Calculating Arc Length | A Guide to Determining the Length of a Curve with the Arc Length Formula

Arc Length

Arc length refers to the length of a curve or a portion of a curve

Arc length refers to the length of a curve or a portion of a curve. In other words, it is the measure of the distance along the curved path between two endpoints. It is commonly used in geometry and calculus to determine the length of a specific section of a curve, such as a circular arc or a segment of a parabola.

To calculate the arc length, we use a formula that incorporates the radius of curvature and the central angle (θ) subtended by the arc. The formula is as follows:

Arc Length = r × θ

Where:
– “r” represents the radius of curvature, i.e., the distance from the center of the circle to the arc.
– “θ” represents the measure of the central angle in radians.

It is crucial to remember that the angle must be in radians for this formula. If the angle is given in degrees, it needs to be converted to radians by multiplying it by π/180.

For example, let’s say we have a circular arc with a radius of 5 units and a central angle of π/3 radians. To find the arc length, we would substitute the values into the formula:

Arc Length = 5 × (π/3)
= (5π)/3
≈ 5.24 units (rounded to two decimal places).

Therefore, the arc length of the given circular arc is approximately 5.24 units.

More Answers: