Arc Length Calculator

Use this free arc length calculator with pi to calculate the arc length of a circle. Not only this, but you can also calculate other related parameters such as radius, diameter, segment height, sector area, chord length, and central angle of a circle by using the length of arc calculator. 

What Is Arc Length?

In geometry:

“The distance among two points along the section of a curve is called its arc length”

Arc Length Formula:

Our exact arc length calculator in terms of pi uses the below formula for getting arc length of a circle:

In Radians:

L = r * θ

where:

r = radius of the circle 

Θ = central angle of the arc (radians)

In Degrees:

where:

C = central angle of the arc (degree)

R = is the radius of the circle

π = is Pi, which is approximately 3.142

360° = Full angle

With the implementation of the above Arc Length Formula, length of arc calculator solves the central angle, radius or arc length easily. Try Circumference Calculator for your practice regarding circumference.

How To Calculate Arc Length In Terms of Pi?

Consider we have a circle having a central angle as \(θ=51^{text{o}}\) and radius as \(r=2.5cm\). How to determine its arc length?

Solution:

As we know that 

s =2r*(C/360 degrees)

where:

C = central angle of the arc (degree)

R = is the radius of the circle

π = is Pi, which is approximately 3.142

360° = Full angle

With the implementation of the above Arc Length Formula, the length of arc calculator solves the central angle, radius, or arc length easily. Try Circumference Calculator for your practice regarding circumference.

How to Use Arc Length Calculator Calculus?

To use our length of curve calculator, you need to set certain inputs and enter their values to calculate results:

Input:

• Select the parameters on the basis of which you want to calculate outputs
• Once selected, enter the values of the parameters in their respective fields 
• Select the units for each entered parameters
• Tap Calculate

Output:

• Arc length
• Area of a sector 
• Chord length
• Segment height
• Diameter and radius
• Central angle

Faqs

How to Find Curve Length?

The length of a curve or line is curve length. The length of an arc can be found by following the formula for any differentiable curve.

$$ s=\int_{a}^{b}\sqrt{1+\frac{dy}{dx}^{2}, dx} $$

These curves are defined by rectangular, polar, or parametric equations. And the exact arc length calculator integral employs the same equation to calculate the length of the arc using the integral notation.

Does Arc Length Have To Be In Radians?

The arc length is basically the distance and that is why, it cannot be represented in terms of radians. Conversion of angle in radians just makes the calculations easy. But it cannot be the final unit to define this geometrical parameter.

References:

From the source Wikipedia: Arc length, Finding arc lengths by integration, Arcs of circles, Curves with infinite length