How to Calculate Arc Length

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These central angles are expressed in the forms of radians or degrees. Example 1 Determine the length of y lnsecx y ln sec x between 0 x π 4 0 x π 4.


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Rounded to 3 significant figures the arc length is 628cm.

. A full 360 degree angle has an associated arc length equal to the circumference C. But if the angle is measured in degrees then multiply the angle with π180. Arc Length Formula which is in Integral Form s ba1 dydx2dxab1 dydx2dx.

The arc length of a circle is calculated by the product of θ times of the radius of the circle. In this way C 2π r where r is the circles radius and Ø is in radian equals 360 because one radius equals 180 degrees. Mathematically the formula is written as.

The formula to calculate the arc length is. Arc length θ r. You can work out the length of an arc by calculating what fraction the angle is of the 360 degrees for a full circle.

L r θ. Example 2 Determine the length of x 2 3y13 2 x 2 3 y 1 3 2 between 1 y 4 1 y 4. So 360 degrees corresponds to an arc length C 2πR.

R is the radius of the circle. The arc length is frac14 times pi times 8 2 pi. So the angle made by an arc with length C at the centre will be θ 360 2 π r L.

Divide by 360 to find the arc length for one degree. The arc length for the function of y is given below. The length of circumference is L 2 π r.

The central angle θ in radians. S a b 1 d y d x 2 d x. Which is the formula to find the arc length of an arc.

A r c l e n g t h c d 1 g y 2 d y. According to this formula arc length of a circle is equals to. Radius of the circle θ.

L r θ π180. L θ 180 π r. Where g y is the continuous function of y over the interval cd and g y is the derivative of the function with respect to y.

Arc Length Formula Integral Form. Learn how to find the arc length in a circle using radian angle measures in this free math video tutorial by Marios Math Tutoring026 Formula for Finding A. L Ø C 2π.

How to Find the Length of an Arc. Central angle of a circle. This formula is applicable when the central angle is given in radians.

TextArc length frac. This is the simplified formula of arc length. The arc length equals the perimeter of a circle ie circumference.

The major difference between arc length and sector area is that an arc is a part of a curve whereas A sector is part of a circle that is enclosed between two radii. Arc Length Formula when θ is in degrees then s 2 π r θ360 Arc Length Formula when θ is in radius then s ϴ X r. θ 180 π r L.

Arc length of the circle r. Arc length θ π180 r. Now that weve derived the arc length formula lets work some examples.

Square root of 2 times the area A that is divided by θ. Where θ is the angle expressed in radian.


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