By Sean Kotz Updated Mar 24, 2022
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A curved line, or arc, represents a segment of a circle. While a straight ruler cannot measure its length precisely, geometry offers a straightforward method to calculate it. By using a protractor and knowing the circle’s diameter, you can apply the formula:
arc length = diameter × 3.14 × angle ÷ 360.
π ≈ 3.14. Length = diameter × π × angle ÷ 360.
If you only have the radius, double it to obtain the diameter. For instance, a radius of 5 inches yields a diameter of 10 inches.
Place the protractor’s center point over the circle’s center. Align the protractor’s zero edge with the radius, ensuring the zero-degree mark sits at the arc’s starting point.
Identify where the arc’s upper endpoint meets the protractor’s scale; that number is the arc’s angle. For example, if it aligns with 40°, the angle is 40°.
Multiply the diameter by 3.14, then by the angle. Using a 10-inch diameter and a 40° angle: 10 × 3.14 × 40 = 1,256.
Since a full circle contains 360°, divide the product by 360. In the example: 1,256 ÷ 360 ≈ 3.488.
Round the result to the nearest hundredth or tenth. Here, 3.49 inches (hundredths) or 3.5 inches (tenths) would be appropriate.
The arc length shares the same units as the diameter. If the diameter is in centimeters, the arc length will be in centimeters. For practical measurements where diameter and angle are hard to determine, lay a flexible string along the curve, cut it to fit, and measure the string.
