Length of an Arc Calculator

The length of any curve in a circle formed by the sector is called as the arc length. A portion of the circumference of the circle is the arc. If you cut a pizza into four shapes, the curved edge of one part is the arc. This is an online calculator to find the length of the arc formed in a circle with width and height of the curve.

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The length of any curve in a circle formed by the sector is called as the arc length. A portion of the circumference of the circle is the arc. If you cut a pizza into four shapes, the curved edge of one part is the arc. This is an online calculator to find the length of the arc formed in a circle with width and height of the curve.

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Formula:

Length of Arc Image
r = (h/2) + (w2/(8h)) C = 2 tan-1(w/(2×(r-h))) if(C < 0) C = 360 + C l = C × 2 Π r / 360 Where, r = Radius of Arc h = Height of Arc w = Width of Arc C = Center Angle of Arc l = Length of Arc

Example:

If the height of the arc is 1 m and width is 2 m.

Step 1 : Find the Radius

r = (h/2) + (w2/(8h))

r = (1/2) + (22/(8x1))
= 0.5 + (4/8)
= 0.5 + 0.5
= 1
The radius is 1 m

Step 2 : Find the Center Angle of Arc

C = 2 tan-1(w/(2×(r-h)))
if(C<0)
C = 360 + C

C = 2 tan-1(2/(2 × (1-1)))
= 2 tan-1(2/(2 × 0))
= 2 tan-1(2/0)
= 2 tan-1(∞)
= 2 × 90
C = 180
Round the result, center angle is 180°

Step 3 : Find Length of Arc

l = C × 2 Π r / 360

l = 180 × 2 Π * 1 / 360
= 3.14159
Arc Length is 3.14159 m


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