For any circle:
If the θ is in radians
Arc Length = θ × r
If the θ is in degrees
Arc Length = 2 π r × (θ / 360°)
The length of an arc relies on two things; the radius of a circle and the central angle denoted with 'θ' theta. We know that we can calculate angles in degrees and radians, so 360 degrees is always equal to 2π radians. The arc length of 360 degrees and 2π radians is similar to its circumference. Therefore, as the proportion between angle and arc length is constant, we can conclude that:
L / θ = C / 2 π
As for circumference C = 2 π r, now substituting the value of C in the above equation
L / θ = 2 π r / 2 π
L / θ = r
We find out the arc length formula in radians when multiplying this equation by θ:
L = r * θ
Therefore, the arc length (in radians) is equal to the product of radius and the central angle.
Example Question Using the Formula for Arc Length
Question: Calculate the length of an arc if the radius of an arc is 4 cm and the central angle is 60°.
Data:
Radius of an arc = r = 4 cm
Central angle = θ = 60°
Length of an arc = L = ?
Solution:
As we already know, the formula for the length of arc when the central angle is given in degrees;
Arc length = 2 π r × (θ/360°)
Arc length = 2 × π × 4 × (60°/360°)
Arc length = 4.189 cm
How you can figure out the Area of a sector of a circle?
Similarly, we can figure out the area of a circle's sector. The area of any circle is equal to π r². Therefore,
A / θ = πr² / 2π
A / θ = r² / 2
The formula for the area of a sector will be:
A = r² * θ / 2
Example Question Using the Formula for Area of a sector of a circle
Question: What is the Area of the circle's sector if the circle radius is 7 millimetres and the angle of the sector is 40 radians?
Data:
Radius of a circle = r = 7 mm
Central angle = θ = 40 rad
Area of the sector = A = ?
Solution:
As we already know, the formula for the Area of a sector:
Area of sector = r² * θ / 2
Area of sector = 7² * 40 / 2
Area of sector = 49 * 40 / 2
Area of sector = 980 mm²
How to calculate the Chord of a Circle?
The chord of a circle can be defined as a line segment joining two points on the circle's circumference. The diameter is the most extended chord of the circle that passes through the circle's center.
There are two basic formulas for finding the length of the chord of a circle are as follows:

Chord Length Using Perpendicular Distance from the Centre of the circle:
Chord length = 2 square root r²d²

Chord Length Using Trigonometry with angle θ:
Chord length = 2 × r × sin (θ/2)
Example Question Using the Formula for Chord of a circle
Question: Calculate the length of the chord where the radius of the circle is 7 mm, and the perpendicular distance drawn from the center of the circle to its chord is 4 mm.
Data:
Radius of a circle = r = 7 mm
Perpendicular distance = d = 4 mm
Chord length = c = ?
Solution:
As we already know, the formula for the chord length.
Chord length = 2 square root r²d²
Chord length = 2 square root 7²4²
Chord Length = 2 square root 33
Chord Length = 11.488 mm
Which tool is best for calculating the Arc length of a circle?
Tools City’s Arc Length calculator is one of the best tools you will see all over the internet. It calculates not only the arc length of a circle but also measures the chord length, sector area, and much more. You can use many different units in Tools City’s Arc Length calculator as it provides a variety of units used in daily life, i.e, metre, centimetre, kilometres, etc.
How to use Tools City’s Arc Length calculator?
Tools City's Arc Length calculator is very easy to use; you must know the values of a few parameters. If you want to calculate Arc length, you must be aware of the radius 'r' and central angle 'θ'. Following are the few steps to use Arc Length calculator.

Log on to the Tools City's Arc Length calculator.

You will see a picture and six different boxes for different values. The first box is for central angle, the second box for radius, the third for diametre, the fourth for sector area, the fifth for chord length, and the final for Arc Length.

You will now put the values for the parameters you know. For example, you put 1 mm in the radius box and 45 degrees in the central angle box. You will come up with all those remaining boxes as its results.