Circular Segment Calculator

Circular Segment Calculator is the fastest way to solve any circular segment - enter just two values and instantly get all six properties: radius, central angle, arc length, chord length, segment height, and area. Whether you're a student, engineer, architect, woodworker, or CNC machinist, this calculator handles the geometry so you don't have to.

TWO FLEXIBLE INPUT MODES Angle & Radius - Know the circle's radius and the central angle? Every other property is solved instantly. Chord & Height - Working from a physical measurement? Enter the chord length and segment height (sagitta) to back-calculate the radius, angle, and everything else.

WHAT YOU GET Arc length - exact curved distance along the segment Chord length - straight-line distance between the two endpoints Segment height - the sagitta, from chord midpoint to arc Central angle - in degrees or radians, your choice Radius - recovered from any two known values Segment area - precise enclosed area calculation

BUILT FOR REAL WORK • Real-time results — calculations update as you type, no submit button needed • Step-by-step explanations — every formula shown with your actual numbers • Tap to copy — tap any result row to copy the value instantly to clipboard • Unit flexibility — switch between cm, m, inches, and feet; degrees or radians • Visual diagram — live canvas updates as you enter values, labeled with r, θ, c, h, and L • Reference sheet — full formula reference with annotated diagram, always one tap away • Dark Mode — full system dark and light mode support

WHO USES THIS Students working through geometry, trigonometry, or engineering coursework Engineers & architects calculating curved structural elements, arches, and vaults Woodworkers & makers laying out curved cuts, jigs, and templates CNC & CAM operators computing toolpaths for circular profiles Surveyors working with circular curves and road alignment Anyone who needs quick, reliable circular segment math on the go

Circular segment - is an area of a circle which is "cut off" from the rest of the circle by a secant (chord).

A circular sector or circle sector, is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. In the diagram, θ is the central angle in radians, r the radius of the circle, and L is the arc length of the minor sector.

A sector with the central angle of 180° is called a half-disk and is bounded by a diameter and a semicircle. Sectors with other central angles are sometimes given special names, these include quadrants (90°), sextants (60°) and octants (45°), which come from the sector being one 4th or 6th or 8th part of a full circle, respectively.

The angle formed by connecting the endpoints of the arc to any point on the circumference that is not in the sector is equal to half the central angle.

PRIVACY No account required. No ads. No tracking. All calculations run entirely on your device.

Download Circular Segment Calculator and solve segment geometry in seconds.

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