Radius of Circle Calculator Using Degrees and

This calculator helps you determine the radius of a circle when you know the central angle in degrees and the arc length. Understanding how to calculate the radius from degrees and arc length is essential in geometry, engineering, and various scientific applications.

How to Use This Calculator

Using the radius of circle calculator is straightforward. Follow these steps:

Enter the central angle in degrees in the first input field.
Enter the arc length in the second input field.
Click the "Calculate" button to compute the radius.
The result will appear in the result panel below the calculator.

The calculator will display the radius in the same units as the arc length you entered. If you need the radius in a different unit, you can convert it manually using the conversion factor.

The Formula Explained

The relationship between the radius (r), central angle (θ), and arc length (L) is given by the formula:

L = r × θ

Where:

L is the arc length
r is the radius of the circle
θ is the central angle in radians

Since the calculator accepts the central angle in degrees, we first convert degrees to radians using the conversion factor π/180. The formula becomes:

L = r × (θ × π/180)

To solve for the radius (r), we rearrange the formula:

r = L / (θ × π/180)

This is the formula implemented in the calculator. The calculator uses this formula to compute the radius when you provide the central angle in degrees and the arc length.

Worked Examples

Let's look at a couple of examples to understand how the calculator works.

Example 1

Suppose you have a circle with a central angle of 60 degrees and an arc length of 10 units. To find the radius:

Convert 60 degrees to radians: 60 × π/180 ≈ 1.047 radians
Use the formula: r = 10 / 1.047 ≈ 9.55 units

The radius is approximately 9.55 units.

Example 2

Consider a circle with a central angle of 90 degrees and an arc length of 5 units. To find the radius:

Convert 90 degrees to radians: 90 × π/180 ≈ 1.571 radians
Use the formula: r = 5 / 1.571 ≈ 3.18 units

The radius is approximately 3.18 units.

These examples demonstrate how the calculator applies the formula to compute the radius from the given central angle in degrees and arc length.

Frequently Asked Questions

What is the difference between central angle and inscribed angle?: A central angle is an angle whose vertex is at the center of the circle and whose sides (rays) extend to the circumference. An inscribed angle is an angle whose vertex lies on the circle and whose sides are chords of the circle.
How do I convert degrees to radians?: To convert degrees to radians, multiply the degree measure by π/180. For example, 90 degrees is equal to 90 × π/180 ≈ 1.5708 radians.
Can I use this calculator for any unit of measurement?: Yes, the calculator accepts any unit of measurement for the arc length. The result will be in the same units as the arc length you entered.
What if I enter a negative value for the central angle or arc length?: The calculator will display an error message if you enter a negative value. Please ensure that both the central angle and arc length are positive numbers.