude number as a dimensionless comparison of inertia and gravity effects. This calculator uses loaded waterline length as the declared characteristic length.

Fn = V ÷ √(g × L)

Speed at target Fn = target Fn × √(g × L)

Here, V is speed in m/s, g is standard gravity (9.80665 m/s²), and L is loaded waterline length in meters. Units are converted before calculation.

What the planing-speed estimate means

The target speed is the speed at which the entered waterline length reaches the selected length Froude number. Fn 0.40 is close to the conventional wave-length or displacement-hull-speed reference. Fn 1.00 is included as a transparent high-speed planing-range comparison, not a universal takeoff threshold.

Published planing studies use different reference lengths, including beam and the cube root of displacement volume. Their values must not be substituted directly into this length-based formula.

Verify the reference definition. A quoted “Froude number” is incomplete unless its characteristic length is stated.

How to use this calculator

  1. Enter the boat's loaded length at waterline and select feet or meters.
  2. Optionally enter observed or design speed. Use speed through water for hull-performance comparisons.
  3. Choose a preset Froude-number marker, or enter a custom target supported by a source that uses the same length definition.
  4. Calculate and compare the current Fn with the target speed and reference table.
  5. Use designer data, resistance prediction, sea trials, and qualified marine guidance for decisions about power, trim, loading, or operation.

Example for a 20-foot waterline

A boat with a loaded waterline length of 20 ft has a length-based Fn 1.00 comparison speed of approximately 15.03 knots. At 20 knots, its length Froude number is approximately 1.33.

20 kn × 0.514444 ÷ √(9.80665 × 6.096 m) ≈ Fn 1.33

This says where the speed lies on a length-scaled comparison. It does not calculate lift, resistance, horsepower, trim angle, or stability.

Frequently asked questions

What is a boat's length Froude number?

It is speed divided by the square root of gravity times a stated hull length. The result has no units and helps compare gravity-influenced wave behavior across differently sized boats.

Does Fn 1.00 mean every boat is planing?

No. It is a useful high-speed comparison marker, not a universal planing switch. Actual planing involves dynamic lift and depends on hull geometry, displacement, trim, center of gravity, power, and conditions.

Why use loaded waterline length instead of length overall?

Waterline length represents the hull length interacting with the water in the entered condition. Overhangs, bow pulpits, and platforms can increase overall length without increasing loaded waterline length equally.

Should I enter GPS speed?

GPS provides speed over ground, so current affects it. Use reliable speed through water or correct the current effect, such as by averaging comparable reciprocal runs where appropriate.

Is this beam Froude number or displacement Froude number?

No. This page calculates length Froude number using LWL. Beam-based and volume-displacement forms use different denominators and produce different values.

Can this calculator tell me how much horsepower is needed to plane?

No. Froude scaling does not calculate resistance or required shaft power. Those require hull geometry, weight, running trim, wetted surface, propulsive efficiency, and validated prediction or test data.

Limits and safety disclaimer

  • The result is a deep-water, length-scaled comparison and does not model hull lift, resistance, shallow water, waves, current, wind, spray, ventilation, cavitation, or porpoising.
  • LWL may change with load, trim, heel, and speed. A planing hull's running wetted length can differ substantially from its static LWL.
  • The preset values are comparison markers, not universal boundaries between displacement, semi-planing, and planing operation.
  • The tool does not determine required horsepower, structural loads, safe speed, stability, visibility, stopping distance, or legal operating limits.

Safety disclaimer: This educational calculation is not a design approval or operating recommendation. Follow the boat and engine manufacturers' limits, applicable navigation rules, local conditions, and qualified marine guidance.

Methodology and sources

Last reviewed: August 2, 2026. The formula, symbols, characteristic-length warning, and interpretation were checked against naval-architecture sources:

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