Arc Length Calculator
The Arc Length Calculator finds the length of a circular arc from the circle's radius and the central angle. The formula used is: Arc length = r × θ (with θ in radians) = r × angle × π/180; Fraction of circle = angle/360.
Formula
Arc length = r × θ (in radians) = r × angle × π/180; Fraction = angle/360
- The Arc Length Calculator updates instantly as you change the radius or central angle.
- Formula: Arc length = r × θ (in radians) = r × angle × π/180; Fraction = angle/360
- Input definitions: • Radius: the radius of the circle • Central Angle: the angle the arc subtends at the center, in degrees
- The angle is converted to radians before multiplying by the radius.
- Fraction of circle = angle ÷ 360, so a 90° arc is one quarter of the circumference.
- Arc length and circumference share the same unit as the radius.
Example Calculation
Inputs
- Radius (cm): 10
- Central Angle (degrees): 45
For a radius of 10 and a 45° angle: arc length = 10 × 45 × π/180 ≈ 7.85, which is 45/360 = 12.5% of the full circumference.
Frequently asked questions
How is arc length calculated?
Multiply the radius by the central angle in radians: arc length = r × θ. In degrees, that is r × angle × π/180.
What is the central angle?
It is the angle the arc makes at the center of the circle, measured here in degrees.
What fraction of the circle is the arc?
The fraction equals the angle divided by 360. A 90° arc covers a quarter of the circle.
What units does the result use?
Arc length and circumference use the same unit as the radius you enter.
How do I find the angle from a known arc length?
Rearrange the formula: angle (degrees) = arc length ÷ radius × 180/π.
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