Find the length of the arc calculator

Arc length is the length of the curved line which makes up the arc. Measuring the length of an arc with a ruler is impossible unless its a straight line. In this situation arc length formula comes very handy to figure out the exact length of the arc.

As shown in the below figure when we know the central angle and radius of the arc we can calculate the arc length of that typical arc.

Find the length of the arc calculator

Formula to calculate arc length is given by:
Find the length of the arc calculator

In our below online arc length calculator, enter the central angle and radius of the arc and click calculate to find the length of an arc for the given circle.
Central Angle (no):[degrees]Radius (r):[cm]Arc Length (L):[cm]
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Find Arc Length Calculator is a free online tool that displays the arc length when the radius and the central angle is given. BYJU’S online find arc length calculator tool makes the calculation faster, and it displays the arc length in a fraction of seconds.

How to Use the Arc Length Calculator?

The procedure to use the arc length calculator is as follows:
Step 1: Enter the radius and central angle in the respective input field
Step 2: Now click the button “Solve” to get the result
Step 3:Finally, the arc length will be displayed in the output field

What is Meant by Arc Length?

In Mathematics, the length of the arc is determined by using the radius and the central angle θ(either in degrees or radians). It is known that when the arc length is equal to the circumference of the circle, the angle is equal to 360° (2π). In this case, the proportion between the central angle and the arc length is constant, and the arc length formula is given as
Arc length, L = r × θ
Similarly, we can find the area of a sector of a circle. From the proportion, the area of a sector is defined by
Area of the sector, A = 1/2r2θ

Disclaimer: This calculator development is in progress some of the inputs might not work, Sorry for the inconvenience.

Solves all twenty one cases when given any two inputs. This calculator calculates for the radius, length, width or chord, height or sagitta, apothem, angle, and area of an arc or circle segment given any two inputs. Please enter any two values and leave the values to be calculated blank. There could be more than one solution to a given set of inputs. Please be guided by the angle subtended by the arc. If the angle is greater than 180 degrees then the arc length described is greater than the arc length of a semi-circle (Click here for illustration). More length units have been added. The length unit choices are feet (ft), inch (in), meter (m), centimeter (cm), millimeter (mm), yard (yd), kilometer (km), mile (mile). The angle unit choices are degree (deg), radian (rad).

Find the length of the arc 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

Find the length of the 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.

Find the length of the arc calculator

Arc Length Formula:

Arc length formula can be understood by following image:

Find the length of the arc calculator

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:

How do you find the length of an arc?

How to Find Arc Length With the Radius and Central Angle? The arc length of a circle can be calculated with the radius and central angle using the arc length formula, Length of an Arc = θ × r, where θ is in radian. Length of an Arc = θ × (π/180) × r, where θ is in degree.