Inscribed Angle Calculator

How it is calculated

The tool applies the inscribed angle theorem in one step: inscribed angle = central angle / 2. The input is the central angle in degrees, measured at the centre of the circle between the two radii that reach the ends of an arc. The output is the angle that an inscribed angle, with its vertex anywhere on the circle outside that arc, makes over the same arc. Both values are shown with two decimals and a degree sign. The central angle must lie between 0° and 360° inclusive; negative values or anything above 360 return no result. A central angle of 180° gives 90°, the right angle of a semicircle, and 360° gives 180°. The tool works only from central to inscribed; it does not go the other way.

Common mistakes

• Entering the inscribed angle in the central angle field. The tool halves whatever you enter, so you would get a quarter of the true central angle; double the inscribed angle to get the central one.
• Typing the angle in radians. The field expects degrees, so 1.2 would be read as 1.2°.
• Entering the full angle at the circumference when the vertex lies on the arc itself. The half rule applies to the angle that subtends the arc from the opposite part of the circle.
• Entering the arc length instead of the angle. The tool needs an angle between 0 and 360.