Central Angle Calculator

Calculate the central angle of a circle segment given the arc length and radius.

Circle Measurements

Arc Length (s)

Radius (r)

Angle Results

Angle in Radians (rad)2.0000

Angle in Degrees (°)114.59

Sector Area25.00

What is a Central Angle?

A central angle is an angle whose vertex is the center of a circle and whose sides (radii) intersect the circle at two distinct points. The measure of this angle determines the size of the sector (slice) and the length of the arc along the circle's edge.

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Pro Tips

Ensure your arc length is not greater than the circumference of the circle (2πr), or the angle will be greater than 360 degrees.
Radians are often vastly more useful in higher mathematics and physics than degrees.
The 'Sector Area' is the area of the pie slice formed by the central angle.

Fun Facts

"There are 2π radians in a full circle, which equals 360 degrees."
"The concept of degrees (360) is believed to originate from ancient Babylonian astronomy."
"A central angle of 1 radian subtends an arc equal in length to the circle's radius."

Formula: θ (radians) = s / r | θ (degrees) = (s / r) * (180 / π)

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