Free Surface Correction (FSC)

Reduction in GM due to slack liquids. Calculate directly from ΣFSM or build from rectangular tank free-surface geometry.

Common Inputs
Sea ≈ 1.025, fresh ≈ 1.000
Direct Free Surface Moment
FSC = ΣFSM / Δ
Rectangular Tank Free Surface Builder

FSMi = ρ · L · B³ / 12 · k   (t·m)

Free Surface Correction Result

Total ΣFSM: — t·m

FSC: — m

Report: Free Surface Correction (FSC)
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Free Surface Correction (FSC) in Ship Stability

Free Surface Correction (FSC) accounts for the reduction in transverse metacentric height (GM) caused by liquids in partially filled (slack) tanks. When a vessel heels, liquid shifts transversely, generating a virtual rise in the ship’s centre of gravity and reducing initial stability.

FSC is applied as a correction to the intact GM value and is especially important during loading, ballast exchange, fuel consumption, and damage stability assessments. Neglecting free surface effects can significantly overestimate stability margins.

Free Surface Moment (FSM)

The free surface effect of a tank is quantified by its Free Surface Moment (FSM), which depends on tank geometry, liquid density, and internal subdivisions such as swash bulkheads.

For a rectangular tank, the transverse free surface moment is approximated as:

FSM = ρ · L · B³ / 12 · k

  • ρ – liquid density (t/m³)
  • L – free surface length (m)
  • B – free surface breadth (m)
  • k – swash/baffle effectiveness factor (0–1)

The total free surface moment is obtained by summing individual tank FSMs:

ΣFSM = FSM₁ + FSM₂ + …

Free Surface Correction Formula

The free surface correction applied to GM is calculated as:

FSC = ΣFSM / Δ

  • ΣFSM – total free surface moment (t·m)
  • Δ – ship displacement (t)

FSC is always subtracted from the uncorrected GM value:

GMcorrected = GM − FSC

Calculation Modes

This calculator supports two practical methods used in naval architecture and onboard stability calculations:

  • Direct ΣFSM Mode – use when free surface moments are provided directly in the vessel’s stability booklet.
  • Tank Builder Mode – estimate FSM values from tank geometry when handbook data is unavailable.

Operational Notes

  • Only slack tanks contribute to free surface effect.
  • Fully pressed-up or empty tanks generate no FSC.
  • Swash bulkheads reduce FSM but do not eliminate it entirely.
  • FSC is most critical for small GM values and ballast conditions.

Related Stability Calculators

This tool is intended for preliminary design, onboard checks, and training purposes. Always verify final stability compliance against approved stability documentation and class requirements.