Inscribed Angle Calculator

About this calculator

The inscribed angle theorem, one of the foundational results in circle geometry, attributed to Euclid and often credited even earlier to Thales, states that an inscribed angle, formed by two chords meeting at a point on the circle, is always exactly half the central angle that subtends the same arc. Formally, inscribed angle = central angle ÷ 2, and a corollary of the theorem is that any inscribed angle subtending a semicircle, a diameter, is always a right angle.

This relationship underlies many circle-geometry proofs taught in secondary school and is used practically wherever arcs and angles need to be related without direct measurement — surveying and civil engineering layouts involving circular curves, architectural design of arches and domes, and CAD software's internal geometry checks when constrained circular sketches are solved.

Enter a central angle and this calculator returns the corresponding inscribed angle that subtends the same arc.