Hull Speed Calculator for Displacement Boats

Estimate the wave-resistance threshold of a conventional displacement hull from its loaded waterline length. Results include knots, mph, km/h, m/s, speed-length ratio, and Froude number.

Hull speed is a rule of thumb, not a hard speed limitIt describes a region where wave-making resistance usually rises steeply. Hull shape, displacement, power, sea state, loading, and whether a boat can plane or surf all affect actual performance.

Boat measurements

Waterline and formula

Use loaded waterline length, not length overall.

1.34 is the conventional displacement-hull rule.

Optional speed comparison

Leave blank for a hull-speed estimate only.

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Estimated hull speed

Enter the boat's length at the waterline and calculate.

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Hull speed formula

The familiar estimate uses the boat's loaded length at the waterline (LWL), not total deck or spar length:

Hull speed (kn) ≈ 1.34 × √LWL (ft)

Hull speed (kn) ≈ 2.43 × √LWL (m)

The metric coefficient is the same relationship after converting meters to feet. A 1.34 coefficient corresponds to a traditional speed-length ratio of 1.34 and a length-based Froude number of about 0.40.

What the estimate means

A displacement hull creates a wave system as it moves. When the wave length approaches the waterline length, the hull sits between a bow crest and stern crest and additional speed commonly demands sharply more power.

This is better understood as an approximate efficient-speed threshold than a fixed maximum. Actual resistance curves depend on hull form, length-to-beam ratio, displacement, appendages, trim, and loading.

Square-root relationship: Four times the waterline length produces only twice the rule-of-thumb hull speed.

How to use this calculator

  1. Find the boat's loaded length at waterline (LWL). Do not substitute length overall unless it is genuinely the same.
  2. Enter LWL and select feet or meters.
  3. Keep the standard coefficient at 1.34 unless you have a documented reason to compare another speed-length ratio.
  4. Optionally enter a target or observed speed to see its percentage of hull speed and the LWL implied by the same rule.
  5. Compare the estimate with the vessel designer's data and real trials under known load and conditions.

Example for a 30-foot waterline

For a displacement boat with a 30 ft loaded waterline and the standard 1.34 coefficient:

1.34 × √30 = 7.34 knots

That is approximately 8.45 mph or 13.59 km/h. It does not promise that the boat has enough power or sail area to reach that speed, and it does not prevent a suitable boat from exceeding it.

Frequently asked questions

Why does the calculator use waterline length instead of overall length?

The wave system is related to the hull length interacting with the water. Bow sprits, swim platforms, and overhangs can increase length overall without adding the same amount of loaded waterline length.

Is 1.34 always the correct coefficient?

No. It is a widely used rule-of-thumb coefficient for conventional displacement hulls. Actual resistance is design-specific, so a naval architect's resistance prediction or measured performance data is more authoritative.

Can a displacement boat exceed hull speed?

Yes, given sufficient power and a suitable design, but a conventional heavy displacement hull usually encounters rapidly increasing wave-making resistance near this region. The formula is not a physical speed barrier.

Does this formula work for catamarans?

Not reliably. Slender multihulls have different wave-interference and resistance characteristics. Use design-specific polar, resistance, or sea-trial data instead.

Does hull speed tell me the best cruising speed?

No. Economical cruising speed depends on the full resistance curve, propulsion efficiency, fuel or battery use, sea state, load, and operating goals. It is often below the rule-of-thumb hull speed.

Should comparison speed be speed over ground or through water?

Use speed through water when evaluating hull performance. GPS speed over ground includes current, so reciprocal runs or current correction are needed for a closer comparison.

Limits and safety disclaimer

  • The calculator assumes a conventional displacement hull in deep water and does not model shallow-water effects, waves, current, wind, surfing, or planing.
  • It does not calculate required horsepower, sail area, stability, fuel use, range, structural loads, safe speed, or controllability.
  • Loaded LWL can change with displacement, trim, and heel. Published LOA is not a substitute.
  • The custom coefficient is for transparent comparisons; changing it does not make the result a design-specific prediction.

Safety disclaimer: This educational estimate is not an operating limit, navigation instruction, or engineering assessment. Follow vessel documentation, local rules, conditions, and qualified marine guidance when planning or operating.

Methodology and sources

Last reviewed: August 1, 2026. The standard formula and its interpretation were checked against naval-architecture and sailing references:

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