Block Coefficient Calculator: Ship Hull Formula

This calculator works out the block coefficient (Cb) of a ship or boat hull, which is the ratio of the vessel’s underwater volume to the volume of a rectangular box with the same length, breadth, and draft. You enter the ship’s length, breadth, draft, and displacement volume, and you get the block coefficient, a dimensionless number between 0 and 1 that tells you how full or fine the hull shape is.

Formula

The block coefficient is defined by the formula:

Cb = V / (L × B × T)

Where:

• Cb = block coefficient (dimensionless)
• V = volume of displaced water (cubic metres, m³)
• L = length of the waterline (metres, m)
• B = breadth (beam) at the waterline (metres, m)
• T = draft (metres, m)

The product L × B × T is the volume of a rectangular box that just encloses the underwater part of the hull. The block coefficient is the fraction of that box that is actually filled by the hull.

Worked Example

Using the default values from the calculator:

• Length (L) = 100 m
• Breadth (B) = 20 m
• Draft (T) = 8 m
• Displacement volume (V) = 12,000 m³

First, compute the box volume:

L × B × T = 100 × 20 × 8 = 16,000 m³

Now divide the displacement volume by the box volume:

Cb = 12,000 / 16,000 = 0.75

The calculator shows 0.750, which matches. This means the hull fills 75% of the enclosing rectangular box.

Why the Block Coefficient Matters

The block coefficient is one of the most important hull form parameters in naval architecture. It directly influences resistance, propulsion power, cargo capacity, and seakeeping behaviour.

• Full hulls (Cb > 0.7) are typical for cargo ships, tankers, and bulk carriers. They maximize cargo volume for a given size, but they create more wave-making resistance at high speeds.
• Medium hulls (Cb between 0.5 and 0.7) are common for general cargo ships, ferries, and fishing vessels. They balance capacity and speed.
• Fine hulls (Cb < 0.5) are used for fast vessels like container ships, naval ships, and passenger liners. They cut through water efficiently but have less internal volume for their dimensions.

The coefficient also helps estimate displacement when the hull is not fully modelled, and it is used in early-stage ship design to predict resistance and power requirements.

How to Read the Result

A block coefficient is always between 0 and 1. A value near 0 means the hull is very streamlined and slender (like a canoe). A value near 1 means the hull is almost a rectangular box (like a barge). Most ships fall between 0.4 and 0.85.

If you get a value greater than 1, check your inputs: the displacement volume cannot exceed the enclosing box volume. If you get a negative value, you likely entered a negative length, breadth, or draft, which is physically impossible.

Remember that the block coefficient is based on the waterline length and the moulded breadth and draft, not the overall length or the extreme beam. Using the wrong dimensions is a common mistake.

Common Mistakes and Limits

• Unit mix-ups: All dimensions must be in the same unit. If you use metres for length and centimetres for draft, the result will be wrong. Convert everything to metres first.
• Using overall length instead of waterline length: The L in the formula is the length at the waterline, not the length overall (LOA). For many ships, the waterline length is slightly shorter.
• Confusing displacement volume with displacement mass: Displacement volume is the volume of water displaced, usually in cubic metres. Displacement mass is that volume multiplied by the density of water (about 1,025 kg/m³ for seawater). The calculator uses volume, so enter the volume directly, not the mass in tonnes.
• Rounding too early: Round only the final result, not intermediate values.

The block coefficient is a global measure; it does not tell you how the volume is distributed along the hull. Two hulls with the same Cb can have very different shapes (e.g., one with a full bow and fine stern, another the opposite). For more detail, naval architects use other coefficients like the prismatic coefficient (Cp) and the waterplane area coefficient (Cwp).

How to Choose a Target Block Coefficient

In ship design, the block coefficient is chosen based on the ship’s intended speed and function. A common guideline is the Froude number (Fn = V / √(gL)), where V is speed in m/s, g is 9.81 m/s², and L is waterline length in metres. For displacement hulls, the following approximate ranges are often used:

• Slow cargo ships (Fn < 0.2): Cb around 0.75–0.85
• Medium-speed freighters (Fn 0.2–0.3): Cb around 0.6–0.75
• Fast vessels (Fn > 0.3): Cb below 0.6

These are general values; actual design involves complex optimization and model testing.

Frequently Asked Questions

What is a good block coefficient?

There is no single “goodâ€� value. It depends on the ship’s role. A bulk carrier might have a Cb of 0.85 because it prioritizes cargo volume over speed. A container ship might have a Cb of 0.6 because it needs to maintain a higher speed. The “bestâ€� value minimizes resistance for the required speed and capacity.

What is the difference between block coefficient and prismatic coefficient?

The block coefficient compares the hull volume to a rectangular box. The prismatic coefficient (Cp) compares the hull volume to a prism with the same length and the maximum cross-sectional area. Cp indicates how the volume is distributed along the length; a low Cp means the ends are fine, a high Cp means the midsection is full.

Can the block coefficient be greater than 1?

No. The displacement volume cannot exceed the volume of the enclosing box, so Cb is always ≤ 1. If your calculation gives more than 1, you likely entered the wrong dimensions or used inconsistent units.

How do I calculate displacement volume if I only know displacement mass?

Divide the displacement mass (in tonnes) by the density of the water. For seawater, density is about 1.025 t/m³. For freshwater, about 1.0 t/m³. For example, a ship displacing 10,000 tonnes of seawater has a volume of about 9,756 m³.

Why do different sources give different block coefficients for the same ship?

Because they may use different lengths (waterline vs. overall), different drafts (design vs. scantling), or different displacement definitions (including or excluding appendages). Always check which definitions were used.

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in L | Length (L) | m | 100 | 0
in B | Breadth (B) | m | 20 | 0
in T | Draft (T) | m | 8 | 0
in V | Displacement volume (V) | m³ | 12000 | 0
out Cb | Block coefficient | - | V / (L * B * T) | 3