About Arc Length
The distance along a portion of the circumference of any circle or curve is best characterised as arc length (arc). The arc length is any distance along the curved line that makes up the arc. Arc refers to a portion of a curve or the circumference of a circle. Their shapes all have a curvature to them. An arc's length is greater than any straight line distance between its ends (a chord).
What is Arc Length?
The interspace between two locations along a portion of a curve is defined as the arc length. Any section of a circle's circumference is considered an arc. An arc's subtended angle at any location is the angle generated by the two line segments connecting that point to the arc's endpoints. OP, for example, is the arc of the circle with centre Q in the diagram below. L denotes the arc length of this arc OP.
Arc Length Formula
Different formulas can be used to compute the length of an arc based on the unit of the arc's central angle. The centre angle can be measured in degrees or radians, and the arc length of a circle is calculated appropriately. The arc length formula for a circle is times the radius of a circle.
The arc length formula in radians can be expressed as
arc length = θ × r, when θ is in radians.
Arc Length (L) = θ × (π/180) × r, where θ is in degree, where,
L = Length of an Arc
θ = Central angle of Arc
r = Radius of the circle
Arc Length Formula in Radians
Different formulas can be used to compute the arc length of a circle based on the unit of the arc's centre angle. The arc length formula in radians is as follows:
Arc Length = θ × r
where,
L = Arc Length
θ = Centre angle of the arc in radians
r = Radius of the circle
To get all the Maths formulas, check out the main page.
FAQs for Arc Length Formula
The arc length formula calculates the distance along a curve or circular segment. For a circle, it is given by:
L=rθ
where L is the arc length, r is the radius, and θ is the central angle in radians. This formula is essential in geometry, physics, and engineering applications.
If the central angle θ\thetaθ is in degrees, use the formula:
L=πrθ/180. This conversion helps in practical problems where angles are given in degrees instead of radians.
The arc length formula is widely used in architecture, road construction, satellite dish designs, and physics to measure curved distances, design circular structures, and calculate trajectories.