Find the Center and Radius of Any Arc With a Compass and Straightedge
One of 2 takes on Finding the Center of an Arc
The Problem
Someone hands you a cardboard template, a curved piece of trim, or a pattern with an arc and says "I need this exact radius." You don't have the architectural plans or any measurements. You just have the curve and need to find the center point and radius so you can reproduce it.
The Technique
This is a geometry trick called the perpendicular bisector method. It works on any arc from any circle, every time.
- Mark three points anywhere along the arc — call them A, B, and C. Space them out for best accuracy.
- Draw a straight line from A to B, and another from B to C
- Find the midpoint of line AB. Mark it.
- Draw a line perpendicular (90 degrees) to AB from that midpoint, extending it well past the arc
- Find the midpoint of line BC. Mark it.
- Draw a line perpendicular to BC from that midpoint, extending it the same way
- Where those two perpendicular lines cross — that's the center of the circle
- Measure from that intersection to any of your three original points — that's the radius
Set your compass, dividers, or trammel to that radius, swing from the center point, and you'll trace the exact arc.
Pro tip: The farther apart your three points are on the arc, the more accurate your result. If the points are too close together, small errors in your lines get magnified. Spread them out as much as the arc allows.
Pro tip: For finding the midpoint, you don't need to measure — just set your compass wider than half the line and swing arcs from both endpoints. Where the arcs cross (above and below the line) gives you two points that define the perpendicular bisector. Pure geometry, no measuring.
Pro tip: This works in any material — metal, wood, drywall, concrete. The creator in the source video is laying this out directly on a sheet of metal with soapstone and dividers. Same method works with a pencil and a framing square on plywood.