Free Surface Effect Calculator
The stability thief in your tanks: how much GM a slack tank's sloshing liquid destroys — width cubed, as every capsize inquiry rediscovers.
The cruelty is in the cube: tank WIDTH matters cubed, fill level barely matters at all (a nearly-full and nearly-empty slack tank slosh alike). Press tanks full or run them empty; the worst tank aboard is the wide one half-full.
Formula
⚠️ For planning and education only — verify with your vessel's documentation, naval-architecture data and official sources. Not for navigation or stability decisions on real voyages without professional data.
The stability thief in your tanks: how much GM a slack tank's sloshing liquid destroys — width cubed, as every capsize inquiry rediscovers.
About Free Surface Effect Calculator
A half-full tank carries a saboteur: as the vessel heels, the liquid runs downhill, shifting its weight toward the low side at exactly the wrong moment — mathematically equivalent to raising the center of gravity by i×ρ/Δ, where i grows with the tank's WIDTH CUBED. This calculator computes the GM each slack tank destroys, by fluid type, and demonstrates the baffle miracle: one centerline division cuts the loss to a quarter.
How to use Free Surface Effect Calculator
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula GM loss = i × ρ_fluid / Δ; i = l·b³/12 — tank WIDTH cubed; a centerline baffle cuts it to ¼ substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Free Surface Effect Calculator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula GM loss = i × ρ_fluid / Δ; i = l·b³/12 — tank WIDTH cubed; a centerline baffle cuts it to ¼ with sources cited on the page
- ✓The cruelty is in the cube: tank WIDTH matters cubed, fill level barely matters at all (a nearly-full and nearly-empty slack tank slosh alike). Press tanks full or run them empty; the worst tank aboard is the wide one half-full.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why does the width enter cubed while fill level barely matters?+
The effect comes from the liquid surface's moment of inertia (l·b³/12), not the liquid's amount: what matters is how far athwartships the surface lets weight migrate when heeled. A wide shallow puddle is worse than a deep narrow column of far more liquid. Fill level only matters at the extremes — pressed full or empty, there's no surface to shift, and the effect vanishes.
How does a baffle achieve the factor of four?+
Cube arithmetic: a centerline division makes two tanks of half width, each contributing (b/2)³ — one-eighth — and two of them total one-quarter of the original. Add two baffles (three compartments): one-ninth. This is why ship tanks are honeycombs, tanker regulations mandate subdivision, and your boat's water tank has those annoying internal walls.
Which everyday situations bite small craft hardest?+
The classics: partially-filled live wells and fish holds (wide, low, exactly wrong), water on deck that can't drain (freeing-port arithmetic is free-surface arithmetic), half-empty wide water tanks under berths, and the dinghy-with-rainwater on davits. Fishing-vessel capsizes repeatedly feature slack holds plus a turn — the combined free-surface loss meeting a heeling moment.
Why do tankers and bulk carriers obsess over this?+
Scale: a VLCC's cargo tank can be 25 m wide — width cubed makes its free surface worth metres of GM, dwarfing the ship's entire stability margin if undivided. Hence center bulkheads, wash bulkheads and loading procedures that press tanks sequentially rather than slack-filling several. Grain shifts in bulkers obey sibling physics (granular free surface), with its own ugly casualty list.
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