This arc length calculator is a tool that can calculate the length of an arc and the area of a circle sector. In this article, we explain the arc length formula in detail and provide you with a step-by-step instruction of how to find the arc length. You will also learn the equation for sector area.
The length of an arc depends on the radius of a circle and the central angle Θ. We know that for the angle equal to 360 degrees (2π), the arc length is equal to circumference. Hence, as the proportion between angle and arc length is constant, we can say that:
L / Θ = C / 2π
C = 2πr,
L / Θ = 2πr / 2π
L / Θ = r
We find out the arc length formula when multiplying this equation by Θ:
L = r * Θ
Hence, the arc length is equal to radius multiplied by the central angle (in radians).
We can find the area of a sector of a circle in a similar manner. We know that the area of the whole circle is equal to πr². From the proportions,
A / Θ = πr² / 2π
A / Θ = r² / 2
The formula for the area of a sector is
A = r² * Θ / 2
L = r * Θ = 15 * π/4 = 11.78 cm.
A = r² * Θ / 2 = 15² * π/4 / 2 = 88.36 cm².