Calculating Arc Length: Formula and Example for Finding the Length of an Arc using Central Angle and Circle Radius

Arc

An arc is a portion of a curve or a circle

An arc is a portion of a curve or a circle. It is a continuous section of the circumference of a circle between two endpoints. Arcs are measured in terms of the angle they subtend at the center of the circle.

To find the length of an arc, you need to know the measure of the central angle (θ) of the arc and the radius (r) of the circle.

The formula to calculate the length of an arc is given by:

Arc Length = (θ/360) * 2πr

Here, θ is the measure of the central angle in degrees, and r is the radius of the circle. The factor (θ/360) converts the angle to radians before multiplying it by the circumference (2πr) of the whole circle.

For example, let’s say you have a circle with a radius of 5 units and a central angle of 60 degrees. To find the length of the arc, substitute the values into the formula:

Arc Length = (60/360) * 2π(5)
Arc Length = (1/6) * 2π(5)
Arc Length = (1/6) * 10π
Arc Length = 10π/6
Arc Length ≈ 5.24 units (rounded to two decimal places)

So, the length of the arc in this example is approximately 5.24 units.

Remember, it’s important to convert the central angle to radians by multiplying by π/180 if the angle is given in degrees before using the formula.

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