Arc Length Calculator

An online arc length calculator helps to find the arc length, central angle, radius, diameter, sector area, segment height, and chord length of the circle. When it comes to figure out arc length of a circle, this arc calculator tells us the value of arc length along with other respective measurements just according to the selected field.

What is Arc Length?

Length of an arc can be defined as a total distance that exists between two points along a section of any curve. Calculation of the length of an irregular arc segment is known as rectification of a curve. The measure of an arc can be calculated via both:

• Arc length equation
• Arc calculator

Arc and Central Angle:

Apex or vertex of the central angel is the center \( O \) of any circle. Its sides are radii transecting the circle in two discrete points let’s say A and B. Furthermore, it is subtended by an arc between A and B points.

Arc Length Formula:

Arc length formula can be understood by following image:

If the angle is equal to \( 360 \) degrees or \( 2π \), then the arc length will be equal to circumference. Furthermore, the proportion between angle and arc length remains constant, so the arc length equation will be:

• \(L / θ = C / 2π\)
• In the formula for arc length the circumference \(C = 2πr\)
• \(L / θ = 2πr / 2π\)
• After division there will be only: \(L / θ = r\)
• To calculate arc length formula, you have to multiply this equation by \(θ: L = r * θ\)

In radians:

• To find arch length with radius the formula will be: \(s = ϴ × r\).

In degrees:

• To find arch length degrees the formula will be:\( s = 2 π r (θ/360°)\).

How to Find Length of an arc (Solved Examples)?

Finding arc length is not a tricky method anymore as you can use length of arc calculator for quick calculations. Also, length of arc formula is best, but time consuming way to determine the arc length. Look the given examples for better understanding:

Example:

If radius of a given circle is \(50 cm \) and its central angel is \(π/4 \) then what will be the area of arc?

• As there are two measures are given; radius and central angel. So we will apply formula to find arc length in radians:\( s = ϴ × r\). just put the values in it.
• \( S = 50 * π/4 = 25π/2cm = 39cm\).

How does Arc Length Calculator work?

This online arc calculator offers a very simple interface through which you can readily determine the arc length and different related parameters. Steps are:

Input:

The calculator helps you to calculate arc length by:
1. Central angel and radius
2. Radius and segment height
3. Radius and sector area
4. Radius and chord length
5. Central angel and diameter
6. Central angel and sector area
7. Central angel and chord length
8. Chord length and segment height

• Select the one option from above others in the drop down menu.
• On the basis of selected option just fill in the given fields and select the unit of measurement.
• Hit the calculate button.

Output:

This arch length calculator will display:
• Arc length
• Different other values that depends on the selected option

References:

From the source of Wikipedia: Arc length, it’s general approach, smooth curve and a lots more

Explore the source of khanacademy: length of an arc (practices)