Boat Speed

Convert boat speed between knots, mph, and km/h, then layer on hull speed (1.34 × √LWL), Froude number, fuel burn per nautical mile, and total range.

Everyday Knots / mph / km/h Hull speed + Froude Range from fuel burn
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How fast is your boat - really?

Knots · mph · km/h · hull speed · Froude · range

Instructions — Boat Speed

1

Enter the boat speed and unit

Type the speed and pick knots, mph, or km/h. The calculator shows all three conversions plus the m/s value used by the physics formulas downstream.

2

Add hull waterline length

Optional, but enables Hull Speed (1.34 × √LWL) and the Froude number. Use waterline length (LWL), not overall length — the overhangs do not contribute to the wave-making physics.

3

Add fuel burn and tank size

Cruising gallons per hour gives fuel per nautical mile. Add tank capacity for total range. Always plan with at least a 20–30% reserve on the calculated range.

Speed through water vs over ground: the calculator handles boat speed (through the water). Currents and tides shift speed-over-ground — GPS gives that; a paddle wheel or pitot tube gives this.
Knot etymology: 1 knot = 1 nautical mile per hour. The name comes from log lines with knots tied at 47 ft 3 in intervals, counted as they paid out in a 28-second sand glass.

Formulas

Four formulas cover the lot: unit conversion, hull speed, Froude number, and fuel economy.

SPEED UNIT CONVERSION
$$ 1 \text{ knot} = 1.15078 \text{ mph} = 1.852 \text{ km/h} $$
A knot is one nautical mile (1,852 m) per hour. Statute miles (mph) use 1,609 m, so the same speed reads slightly higher in mph than in knots.
HULL SPEED
$$ V_{hull} = 1.34 \times \sqrt{LWL} $$
V in knots, LWL in feet. The metric form is V = 2.43 × √Lm. This is the theoretical top speed of a displacement hull before wave-making resistance climbs vertically.
FROUDE NUMBER
$$ F_n = \frac{V}{\sqrt{g \times L}} $$
V in m/s, L in meters, g = 9.81 m/s². Fn < 0.5 = displacement, 0.5–1.0 = semi-displacement, > 1.0 = planing. Dimensionless, comparable across any boat size.
FUEL PER NAUTICAL MILE & RANGE
$$ GPM = \frac{\dot{F}}{V} \;\;;\;\; R = \frac{F_{tank}}{\dot{F}} \times V $$
F-dot is gallons per hour, V in knots. Range is direct: hours of fuel multiplied by speed gives nautical miles — before reserve.

Reference

Speed unit conversions
FromTo knotsTo mphTo km/h
1 knot1.0001.1511.852
1 mph0.8691.0001.609
1 km/h0.5400.6211.000
1 m/s1.9442.2373.600
Hull speed by waterline length
LWL (ft)Hull speed (kn)Typical boat
165.4Day sailer
226.3Pocket cruiser
307.3Cruising sailboat
408.5Offshore yacht
509.5Trawler
6510.8Large yacht
10013.4Mini ship
Quick reference: hull regime by Froude number
Froude (Fn)RegimeBehaviourTypical fuel burn
0.0 – 0.4DisplacementHull pushes water aside, low wakeLowest, scales linearly
0.4 – 0.5Approaching hull speedBow wave equals waterline lengthRises sharply per knot
0.5 – 1.0Semi-displacementHull climbing its own bow wavePeak resistance zone
1.0 – 1.5Transitional planingStern squat, bow risingDrops as planing locks in
> 1.5Full planingSkipping on top of water2–4× displacement boats

Article — Boat Speed

A 30-foot waterline sailboat hits its theoretical boat speed ceiling at about 7.3 knots — the formula 1.34 × √LWL has held for over a century. Push past that and fuel burn doubles for the last knot. The same hull at 6 knots sits at a Froude number of 0.32, deep in the efficient displacement regime where it can cross oceans on the energy a planing boat burns crossing a bay. This calculator converts between knots, mph, and km/h, then lets you layer on hull speed, Froude number, fuel per nautical mile, and total range — the four numbers that decide whether a passage is feasible.

The unit of measure matters: knots are the global maritime and aviation standard because 1 knot equals 1 nautical mile per hour, and a nautical mile is one minute of latitude. That makes navigation arithmetic trivial when speeds, distances, and chart coordinates share the same base.

Knots, mph, and km/h: which boat speed unit to use

Three units cover almost all civilian boat speed reporting. Knots dominate offshore work, professional yacht delivery, commercial shipping, and naval traffic. Statute miles per hour (mph) appears mostly on US recreational powerboats and trailerable craft where the manufacturer expects highway-context comparisons. Kilometres per hour (km/h) appears on inland European waterways and Asian recreational craft.

The relationships are exact: 1 knot equals exactly 1.852 km/h (by international definition since 1929) and approximately 1.15078 mph. A boat speed of 10 knots is the same as 11.51 mph or 18.52 km/h. The calculator above does all three at once.

Did you know

The nautical mile was originally defined as one minute of arc along a meridian of the Earth. The modern definition pegs it at exactly 1,852 metres, but the spherical-geometry roots are why ships and aircraft still use it — a vessel running due north for 60 minutes at 10 knots has covered exactly 10 minutes of latitude on the chart.

Hull speed: the boat speed ceiling for displacement hulls

Hull speed is the theoretical maximum boat speed for a displacement hull, set by the physics of the bow wave the boat creates. The formula V = 1.34 × √LWL gives the speed in knots from the waterline length in feet. A 16-foot waterline gives 5.4 knots. A 40-foot waterline gives 8.5 knots. A 100-foot waterline gives 13.4 knots. Doubling the boat length only multiplies hull speed by √2.

The mechanism is wave-making resistance. As a displacement boat moves forward it creates a wave at the bow and another at the stern. When boat speed matches the natural wavelength of those waves, the hull is effectively trying to climb its own bow wave. Power demand spikes vertically. For a typical cruising sailboat or trawler, doubling engine power past hull speed yields only a few tenths of a knot extra.

  • 16 ft LWL — hull speed 5.4 knots (day sailer)
  • 22 ft LWL — hull speed 6.3 knots (pocket cruiser)
  • 30 ft LWL — hull speed 7.3 knots (cruising sailboat)
  • 40 ft LWL — hull speed 8.5 knots (offshore yacht)
  • 50 ft LWL — hull speed 9.5 knots (trawler)
  • 65 ft LWL — hull speed 10.8 knots (large yacht)
Hull speed does not apply to planing boats

A planing boat lifts itself onto the top of the water once it has enough power and the hull shape is right. From that point on, hull speed stops being the ceiling — the boat is no longer purely displacing water. Performance is set by power-to-weight ratio and hull form, not LWL. Apply the 1.34 × √LWL rule only to displacement and semi-displacement hulls.

Froude number: the universal boat speed yardstick

The Froude number Fn = V / √(g × L) is the dimensionless way to compare boat speed across very different vessels. It is the ratio of inertial forces to gravitational forces in the wave-making physics. Two boats with the same Froude number behave the same way regardless of absolute size — that is why naval architects test scale models in tow tanks at matched Fn.

For Fn below 0.5 the boat is firmly in displacement mode, riding within its own bow wave and burning the least fuel per nautical mile. Between 0.5 and 1.0 the boat is climbing the bow wave — the semi-displacement regime, where fuel burn climbs sharply. Above 1.0 the boat is planing, riding on top of the water rather than pushing through it.

Did you know

The Froude number is named after William Froude, the 19th-century English engineer whose tow-tank experiments at Torquay (1872) revealed why scaling hull resistance from small models was failing. Modern ship design still uses his "law of comparison" — matching Froude number between model and full-size ship — because the wave physics depends on this dimensionless ratio, not absolute speed.

Boat speed and fuel burn

Fuel burn does not scale linearly with boat speed. Hydrodynamic resistance grows roughly with the square or cube of speed in the displacement range, and power demand grows even faster because the propeller efficiency also shifts. A typical 30-foot cruiser burning 2 gallons per hour at 5 knots might burn 5 gallons per hour at 6.5 knots and 12 gallons per hour at 7.5 knots — the same fuel pays for fewer nautical miles at every step up.

The minimum fuel-per-mile point for most displacement boats sits around 60–70% of hull speed. That is the cruise speed that maximises range. Push to hull speed itself and gallons-per-mile typically jumps 50–100% over the cruise number. The US Coast Guard recommends planning long passages around the 60% point as the "maximum range cruise" and reserving full power for emergencies and adverse conditions.

Throttle position is not boat speed

Fuel burn scales with throttle, not boat speed. A boat pushing into a 2-knot head current at 6 knots through the water makes 4 knots over the ground but burns fuel for the higher speed. Always plan fuel from speed-through-water (paddle wheel, pitot, manufacturer curves), then check actual progress against speed-over-ground (GPS).

Calculating boat speed range and reserves

Range is straightforward arithmetic: tank capacity divided by burn rate gives endurance in hours, multiplied by speed in knots gives range in nautical miles. A 100-gallon tank, 8 gallons per hour at 10 knots, gives 12.5 hours and 125 nautical miles — on paper. The American Boat and Yacht Council (ABYC) and most maritime safety authorities recommend planning to use no more than 70% of theoretical range. The remaining 30% covers headwinds, adverse currents, sea state, navigation errors, and the basic precaution of not arriving at the destination with empty tanks.

Tank capacity itself is rarely the listed number. Usable fuel is typically 90–95% of nameplate capacity — pickup tubes do not reach the very bottom of the tank, and fuel sloshing in a seaway makes it unsafe to draw the last gallons. Always plan range from usable, not nominal, capacity.

  • 30% reserve rule — standard maritime planning margin
  • Usable fuel — 90–95% of nameplate tank size
  • Headwind penalty — 1 knot of true wind reduces range ~5–8%
  • Current effect — adverse 2 kn current can halve range on short legs
  • Loaded vs light displacement — full water and provisions can cut range 10–15%

Common boat speed mistakes

Confusing length overall with waterline length

Hull speed and Froude number both depend on LWL (waterline length), not LOA (length overall). Bowsprits, anchor rollers, and reverse-transoms add to LOA but contribute nothing to the wave-making physics. A modern 40-foot sailboat often has only 35 feet of waterline — hull speed is 7.9 knots, not the 8.5 the LOA would suggest.

Quoting GPS speed as "boat speed"

GPS reads speed-over-ground (SOG): the actual rate of progress across the planet. It includes all current and tide effects. Speed-through-water (STW) is what the boat is doing relative to the water and is what hull speed and fuel-burn formulas use. The difference can be 2–3 knots in coastal current — enough to wreck a passage plan if you mix them up.

Ignoring the cube law on fuel

Adding 20% more speed in the displacement range typically demands 70–100% more power and burns 50–80% more fuel per hour. A boat that crosses a 100 NM bay in 14 hours at 7 knots might do it in 12 hours at 8.3 knots, but the trip costs 60% more fuel. For long passages the slower speed almost always wins on total fuel and engine wear.

FAQ

A knot is one nautical mile per hour; mph is one statute mile per hour. A nautical mile is 1,852 m (one minute of latitude); a statute mile is 1,609 m. Because the nautical mile is longer, 1 knot equals about 1.15 mph. Knots are the standard for marine and aviation use because of the direct link to latitude on charts.
Hull speed is the theoretical top speed of a displacement hull, set by 1.34 × √LWL (knots, LWL in feet). It applies to sailboats, trawlers, and most cargo vessels. It does not apply to planing boats — those climb out of the water and break free of the bow-wave physics. A 30-foot waterline displacement hull has a hull speed of about 7.3 knots.
It depends on power. Hull speed is the theoretical ceiling; many boats are under-powered to reach it. A typical displacement sailboat needs roughly 2–4 hp per ton of displacement to motor at hull speed. Cruising at 80% of hull speed usually requires only half that power because of the cube-law fuel curve.
Average cruising sailboats (35–40 ft LOA) have a hull speed of 7.5–8.5 knots and cruise at 5–7 knots in normal conditions. Under engine, most diesel-powered cruisers do 6–7 knots. Performance designs and multihulls can break hull speed by surfing or planing in strong winds.
Fn > 1.0 means the boat is in the planing regime — lifted onto the top of the water, with much-reduced wetted surface and drag. Planing boats reach 30–50+ knots but burn 2–4× more fuel per nautical mile than equivalent displacement craft. Most speedboats and runabouts operate here at cruise.
Range = (tank capacity in gallons ÷ burn rate in gal/hr) × speed in knots. Example: 100 gallons, 8 gal/hr at 10 knots gives 12.5 hours and 125 nautical miles on paper. Always reserve 20–30% for headwinds, current, weather, and the practical limit of not running tanks dry.
Hydrodynamic resistance grows roughly with the square or cube of speed in the displacement range, and propeller losses widen at higher rpm. Doubling speed usually demands 4–8× the power. That is why the most fuel-efficient cruise sits at 60–70% of hull speed for displacement boats.
Displacement: the hull stays submerged, pushing water aside as it moves, fuel-efficient at moderate speeds. Planing: at higher power the hull rises and skims along the surface, allowing much higher speeds at the cost of much higher fuel burn. Sailboats and trawlers are displacement; runabouts and speedboats are planing.
They affect speed-over-ground, not speed-through-water. The figures in this calculator are through-the-water speeds. Currents add or subtract directly: a boat doing 6 knots through the water in a 2-knot following current makes 8 knots over the ground. Always navigate with the appropriate one for the task.
Boats run with the lowest Froude number tend to have the best fuel economy — they are operating where wave-making resistance is small. The sweet spot for long-range cruising sits at Fn 0.3–0.4 for most hulls. Above Fn 0.5 the bow wave starts to dominate and economy collapses; full planing (Fn > 1.0) recovers some efficiency but never matches displacement.