Chord Calculator

A chord is a straight line segment joining any two points on a circle. The diameter is the longest possible chord because it passes through the center. Chords appear in geometry, surveying, machining, architecture, road design, tank fabrication, and any task involving circular arcs. This calculator uses a known circle radius and central angle to find the chord length, the corresponding arc length, and the sagitta or rise of the minor arc. The chord-length formula is two times the radius times the sine of half the central angle. Trigonometric functions use radians internally, so the entered degree value is first multiplied by pi and divided by 180. Arc length is the radius multiplied by that angle in radians. Sagitta is the radius times one minus the cosine of half the angle. All linear outputs use the same unit as the radius, which means a radius in millimeters produces millimeter results and a radius in feet produces feet. For a 60-degree central angle, the chord equals the radius. At 180 degrees, the chord is the diameter and the sagitta equals the radius. Angles larger than 180 degrees describe a major arc; the straight chord remains the same as the chord for the complementary minor central angle, while the displayed arc length follows the entered major angle. At 360 degrees the two endpoints coincide, producing a chord of zero and a full-circumference arc. Measure or derive the central angle carefully. It is the angle at the circle's center between radii drawn to the chord endpoints, not an angle at the circumference. If you know only chord length and radius, a different inverse formula is needed to recover the angle. Small angles can also amplify measurement and rounding effects when used for layout. Use the chord result for straight spans, offsets, hole spacing, or polygon construction. Use arc length when estimating material that follows the curved edge. Use sagitta to determine the maximum distance between the chord and its minor arc. Keep full precision during intermediate work and round only the final physical measurement according to the tolerance of the project.