Boat Displacement Calculator
Calculate hull displacement, waterline length, and displacement-to-length ratio for sailboats and powerboats.
Displacement is the weight of water a boat pushes aside when floating. By Archimedes’ principle, this equals the total weight of the boat and everything aboard. Displacement is the single most important number in boat design — it determines speed potential, stability, and seakeeping ability.
Archimedes’ Principle
Displacement (lbs) = Volume of submerged hull (cubic feet) × Water density
Seawater density: 64.0 lbs/ft³ (1025 kg/m³) Freshwater density: 62.4 lbs/ft³ (1000 kg/m³)
Displacement-to-Length Ratio (D/L)
The D/L ratio is the standard comparison metric for how heavy or light a boat is relative to her length:
D/L = Displacement (long tons) / (0.01 × LWL in feet)³
Where: 1 long ton = 2,240 lbs.
| D/L Range | Classification | Examples |
|---|---|---|
| < 100 | Ultra-light | Racing multihulls, skiffs |
| 100–150 | Light | Racing sailboats, sport boats |
| 150–250 | Moderate | Coastal cruisers, family sailboats |
| 250–350 | Heavy | Traditional cruisers, motorsailers |
| > 350 | Very heavy | Full-keel bluewater yachts, workboats |
Hull Speed Formula
The theoretical maximum speed for a displacement hull is:
Hull speed (knots) = 1.34 × √(LWL in feet)
A boat with 30 ft LWL: hull speed = 1.34 × √30 = 7.34 knots. A boat with 40 ft LWL: hull speed = 1.34 × √40 = 8.47 knots.
Lighter boats (lower D/L) can exceed hull speed more easily and may plane. Heavier boats are effectively limited to hull speed.
Sail Area to Displacement Ratio (SA/D)
SA/D = Sail area (sq ft) / (Displacement in lbs / 64)^(2/3)
| SA/D Range | Performance |
|---|---|
| < 14 | Underpowered — needs engine in light air |
| 14–17 | Average — good balance of comfort and performance |
| 17–20 | Fast — responsive in moderate conditions |
| > 20 | Racing — overpowered for casual sailing |
Worked Example — 35-foot Coastal Cruiser
LWL: 30 ft, Displacement: 14,000 lbs. D/L = (14000 / 2240) / (0.01 × 30)³ = 6.25 / 0.027 = 231.5 — moderate displacement. Hull speed = 1.34 × √30 = 7.34 knots. With 550 sq ft sail area: SA/D = 550 / (14000/64)^(2/3) = 550 / 27.23 = 20.2 — well powered.
Prismatic Coefficient
The prismatic coefficient (Cp) describes hull shape — how much of the underwater volume is concentrated at the ends versus the middle:
Cp = Displaced volume / (Maximum cross-section area × LWL)
Optimal Cp for hull speed: 0.55–0.60. Higher Cp (0.60–0.65): better for higher speed-to-length ratios.