Heel Angle from Weight Shift Calculator
How far she'll lean: heel angle from a weight moved or loaded off-center — the GM-based list formula behind crane lifts, crowd shifts and cargo stows.
The list formula runs every practical stability question: the crane load swung outboard, the catch piled to port, sixty passengers rushing one rail. Valid to ~10° of heel — beyond that the metacenter wanders and GZ curves take over.
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.
How far she'll lean: heel angle from a weight moved or loaded off-center — the GM-based list formula behind crane lifts, crowd shifts and cargo stows.
About Heel Angle from Weight Shift Calculator
Every off-center pound levers the boat over, and GM is the spring that answers: tan(heel) = weight × offset ÷ (displacement × GM). This calculator runs the classic list formula for any weight shift — the outboard crane swing, the side-stacked catch, the wedding party at one rail — returning the heel angle and the vessel's moment-per-degree stiffness, with honest flags where the small-angle model hands off to full righting curves.
How to use Heel Angle from Weight Shift 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 tan(θ) = w×d / (Δ×GM) — heeling moment against the stability moment, small angles substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Heel Angle from Weight Shift Calculator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula tan(θ) = w×d / (Δ×GM) — heeling moment against the stability moment, small angles with sources cited on the page
- ✓The list formula runs every practical stability question: the crane load swung outboard, the catch piled to port, sixty passengers rushing one rail. Valid to ~10° of heel — beyond that the metacenter wanders and GZ curves take over.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
What can I do with the moment-per-degree number?+
It's your vessel's exchange rate: 1,500 ft·lb per degree means a 300-lb crewmate at the 5-ft rail costs one degree — and you can audit GM in reverse by observing actual heel from a known shift (a poor man's inclining experiment). Crane barges, fishing boats stowing catch, and ferry loading officers all think in this currency.
Why does the formula break past ten degrees?+
The metacenter M is only stationary for small heels: as angles grow, the waterplane shape changes, M migrates, and the true righting arm GZ departs from the linear GM·sinθ. Past ~10–15°, real stability work uses the GZ curve (righting arm vs angle) from the vessel's stability book. The formula's job is the everyday regime; its validity limit is part of its honesty.
How do passenger-crowd shifts capsize small ferries?+
Run the numbers: 60 passengers (9,000 lb) moving 8 ft to one rail of a 60,000-lb ferry with a degraded 1.5-ft GM heels her tan⁻¹(72,000/90,000) = 39° by this formula — far beyond its validity and likely beyond the deck edge. Overloading (raises KG, cuts GM) plus a crowd event is the recurring fatal pattern in ferry casualty reports worldwide. The formula shows how little margin overloading leaves.
Does the same math govern loading a small boat at the dock?+
Identically: step on the gunwale of a 14-ft skiff (your 180 lb at 2 ft offset, against maybe 900 lb × 1 ft of Δ·GM) and the formula predicts ~22° — your wet sneakers already knew. It's why you step into the CENTER of small craft, why coolers ride amidships, and why the capacity plate assumes the load stays low and centered.
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