How to Calculate Arc Length of a Circle: Step-by-Step Formula Explained

Learn how to calculate the arc length of a circle using the radius and central angle, with easy conversion from degrees to radians.

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To calculate the arc length of a circle, you need the central angle in radians and the radius of the circle. The formula is Arc length = Radius × Central Angle (radians). If the angle is in degrees, first convert it to radians by multiplying the degrees by π/180. For example, for a 60-degree angle in a circle with a 5cm radius, convert 60 degrees to radians (60 × π/180), which gives 1.047 radians. Then, multiply by the radius: 5cm × 1.047 = approximately 5.24cm.

FAQs & Answers

  1. What is the formula to calculate the arc length of a circle? The arc length is calculated by multiplying the radius of the circle by the central angle in radians: Arc length = Radius × Central Angle (radians).
  2. How do you convert degrees to radians for arc length calculations? To convert degrees to radians, multiply the angle in degrees by π divided by 180: Radians = Degrees × π⁄180.
  3. Can you calculate arc length if the central angle is given in degrees? Yes, first convert the degrees to radians using the formula Radians = Degrees × π⁄180, then use the arc length formula.

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For a deeper understanding of circle geometry, check out our related videos on calculating the area of a sector, understanding radians, and solving problems involving central angles.

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