Geometry and layout calculator
Circle and Arc Calculator
Calculate common circle and arc measurements, including circumference, area, chord length, arc length and segment height.
What the result means
The radius reaches from the center of the circle to the edge. The diameter is twice the radius. A chord is a straight line between two points on the circle, while an arc is the curved distance between those same points. Segment height, sometimes called sagitta, tells you how far the arc rises above the chord.
Formula
Circumference = 2 × π × radius
Area = π × radius²
Arc length = radius × included angle in radians
Worked example
A circle with a 3 inch radius has a 6 inch diameter, an 18.8496 inch circumference, and an area of about 28.2743 square inches. If the included angle is 120°, the arc length is one third of the full circumference.
Common mistakes
- Confusing radius and diameter.
- Using the straight chord length where the curved arc length is needed.
- Forgetting that a segment height depends on both the chord and the radius.
- Rounding too early and carrying that rounding into the next step.
Practical note
Real material may spring back, stretch, or flatten. The geometry here describes the ideal shape, not what bent metal, wood, plastic, or tubing will always do in the shop.