An arc is a section of the outline, or circumference, of a circle. This common shape appears in many forms, like the arch of a bridge or the top of certain windows.

If you want to create a copy of an arc, you can either trace it or build one like it from another circle the same size. Tracing is easy, but if you want to build your own circle, you need to find the radius of that circle. If it’s complete or nearly complete, it’s not hard to find the center, and that will let you measure its radius and diameter. But if the arch is only one small segment of the whole circle, finding those values might seem hopeless. It’s easier than it looks, though: all you need is a tape measure and a pencil. Well, maybe a calculator, too…

What You’ll Need

• Tape measure

• Pencil

• Calculator (optional)

How To

1) Mark two points on the arc

2) Draw a line between the two points and measure the length. Call the length L.

3) Find the midpoint of the line, halfway between your two marks.

4) Measure the distance from the midpoint to the arc. Call this distance H.

5) Divide L by 2 and square the result,

6) Divide the answer by H and add H to the result.

7) Divide the answer by 2. The quotient is R, the radius of the curved arc.

If you need the diameter of the circle instead of the radius, the diameter is the radius times 2.

Example

An arch’s measurements are L = 40 and H = 5

L / 2 = 20

20 * 20 = 400

400 / 5 = 80

80 + 5 = 85

85 / 2 = 42.5, the radius of the arch

the diameter = 85

Hint: the units (meters, feet, inches, miles) don’t make any difference, as long as the units of H and L are the same. The units of the radius will be the same as H and L.