Calculate the length of a circular arc for deck camber, hull curves, and more.
A typical 12ft wide deck
A gentle sheer for a 30ft boat
A common cabin top curve
e.g., inches, mm
degrees
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Download NowCurved work is everywhere in a boat, from the sweep of an arch tube to the length of a canvas cover along a rounded hatch, and the arc length calculator turns a radius and a central angle into the straight-line measurement you actually cut to. It answers the deceptively simple question of how much material a curve consumes.
The mathematics are clean: an arc is a fraction of a full circle, so its length is the radius multiplied by the angle expressed in radians. Alongside the arc the calculator returns the chord, the straight distance across the curve, and the sagitta, the depth of the bow from the chord, the two numbers you measure when you cannot reach the centre.
Enter a radius and a central angle in degrees, and the calculator gives arc length, chord and sagitta, so a single set-out feeds bending, cutting and the reverse problem of recovering a radius from a measured curve.
Angle (rad) = Angle (deg) × π ÷ 180; Arc Length = Radius × Angle (rad); Chord = 2 × Radius × sin(Angle ÷ 2); Sagitta = Radius × (1 − cos(Angle ÷ 2))| Angle | Arc as Fraction of Circle | Common Case |
|---|---|---|
| 30° | 1/12 of circumference | Small return, cutwater |
| 60° | 1/6 of circumference | Arch tube, window head |
| 90° | 1/4 of circumference | Quarter bend, bilge turn |
| 180° | 1/2 of circumference | Half round, hatch coaming |
Fraction of a circle by central angle.
Formula verified against standard naval-architecture references · Updated October 2026
Convert the central angle from degrees to radians by multiplying by pi over 180, then multiply by the radius. A 40 inch radius over 60 degrees is 40 times 1.047, about 41.9 inches. The calculator does the conversion for you and also returns the chord and sagitta, so one entry gives the curved length plus the straight span you check it against.
The arc length is the distance measured along the curve, the length of material you bend or cut; the chord is the straight-line distance between the two ends, the span the finished piece bridges. For a wide sweep they differ a lot, and building to the wrong one produces a piece too short for the curve or too long for the opening.
It is the depth of the curve, measured perpendicular from the midpoint of the chord up to the arc. Together with the chord it defines a gentle curve you can measure on the boat without ever locating the centre, and from chord and sagitta you can recover the radius and hence the arc length, which is exactly how existing hull sections and canopy bows are reverse-engineered.
Because the arc formula length equals radius times angle is only true when the angle is in radians; degrees are a human convention and would need the extra pi-over-180 conversion folded in. The calculator accepts degrees, converts internally, and shows the radian value too, so you can enter the number your protractor reads and still get correct maths.
Start from the arc length, since that is what the curve actually measures, then add a little for stretch when bending and for trimming the ends square. Stretching a tube or rolling a plate shortens the effective straight span slightly, so cutting to the pure arc and nothing more routinely leaves you short at the finish line.
Yes, and it is one of the best uses. A canvas cover over a curved trunk or hatch needs the surface distance along the curve, which is the arc length, plus tucks and seams; measuring the flat opening alone leaves the cover riding up, so compute the arc for the true cloth run before cutting.