The Cm to Degrees Calculator is a versatile tool that helps users convert arc lengths measured in centimeters into the corresponding angle in degrees. This conversion is particularly useful in fields like geometry, physics, and engineering, where precise angle measurements are critical. By inputting the arc length and knowing the circle's radius or circumference, users can quickly and accurately find the angle subtended by the arc at the circle's center.
This calculator eliminates the need for complex manual computations, ensuring accuracy and saving time for professionals and students alike.
Formula of Cm To Degrees Calculator
The formula for converting arc length to degrees is:
Angle (in degrees) = (Arc Length / Circumference) * 360
Breakdown of the Formula:
- Arc Length: This is the portion of the circle's perimeter corresponding to the given angle.
- Circumference: This is the total distance around the circle, calculated as:
Circumference = 2 * π * Radius - 360: The total number of degrees in a circle.
Note: To apply this formula, you must know either the radius of the circle or its circumference.
Reference Table
Below is a table of common arc lengths, radii, and their corresponding angles.
| Arc Length (cm) | Radius (cm) | Circumference (cm) | Angle (degrees) |
|---|---|---|---|
| 5 | 10 | 62.83 | 28.65 |
| 10 | 10 | 62.83 | 57.30 |
| 15 | 10 | 62.83 | 85.95 |
| 20 | 10 | 62.83 | 114.60 |
| 30 | 15 | 94.25 | 114.60 |
| 50 | 20 | 125.66 | 143.24 |
This table provides quick insights without the need to calculate each time.
Example of Cm To Degrees Calculator
Problem:
Find the angle in degrees if the arc length is 12 cm, and the circle's radius is 8 cm.
Solution:
- Calculate the circumference:
Circumference = 2 * π * Radius = 2 * 3.1416 * 8 = 50.27 cm - Use the formula:
Angle (in degrees) = (Arc Length / Circumference) * 360Substituting values:
Angle = (12 / 50.27) * 360 = 85.94 degrees
Answer:
The angle subtended by the arc is approximately 85.94°.
Most Common FAQs
No, this calculator is specifically designed for perfect circles. For non-circular shapes, different geometric principles apply.
You can calculate the radius by dividing the diameter by 2. Use this radius to find the circumference and proceed with the formula.
This calculator provides results in degrees. If you need radians, multiply the degree value by π/180.