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Arc of a Circle

Arc of a Circle

A connected section of the circumference of a circle.

A circle with a short black arc (minor arc) at top right labeled "arc of a circle," rest shown as dashed green line.

Arcs are measured in two ways: as the measure of the central angle, or as the length of the arc itself.

Measurement by central angle
(degrees)

 Circle with a 120° central angle: short red minor arc (120°) and long blue major arc (240°) with two radii shown.

The red arc (minor arc) measures 120°.

The blue arc (major arc) measures 240°.

Measurement by arc length
(radians)		 Circle with radius r=2, central angle 2π/3. Red minor arc (top) and blue major arc (bottom) are labeled.

Formula: s = rθ
s = arc length
r = radius of the circle
θ = measure of the central angle in radians

Red arc:  r = 2 and θ = 2π/3, so s = 4π/3

Blue arc:  r = 2 and θ = 4π/3, so s = 8π/3

See also

Arc length of a curve