how to find central angle

Central Angle
Calculator Calculates
Arc Length, Radius,
Central Angle
and it calculates sector area Scroll down for instructions and sample problems.

You will find these 2 graphics helpful when using this calculator, working with central angles, calculating arc lengths, etc.

This calculator utilizes these equations:

arc length = [radius • central angle (radians)]

arc length = circumference • [central angle (degrees) ÷ 360]
where circumference = [2 • π • radius]

Knowing two of these three variables, you can calculate the third. Even easier, this calculator can solve it for you.

Do you want to solve for
I N S T R U C T I O N S Start by clicking "Arc Length", "Radius" or "Central Angle".
Enter the 2 lines of data.
Click "CALCULATE" and you have your answer.
Clicking "RESET" clears all of the boxes. Example Problems 1) A circle has a radius of 7 and a central angle of 2 radians. What is the arc length?
Click the "Arc Length" button, input radius 7 and central angle =2.
Click "CALCULATE" and your answer is 14.
This calculator also accepts input in degrees as well as radians.
For this problem let's try some new data.
1b) Radius = 3.6 central angle 63.8 degrees. Arc Length equals?
Click the "Arc Length" button, input radius 3.6 then click the "DEGREES" button. Enter central angle =63.8 then click "CALCULATE" and your answer is Arc Length = 4.0087.

2) A circle has an arc length of 5.9 and a central angle of 1.67 radians. What is the radius?
Click the "Radius" button, input arc length 5.9 and central angle 1.67.
Click "CALCULATE" and your answer is radius = 3.5329.

Let's try inputting degrees again. 2b) A circle's arc length is 4.9 with a central angle of 123 degrees. What is the radius?
Click the "Radius" button, enter arc length = 4.9 then click the "DEGREES" button. Enter central angle =123 then click "CALCULATE" and your answer is Radius = 2.2825.

3) An angle has an arc length of 2 and a radius of 2. What is the central angle?
Click the "Central Angle" button, input arc length =2 and radius =2.
Click "CALCULATE" and your answer is 1 Radian and 57.296 degrees.