Length of an arc of circumference

Sometimes, instead of knowing the total length of a circumference, we need to know only a part of it, that is, the length of an arc of circumference. To determine it, we use the following formula:

s = r ∙ θ

Where r is the radius and θ the angle in radians.

Formula

bow lengthThe length of the arc (s) in a circumference, knowing the radius (r) and the angle (θ) that the two radii form, is:

s = r ∙ θ

With the angle in radians.

Example: find the length of the arc of a circle with radius r = 10 cm and central angle θ = 3.5 rad.

Applying the formula, we have:

s = r ∙ θ = (10 cm) (3.5 rad) = 35 cm

s = 35 cm

When the angle is in degrees

Considering that an angle of 360 ° is equivalent to 2π radians, then the length of an arc of circumference, when the angle is in degrees is:

s = (2 ∙ π ∙ r ∙ θ) / (360 °)

Example: Find the length of the arc of a circle with radius r = 20 cm and central angle θ = 60 °.

Applying the formula, we have:

s = (2 ∙ π ∙ r ∙ θ) / (360 °) = [2π (20 cm) (60 °)] / 360 = 7539.82 cm / 360

s = 20.94 cm