Calculate the distance along the curve of a circle given the radius and central angle.
Arc length is the distance along a curved line, which is in the case of a circle, a portion of the circumference. It represents the actual distance you would travel if you walked along the edge of the circular sector from one radius to the other.
Arc length is different from the straight-line distance (chord) between two points on a circle. It's used in many applications including calculating distances on maps, designing curved paths, and analyzing circular motion.
s = Arc length
θ (theta) = Central angle in radians
r = Radius of the circle
Arc length is measured along the curve of the circle. Chord length is the straight-line distance between two points. Arc length is always ≥ chord length.
The formula s = θ × r only works when θ is in radians. Radians are defined so arc length equals the angle times radius.
Arc length is a portion of circumference. When angle = 2π radians, arc length = 2πr (full circumference).
No, arc length is always positive. It's a distance measurement, not a vector.
The formula still works. The arc wraps around the circle multiple times. Arc length = θ × r regardless.
Arc length is used in physics (circular motion), engineering (curved structures), and cartography (map distances).
You need additional info like radius or central angle. Chord length alone doesn't uniquely determine arc length.
Yes, for a fixed angle, arc length is directly proportional to radius. Doubling radius doubles arc length.
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