Compute CB directly from volume or estimate a target via Froude & speed.
CB = —
Froude number: —
Suggested target: CB ≈ — (range —)
The block coefficient describes how much of an imaginary rectangular block is occupied by a ship's underwater hull. The comparison block has the same selected length, beam and draft as the vessel. A fine hull occupies a smaller part of that block, while a full hull occupies a larger part.
CB is one of the first hull-form coefficients considered during preliminary design. It is also useful when checking principal dimensions, estimating displacement and comparing loading conditions. It does not provide a complete description of the hull, because two ships can have the same block coefficient and still have very different bow shapes, stern shapes and sectional-area distributions.
The block coefficient is the ratio of displaced underwater volume to the volume of the surrounding rectangular block:
CB = ∇ ÷ (L × B × T)
| Symbol | Meaning | Usual unit |
|---|---|---|
| CB | Block coefficient | Dimensionless |
| ∇ | Displaced underwater volume at the stated loading condition | m3 |
| L | Selected ship-length reference, commonly LPP or LWL | m |
| B | Beam used by the calculation, normally moulded beam unless another definition is stated | m |
| T | Draft corresponding to the displaced volume | m |
The result has no unit because both the numerator and denominator are volumes. The length, beam and draft may be entered in metres when the displaced volume is entered in cubic metres. Other consistent length units also work, but metres and cubic metres must not be mixed with feet or cubic feet.
Naval architecture uses the displacement symbol Δ for the vessel's displacement mass and the symbol ∇ for its displaced volume. They are related through water density:
∇ = Δ ÷ ρ
Here, ρ is the water density. A nominal density of 1.025 t/m3 is commonly used for seawater and 1.000 t/m3 for fresh water. When measured dock-water density is available, that value should be used instead of the nominal figure.
Displacement in tonnes must not be entered directly into a field asking for cubic metres. The calculator's displacement mode performs the density conversion before calculating CB.
Consider a vessel at the following loading condition:
∇ = 39,852 ÷ 1.025 = 38,880 m3
L × B × T = 180 × 30 × 10 = 54,000 m3
CB = 38,880 ÷ 54,000 = 0.720
The underwater hull therefore occupies 72% of the reference block defined by the entered length, beam and draft.
A lower CB normally indicates a finer underwater form. A higher value indicates a fuller form with more displaced volume for the same principal dimensions. This is why high-capacity, moderate-speed merchant ships often have higher block coefficients than vessels designed for higher speeds.
The ranges below are broad comparison values rather than design limits. Actual values vary with ship size, service speed, cargo arrangement, loading condition and the dimensional definitions used by the designer.
| Vessel or hull type | Indicative CB range | General description |
|---|---|---|
| Fast displacement craft and patrol vessels | 0.40–0.55 | Fine underwater form with limited fullness |
| Container ships and Ro-Ro vessels | 0.60–0.72 | Moderate fullness, strongly affected by speed and capacity requirements |
| General cargo and multipurpose vessels | 0.65–0.78 | Moderate to full merchant-ship forms |
| Bulk carriers and tankers | 0.75–0.88 | Full forms intended to provide high displacement and cargo capacity |
| Barges and very full displacement forms | 0.85–0.95 | Underwater geometry approaching the reference block |
A value should be compared with vessels of similar type, size, speed and draft. Comparing the fully loaded CB of one ship with the ballast-condition value of another may give a misleading impression.
Block coefficient can be separated into the prismatic coefficient and midship coefficient:
CB = CP × CM
CM describes the fullness of the immersed midship section, while CP describes how the underwater volume is distributed along the vessel's length. This relationship is valid when the coefficients use consistent dimensional and sectional references.
The relationship also explains why CB cannot describe the complete hull form. Two vessels may have the same CB but different combinations of CP and CM, leading to different sectional shapes and longitudinal volume distributions.
The selected length must be stated whenever a block coefficient is reported. Length between perpendiculars, LPP, and waterline length, LWL, do not normally produce identical results. Length overall should not be substituted unless the calculation method specifically defines it as the reference length.
The draft must belong to the same loading condition as the displaced volume. Moulded depth is not draft and must not be used in its place. When a vessel is trimmed, a calculation based on mean draft provides a simplified effective coefficient. Accurate treatment of a trimmed condition requires hydrostatic integration of the actual immersed hull.
Block coefficient can change as the vessel moves from ballast to loaded condition. The submerged hull does not necessarily gain volume in the same proportion as the surrounding L × B × T block.
The direct mode calculates CB from known dimensions and displaced volume. This is the appropriate mode when hydrostatic displacement data or a reliable displacement estimate is available.
The empirical target mode uses vessel type, length and service speed to suggest an early-design value. Speed influence is commonly represented using the Froude number:
Fn = V ÷ √(gL)
Vessel speed must be converted to metres per second when SI units are used in the Froude-number equation. The empirical result is a starting point for preliminary dimension studies. It is not a hydrostatic calculation and should not override a known displaced volume.
Block coefficient is useful for checking hull fullness, comparing preliminary designs and estimating displacement from principal dimensions. It is also an input to several empirical resistance, powering and wetted-surface methods.
CB alone cannot determine resistance, required engine power, intact stability, cargo capacity or seakeeping performance. Those properties also depend on waterline shape, prismatic distribution, wetted surface, appendages, centre of gravity, speed and many other design details.
For a conventional monohull calculation using consistent dimensions, CB should lie between 0 and 1. A result outside this range normally indicates mismatched units, an incorrect dimensional reference or confusion between displacement mass and displaced volume.
The formula and terminology used on this page follow standard naval architecture references:
NauticalSolver calculators are intended for preliminary engineering, study and independent checking. Use approved hydrostatic particulars and vessel-specific documentation for operational, contractual or statutory calculations.