Circular arc and circular segment calculator

A circular arc is a portion of the circumference of a circle, bounded by two points. The chord connecting these two points, together with the arc, forms a circular segment.

To calculate the arc length, chord, height, or area, you need any two known parameters — most commonly the radius and central angle. If these basic parameters are unknown, this calculator allows you to find them using any two other known values.

Note: all linear dimensions (radius, arc length, chord, height) must be entered in the same units of measurement (e.g., millimeters, centimeters, or meters). Areas are calculated in the corresponding square units.

Main Elements of an Arc and Segment

• Radius (R) — the distance from the center of the circle to any point on the circumference.
• Central angle (θ) — the angle between two radii passing through the endpoints of the arc. Measured in degrees (0° < θ < 360°).
• Arc length (L) — the length of the curve between the two endpoints: $$L=\frac{\theta \cdot \pi \cdot R}{180}$$
• Chord (c) — the straight line segment connecting the endpoints of the arc: $$c=2R\cdot \sin \left(\frac{\theta \cdot \pi }{360}\right)$$
• Segment height (h) — the distance from the midpoint of the chord to the arc (sagitta): $$h=R\cdot \left(1-\cos \left(\frac{\theta \cdot \pi }{360}\right)\right)$$
• Sector area (S_sect) — the area bounded by two radii and the arc: $$S_{\text{sect}}=\frac{\theta }{360}\cdot \pi \cdot R^2$$
• Segment area (S_segm) — the area bounded by the chord and the arc: $$S_{\text{segm}}=\frac{R^2}{2}\cdot \left(\frac{\pi \cdot \theta }{180}-\sin \left(\frac{\theta \cdot \pi }{180}\right)\right)$$

Input Combinations

• By radius and angle (R, θ) — full calculation of all parameters.
• By chord and segment height (c, h) — finds radius and angle.
• By radius and arc length (R, L) — determines the central angle.
• By angle and sector area (θ, S) — finds the radius.
• By chord and radius (c, R) — determines the angle and all other parameters.