Hull Speed Calculator

The relationship comes from wave physics: a hull's bow and stern waves grow longer as speed increases, and hull speed is reached when that wave's length matches the waterline length. The mathematical relationship between a wave's speed and its length involves a square root, which is why V = ratio x sqrt(LWL) uses a square root rather than a linear or squared relationship to waterline length.

Because hull speed scales with the square root of length, doubling speed requires quadrupling the waterline length, not just doubling it -- a boat needs 4x the LWL of another to reach twice its hull speed at the same speed-length ratio. This is why very long displacement vessels (large ships) can cruise efficiently at speeds a small sailboat's hull could never reach in displacement mode.

Yes -- hull speed is a resistance inflection point where wave-making drag rises steeply, not an absolute barrier. A displacement hull can be pushed beyond it, but each additional knot demands disproportionately more power as the boat tries to climb its own bow wave. Semi-displacement and planing hull designs are shaped specifically to reduce this effect and can sustain speed-length ratios well above the default 1.34.

1.34 is the figure most commonly cited in naval architecture references for traditional displacement monohulls, corresponding to a Froude number near 0.4. It is an empirical approximation rather than a derived physical constant, which is why this calculator lets the ratio be adjusted from 0.8 up to 1.8 to cover more conservative estimates as well as semi-displacement hull forms that exceed the traditional figure.