Hull Speed Calculator

What is Hull Speed?

Hull speed — sometimes called displacement speed or wave-making speed — is the velocity at which a displacement hull travels fast enough that its bow wave has a wavelength equal to the vessel's waterline length. At that point the boat is sitting in the trough between its own bow and stern waves, and the energy required to push further increases so steeply that it becomes practically impossible for a displacement hull to go much faster without enormous additional power.

The concept was developed by William Froude (1810–1879), the British naval architect and engineer who pioneered the scientific study of ship resistance. Froude established that wave-making resistance scales with the ratio of a vessel's speed to the square root of its waterline length — what we now call the speed-to-length ratio — and that this ratio captures far more about a hull's performance than raw speed alone. A 20-foot dinghy doing 5 knots is working much harder relative to its potential than a 60-foot ketch doing 8 knots, even though the ketch is moving faster.

Hull speed is not a wall — it's a threshold beyond which the physics of wave-making resistance become increasingly punitive for displacement hulls. With enough power or the right conditions, displacement vessels can exceed it temporarily. What hull speed does tell you is the speed at which your vessel is operating most efficiently, and the point beyond which power requirements escalate dramatically.

The Hull Speed Formula

Hull speed is determined by the speed at which a gravity wave travels at the water's surface. Surface gravity waves travel at a speed dependent on their wavelength — longer waves travel faster. When a vessel's bow wave wavelength equals the waterline length, the wave system locks to the hull.

The physics derivation

Practical formula

The factor 1.34 is the practical constant used by naval architects and sailors worldwide when working in feet and knots:

The Froude number

The dimensionless Froude number (Fn) allows comparison across all vessel sizes. For displacement hulls, hull speed corresponds to Fn ≈ 0.40:

Hull Speed by Vessel Length

The table below gives theoretical hull speeds for common waterline lengths in both units. These are the speeds at which the resistance-to-speed curve begins to steepen for a typical displacement hull — realistic offshore passage averages are usually 80–90% of these figures.

Displacement, Semi-Displacement, and Planing Hulls

Hull speed as a concept applies specifically to displacement hulls — vessels whose weight is entirely supported by buoyancy (the displaced volume of water). Understanding the three basic hull types helps clarify when hull speed is the relevant metric and when it isn't.

Displacement hulls

A displacement hull sits in the water and pushes water aside as it moves. At low speeds the resistance is dominated by skin friction. As speed increases, wave-making resistance grows rapidly — it scales roughly with the fourth power of speed in the hull speed region. These hulls are efficient at their design speed but cannot economically exceed hull speed. Traditional monohull sailboats, ship-form motor cruisers, tugboats, and most large commercial vessels are displacement hulls. Their lines are typically fine at the bow, with a rounded or V-shaped cross-section, and a relatively narrow beam.

Semi-displacement hulls

Semi-displacement hulls are designed to operate at speed-to-length ratios above 1.34 — typically in the S/L 1.5–2.5 range (Froude numbers 0.40–0.65). They generate some dynamic lift as speed increases, reducing displacement and therefore wave-making resistance. Many modern motor yachts, patrol vessels, and fast ferries use semi-displacement forms. The underwater sections are flatter aft to generate lift, and the hull runs partially on top of the water. They consume substantially more fuel than a true displacement hull at the same speed, but offer higher maximum speeds.

Planing hulls

A planing hull accelerates past the resistance hump and rides on top of the water surface, with hydrodynamic lift supporting most of the vessel's weight. Wave-making resistance drops dramatically, and the limiting factor becomes available power and aerodynamic drag rather than waterline length. Most powerboats, RIBs, and racing dinghies are planing hulls. Hull speed is not a useful metric for these vessels — their performance is described by power-to-weight ratio and hull efficiency coefficients instead.

Modern sailing yacht design

Contemporary cruising and racing monohulls blur the categories. Wide, flat stern sections and plumb bows maximise waterline length relative to overall length, allowing the hull to approach and sometimes exceed traditional hull speed calculations in a seaway. A heavily loaded passage-maker will behave more like a traditional displacement hull; the same boat sailing fast in 20 knots of breeze may exceed its theoretical hull speed by surfing wave faces. Modern IMS/IRC racing rules have encouraged hull forms that transition from displacement to partial-planing behaviour at higher speeds.

Using Hull Speed for Passage Planning

Hull speed gives you the theoretical ceiling; passage planning requires realistic averages. The standard rule of thumb for offshore sailboat passage planning is to budget 100–120 nautical miles per day for a 30–40 ft cruising yacht, equivalent to roughly 4.2–5.0 knots average — well below the theoretical hull speed of 7–8 knots for that size range.

The gap between hull speed and realistic average reflects several realities: not every hour is spent sailing at maximum speed; time is lost in light wind, during sail changes, entering harbours, and navigating around weather. Upwind passages cover less distance-made-good than boat speed suggests. Strong tidal or ocean current — favourable or adverse — can dramatically shift the effective average.

A practical planning approach:

For faster cruisers or favourable conditions, 85–90% of hull speed is a reasonable planning figure. For heavy-displacement long-keelers or difficult weather routes, 75% is more appropriate. Modern passage-planning software (PredictWind, Expedition, iSailor) uses polars that account for true wind speed and angle, giving more accurate estimates than hull speed alone — but hull speed remains a useful sanity check on any output.

Hull Speeds of Notable Vessels

Seeing hull speed numbers for real vessels — from cruising boats to commercial ships — helps build an intuition for what the formula means in practice.

Common questions

• What is hull speed?
  Hull speed is the theoretical maximum speed of a displacement hull — the speed at which the vessel's waterline length equals the wavelength of the bow wave it generates. At this point, the boat is essentially trapped in a trough between its own bow and stern waves, and wave-making resistance increases so steeply that pushing further requires disproportionate power. The term was coined by William Froude in the 19th century and remains the standard benchmark for displacement vessel performance.
• Why does waterline length — not overall length — determine hull speed?
  The bow wave originates at the point where the hull enters the water, not at the tip of the bow. Its wavelength is tied to the length of the vessel's waterline (LWL) — the distance from where the hull meets the water at the bow to where it meets it at the stern. A boat with a long overhang at bow and stern has a shorter waterline than its overall length suggests, and its hull speed is set by the waterline, not the LOA. Many racing yachts and modern cruisers are designed with bow and stern sections that enter the water at low angles specifically to maximise the waterline-to-overall-length ratio.
• Can a sailboat exceed hull speed?
  Yes — in several ways. A sufficiently powerful sailing vessel can surf down wave faces, temporarily exceeding hull speed without climbing out of the displacement regime. Modern flat-bottomed, wide-stern designs can begin to plane — lifting the bow clear of the water and skimming the surface — which fundamentally changes the resistance curve. Racing multihulls (catamarans, trimarans) and foiling vessels bypass hull speed entirely; they operate in a different physical regime. Even traditional heavy-displacement monohulls can be pushed a few tenths of a knot past their theoretical limit with a strong breeze and following sea, though the power required grows sharply.
• Does hull speed apply to powerboats?
  Hull speed is relevant to displacement powerboats — trawlers, lobster boats, tugs, and motor cruisers designed to run through the water rather than over it. These vessels are economically efficient at or slightly below hull speed. Planing powerboats are designed to accelerate past hull speed and lift onto the surface, entering a completely different resistance regime where speed is governed by available power and hull lift rather than waterline length. Semi-displacement hulls (many motor yachts and patrol boats) operate in between, capable of speeds above hull speed but without fully planing.
• What is the speed-to-length ratio?
  The speed-to-length ratio (S/L ratio) is the vessel's speed in knots divided by the square root of its waterline length in feet. Hull speed corresponds to an S/L ratio of 1.34. Light, easily-driven displacement hulls might achieve 1.4–1.5 in ideal conditions. Semi-displacement hulls operate at S/L ratios of 1.5–2.5. Fully planing hulls leave the concept behind entirely. The ratio is useful because it lets you compare speeds across different vessel sizes on a common scale — a 30-foot boat doing 6.5 knots (S/L 1.19) is making less effort relative to its potential than a 60-foot boat doing 9.5 knots (S/L 1.23), even though the longer boat is travelling faster.
• What is the Froude number, and how does it relate to hull speed?
  The Froude number (Fn) is a dimensionless ratio that describes how a vessel's speed relates to the speed at which gravity waves travel in water of a given depth. For hull speed, the relevant form is Fn = V / √(g × LWL), where V is speed in m/s, g is 9.81 m/s², and LWL is waterline length in metres. Hull speed corresponds to a Froude number of approximately 0.40. Below 0.35 the vessel is firmly in the displacement regime with relatively low wave-making resistance. Between 0.40 and 0.50 the hump in the resistance curve occurs. Above 0.50–0.55 a hull must begin to plane to maintain efficiency.
• How do I use hull speed to estimate passage time?
  Divide the distance in nautical miles by your expected average speed to get hours. For passage planning, experienced sailors typically estimate at 80–85% of theoretical hull speed to account for light winds, adverse current, and time spent tacking. A 35-foot waterline boat (hull speed 7.9 knots) might realistically average 6.5–6.7 knots on an offshore passage. At 6.5 knots a 100-nautical-mile run takes about 15.4 hours. This calculator includes a passage time estimate using both full hull speed and a conservative 85% average.