Arc layout calculator

Lay out a circular arc from its span and rise

Measure the distance between the arc endpoints and the rise wanted at the middle. The calculator gives you the radius and tells you where to put a compass or trammel pivot.

Your measurements

Lay out the arc

Trammel radius

1275mm

Put the pivot 1125mm behind the chord, on the side opposite the crown.

Pivot offset

1125mm

Arc length

1249.4mm

Arc angle

56.14°

Span: 1200mmRise: 150mm
True circular arc drawn to scale from the measured span and centre rise.
This calculator deliberately stops at a semicircle. The rise must be no more than half the span.

When this is useful

This works for an arched rail, apron, opening or template when the width and required crown are known but the circle radius is not. It describes a true circular arc rather than an ellipse or a freehand fair curve.

How to measure span and rise

The span is the straight chord between the two endpoints. The rise is measured square to that chord at its exact midpoint. A rise taken somewhere else does not describe the same circle, so mark the midpoint before measuring or entering the value.

Where the trammel pivot goes

For the minor arcs handled here, the pivot sits behind the chord on the side opposite the crown. Measure the reported pivot offset square from the chord midpoint. A shallow arc can put that point a surprisingly long way from the workpiece, so a batten or temporary floor layout may be easier than a normal compass.

The radius formula

The calculator uses radius = span² ÷ (8 × rise) + rise ÷ 2. It keeps full precision internally and rounds only the displayed workshop measurements.

Check the mark before cutting

Confirm that the arc passes through both endpoints and the centre-rise mark. Use a flexible strip as a visual check if appropriate, then cut outside the line and refine to it. Bent or laminated timber may spring back; this geometry does not predict material movement.

Why does the calculator reject a large rise?

The page is intentionally limited to minor arcs up to a semicircle, where the rise is no greater than half the span. Major arcs need a different and easily misunderstood pivot arrangement.