How to Calculate the Length of an Arc: Simple Formula Explained
Learn how to calculate the length of an arc using radius and central angle with this easy formula and angle conversion tips.
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To calculate an arc, you need the central angle in radians (θ) and the radius (r) of the circle. The formula is Arc length = θ × r. If the angle is in degrees, first convert it to radians by multiplying it by π/180. This formula directly relates the arc length to the proportion of the circle's circumference covered by the angle.
FAQs & Answers
- What is the formula to calculate the length of an arc? The arc length is calculated by multiplying the radius (r) of the circle by the central angle (θ) in radians: Arc length = θ × r.
- How do you convert degrees to radians for arc length calculation? To convert degrees to radians, multiply the angle in degrees by π/180 before using it in the arc length formula.
- Can I use the arc length formula if the angle is given in degrees? Yes, but first convert the central angle from degrees to radians by multiplying it by π/180, then apply the formula Arc length = θ × r.
- Why is the angle used in radians for arc length calculation? Radians provide a direct proportional measure of the angle relative to the radius, making the formula Arc length = θ × r accurate and straightforward.