Circle, arc and chord calculator

For radius r and angle θ in radians, circumference = 2πr, arc length = rθ and chord = 2r sin(θ/2). Sagitta h is the arc height above its chord. Given chord c and h, r = c²/(8h) + h/2; h greater than r selects the major arc. For x² + y² + Dx + Ey + F = 0, centre = (−D/2, −E/2) and r² = D²/4 + E²/4 − F.

The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.

Known circle measurements

Radius and central angle

Radius

10

Central angle

90 °

Primary result: Radius: 10.

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

Use one consistent length unit; areas are in that unit squared. Angles range from 0° to 360°. The blue curve is the arc and the red line its chord. An architectural arch is only described by this model if it is circular. A missing diagram or unspecified labelled segment cannot be inferred.