Central Angle Calculator

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Central Angle Calculator

Central angle calculator is a simple and powerful geometry web tool which helps you to calculate the central angle of a circle within a fraction of a second.

You just have to enter the arc length and radius of the circle in the input field, then you click on the ‘Calculate’ button. This program calculates and displays the central angle in degrees.

What is a Central Angle?

The angle between the two radii of a circle is called the central angle of the circle. The two points of the circle where the radii meet each other form a segment of the circle called the arc length.

In layman’s terms, the angle of rotation the radius needs to move to produce to given arc length is the central angle.

How to Calculate the Central Angle?

There is a mathematical formula to calculate the central angle of a circle:

Central Angle = Arc Length / Radius

Using the above formula give us the central angle in radians, now to convert the central angle in degrees, we need to multiply the radians by 180/π. This will give us the central angle in degrees.

Central Angle (θ) = radians X 180/π

Example: Find the central angle of a circle if the arc length is 12 cm and the radius is 4 cm.

We have, Arc Length = 12 cm and Radius of the circle = 4 cm

Using the mathematical formula, we get:

Central Angle = Arc Length / Radius = 12/4 = 3

This central angle we got is in radians, we need to convert it into degrees by multiplying the radians by 180/π.

Central Angle (θ) = 3 x 180/π = 171.97°.

Therefore, the central angle of the circle is 171.97°.

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