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Arc Length Calculator

Arc Length Calculator

Calculate by:

Central angle (θ)

 

Radius (r)

 

Diameter

 

Sector area (A)

 

Chord length (c)

 

Segment Height (h)

 

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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.
You give a try to this arc calculator to determine the arc length. Well, read the given context to understand how to calculate arc length via this tool and by using an arc length formula. But, let’s begin with some basics!

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 Length 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 Calculator Central Angle

The length of the curve calculator can be a great help while calculating arc lengths that utilizing central angel and radius.

Arc Length Formula:

Arc length formula can be understood by following image:

Arc Length Formula

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:\( s = 2 π r (θ/360°)\).

So, when it comes to circumference calculations, then an online circumference calculator is the best way to find the circumference, radius, and, other relevant values of a circle.

How to find length of an arc (Solved Examples)?

Finding arc length is not a tricky method anymore as you can use 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.
• \( S = 50 * π/4 = 25π/2cm = 39cm\).

However, an online unit circle calculator enables you to figure out trigonometric (sin, cos, tan) values for an angle through which you can readily figure out the coordinates on the unit circle.

Example:

If \(∠ACB\) have a measurement of measured as \(36°\) and given r is \(30cm\) then what will be the arc length?

• We apply formula to find arc length in degrees:\( s = 2 π r (θ/360°)\).
• Plug in the values: \( 2 * π * r = 36° /360°)\).
• \( Π = 3.14 \).
• On simplification: \(s = 18 cm\).
However, the arc length calculator also uses these formulas to find length of an arc.

How to find the area of the sector?

The area of a sector is that region that is enclosed by the two radii of a circle and the arc. Its calculation depends on the following two factors:

• You have to know The total length of radius of circle.
• The measure of the central angle should be known.

Area of a Sector

Formula:

There are three formulas to find area of the sector. You have to select one according to the measurements you have.

  • \( (θ/360) πr2\)
  • \( (θr2)/2\)
  • \( rL/2\)

Example

If angel is \(130\) and radius is \( 28\) then what will be the sector area?

  • As we given \( θ \)and\( r\) so we will apply “\( θ/360) πr2\)”.
  • Put values in the above formula: \((130/360) x 3.14 x 28 x 28 = 888 cm2 \).

How to calculate arc length by using sector area & central angle?

There is an alternative arc length formula that defines how to find it if the sector area and central angle are identified.

Length of arc formula = \( θ × \sqrt {2A ÷ θ} \)

According to this formula arc length of a circle is equals to:

  • The central angle \(θ \)in radians.
  • Square root of \(2 \)times the area \(A\) that is divided by\( θ\).

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. However, they both can be calculated by using an arc length calculator.

How to Find Chord Length?

Every sector is divided into two things:

  • A triangle
  • Outer segment

The line that makes this division is known as the chord. It is represented as a line that connects the points where the radii connect with the arc.  Chord length of a circle can be calculated using the following formula:

chord \( (a) = 2r × sin (1 / 2 * θ) \).

Chord Length

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. It is one step solution to find arc length. All you have to do is to enter the values in this calculator and it will do the rest to give you arc length, 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

FAQ’s:

What is the perimeter of an arc?

It is the distance that exists all around the outside of a shape. You can find it using the values you know. There will be a sector is formed between two radii and an arc. If you want to find the perimeter, add these values together as Perimeter = \( length of arc + 2r\).

How does Arc Length affect circumference?

In a circle, arc length is a portion of its circumference. For example, an arc that has a measure of \( 60º\) is one-sixth of the circle\( 360º \), so if we want to find the length of arc then it will be one-sixth of the circumference of the circle. However, application of arc area formula is the convenient way when it comes to find the length of an arc.

What is the Length of the intercepted Arc?

\( 360°\) is the total angel of the circle and the length of the intercepted arc is equal to the circumference. Hence, the radian of this central angle is the circumference of the circle that is divided by the circle’s radius whereas the circumference of a circle of a radius is \( 2\). Arc length calculator caters all these parameters simultaneously with ease.

What do you call the longest chord?

A chord that is passing through the center of a circle is known as a diameter and it is the longest chord as well.

End-Note:

This arc length calculator is a tool that is functioned to find length of an arc and the area of a circle sector along with all the related parameters. “How to find the measure of an arc” is not a problem anymore as it serves as a complete tool to make such calculation. Hence, it is great platform for students and professors to make easy and quick calculations for arc length & related terms.

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)

Get authorized information from mathbitsnotebook: Length of an arc and Radian Measure.