Online Calculators > Math Calculators > Arc Length Calculator

# Arc Length Calculator

Arc length calculator calculates the length of an arc by knowing its radius or diameter, area, or central angle.

## Arc Length Calculator

Angle
Arc Length
 Radius or     Diameter Area Arc Length
 Angle Degree Radian Area Arc Length

## Arc Length Formula

By knowing the radius and angle for an acr, the arc length formula is

L = 2πr(θ/360°)
where
r = radius of the circle.
θ = degrees.

Or

L = θr

The arc length formula is derived from the perimeter of the circle.
As we know, the perimeter of the circle is:
p = 2πr

Consider an arc as a sector of a circle and one circle is 360 degrees, to calculate this sector of a circle, we divide the sector's degree by 360 which is θ/360.

Therefore, we get the formula:
L = 2πr(θ/360°)

If the central angle θ is in radians, we need to replace degrees with radians.
Degrees = Radians x 180 /π

With the replacement of degrees, we will get:
L = 2πr(Radians x 180 /π /360°)

Simplify it:
L = θr

More Arc Length Formula

There are more derived formulas for arc length.

L = A / r x 2.
where A = area of the arc.
r = radius of the arc.

L=θ √A x 2 / θ
where A = area of the arc
θ = the central angle in radians.

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