Marine & Nautical
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Draft from Displacement

Depth of hull below waterline from displacement and waterplane area.

Formula

T=Δρ AwT = \frac{\Delta}{\rho\, A_w}

Variables

TDraft (m)
ΔDisplacement (kg)
ρWater density
A_wWaterplane area (m²)

Example

Heavier cargo increases draft — the ship sits lower in the water.

How it works

This relation estimates a ship’s draft by dividing its displacement by the mass of water displaced per metre of immersion, which is the product of water density and waterplane area. It is a useful first-order hydrostatics approximation: more mass must be supported by buoyancy, so the hull sinks deeper until the displaced water weighs the same as the vessel. It works best when the waterplane area does not change much with small changes in draft, so it is mainly a linear approximation near a given loading condition.

When to use it

Use this when you need a quick estimate of how deep a vessel will sit after loading, ballasting, or changing water density. It is also useful in preliminary ship design and for checking whether a vessel can safely enter a channel, lock, or berth.

Worked example, step by step

Given: Δ = 12,000 kg ρ = 1,025 kg/m³ (seawater) A_w = 18 m² Formula: T = Δ / (ρ A_w) Substitute: T = 12,000 / (1,025 × 18) Calculate the denominator: 1,025 × 18 = 18,450 Compute draft: T = 12,000 / 18,450 = 0.650 m Final answer: The estimated draft is 0.65 m.

Common mistakes to avoid

  • Using displacement in tonnes without converting consistently with density units
  • Confusing waterplane area with wetted surface area or cross-sectional area
  • Applying the formula in conditions where hull shape changes the waterplane area significantly with draft

Did You Know?

The Plimsoll line painted on hulls marks the safe maximum draft in different waters and seasons.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026