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Arc of a Circle

A connected section of the circumference of a circle.

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)

The red arc (minor arc) measures 120°.

The blue arc (major arc) measures 240°.

Measurement by arc length
(radians)

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

 


  this page updated 28-jul-14
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes