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Block Coefficient Calculator

Enter the displaced volume, length, beam and draft to get the block coefficient.

How it is calculated

The tool divides the volume of water the hull displaces by the volume of the rectangular box that encloses the underwater hull: Cb = V / (L × B × T). V is the displaced volume (m³ or ft³), L the waterline length, B the beam and T the draft, all in one length unit. Use that unit's cube for V, so the result has no unit. Volume may be zero or more, while length, beam and draft must be above zero. Because the hull sits inside its own box, Cb cannot exceed 1: if the volume you enter is larger than L × B × T, the tool shows no result, which signals a measurement or unit error. The answer is rounded to four decimals.

Worked example

A coaster has a waterline length of 100 m, a beam of 16 m and a draft of 6 m, and displaces 6000 m³. Step 1: the box is 100 × 16 × 6 = 9600 m³. Step 2: Cb = 6000 / 9600. Step 3: the tool shows 0.6250, so the hull fills 62.5% of its box. Raising the volume to 10000 m³ would give a ratio above 1, which is impossible, and the tool would show no result.

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Common mistakes

  • Entering displacement in tonnes instead of volume: divide the mass by the water density (about 1.025 t/m³ for seawater) first to get cubic metres.
  • Using length overall instead of waterline length, which makes the box too big and Cb too low.
  • Entering a draft from a different loading condition than the one the displaced volume refers to.
  • Mixing units, for example length in metres and volume in cubic feet; the result then looks plausible but is wrong.
  • Confusing Cb with the prismatic or midship section coefficient; Cb compares the volume with the whole box, not with a single section.

About this calculator

A ship's block coefficient (Cb) is the ratio of its underwater hull volume to the volume of a rectangular box with the same length (at waterline), beam, and draft: Cb = ∇ / (L × B × T). It's a dimensionless number between roughly 0.5 and 0.9 — a slender, fine-lined hull like a naval frigate has a low Cb (~0.5), while a bulk carrier or tanker built to maximize cargo volume has a high Cb (~0.85), since it fills far more of that bounding box.

Naval architects use block coefficient in the earliest stages of hull design to balance cargo capacity against resistance and speed, since a fuller hull (higher Cb) carries more cargo per unit length but pushes more water and burns more fuel at a given speed than a finer one.

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