Generate points to plot a parabolic curve for deck camber, cabin tops, and more.
A slight curve for a wide deck
A more pronounced curve for a cabin
A sharp curve for hull flare
e.g., inches, mm
e.g., inches, mm
Odd numbers work best
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Download NowA surprising amount of boat work is really one smooth arch: the rocker on a sole, the round of a hatch coaming, the belly of a transom, the sweep of a bunk lid. The curve calculator models that arch as a parabola from its span and its depth, plots an even set of points along it for setting out, and returns the true length of the curved line so you know how much to cut.
The shape is fixed by two honest measurements, the width it spans and the height the curve rises at its midpoint. From those the tool lays out your chosen number of coordinate points across the run, which is exactly what you need to mark a batten, set a template or plot the curve on the lofting floor.
Enter the span, the depth and how many points to generate, and the calculator returns the plotted coordinates and the arc length along the curve, turning a rough sketch of an arch into numbers you can build to.
Half Width = Width ÷ 2; Point Height y = Depth × (1 − (x ÷ Half Width)²); Arc Length = (Width ÷ 2) × (√(1+p²) + (1/p)·ln(p + √(1+p²))) where p = 4 × Depth ÷ Width| Depth ÷ Span | Curvature | Typical Use |
|---|---|---|
| About 1/16 | Gentle | Sole rocker, flat panel |
| About 1/8 | Moderate | Hatch coaming, bunk lid |
| About 1/6 | Full | Transom belly, fender |
| About 1/4 | Deep | Round bow section, porterole |
How depth changes a fixed span.
Formula verified against standard naval-architecture references · Updated October 2026
A symmetric parabola defined by its span and its midpoint depth, a good practical match for arches, rockers, coamings and transom bellies. You give the width it bridges and the rise at the centre, and it plots the intermediate points and reports the true curved length, so a shape you can measure on the boat becomes a set of numbers you can build to.
Mark the two ends at the span, strike a centreline and set the depth at the midpoint, then generate a series of points and spring a batten through them. The calculator gives you those coordinates for any point count, so you lay them out, spring a batten along them and trace the fair line rather than eyeballing an arc.
Because the curve travels further than a straight line across the same span, and the deeper the arch, the greater the difference. The reported arc length is the distance a piece of trim, tape or cloth must cover following the curve, so cutting to the flat span alone guarantees a short piece.
Enough that a batten faired through them cannot hide a kink, commonly ten to twenty across a hull feature, with extra density near sharply curving ends. More points give a smoother, more trustworthy line but a longer table, so match the count to how tight the curvature is and how accurate the setting-out must be.
For single-curved features like rocker, a coaming or a transom face it is an excellent and simple model. Genuinely compound hull surfaces need lofted offsets from the lines plan rather than one parabolic slice, so treat this as the tool for arches you can span and depth, and use full lofting for double-curved shell.
Any consistent unit for width and depth, inches or centimetres alike, since the shape and arc length are computed as ratios and returned in the same unit you entered. Just keep both dimensions in one system; the point count is a plain number with no unit at all.