April 16, 2023

How to Measure an Arc in a Circle

major arc cbd measures 300 which is the radian measure of its corresponding central angle

arc measures

The measure of an arc is the size of the angle that it subtends. It is equal to the length of the arc divided by the radius of the circle.

radian measures

Radians are the standard units for angular measure; one degree is equivalent to p/180 radians, and a radian is a right angle (90 degrees or p/2 radian).

central angles

A central angle is an angle whose vertex is on the center of the circle. Its endpoints are also on the circle. When the endpoints of an arc intersect a central angle, we say that the arc subtends the angle.

major arcs

If an arc has a length greater than 180deg, it is a major arc. If its length is less than 180deg, it is a minor arc.


If the length of an arc is equal to the distance between two radii, then it is a semicircle. Arcs that have equal measures are called adjacent arcs.

arcs and semicircles

Central angles define regions within circles, which are called sectors and segments. Sectors and segments are bounded by the circle itself, and by the ends of the chord that defines the arc.

arcs, major and minor arcs, and semicircles

A major arc is a longer arc connecting two points on the circle. A minor arc is a shorter arc that connects the same points on the circle. A semicircle is an arc that has no endpoints but contains points on or outside the sides of a central angle.


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