Arc Length Degrees Calculator
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Reviewed by Calculator Editorial Team
Calculate the arc length of a circle when given the angle in degrees. This calculator provides accurate results using the standard arc length formula. Simply enter the radius of the circle and the angle in degrees to find the arc length.
How to Use the Arc Length Degrees Calculator
Using the arc length degrees calculator is straightforward. Follow these simple steps:
- Enter the radius of the circle in the first input field.
- Enter the angle in degrees in the second input field.
- Click the "Calculate" button to compute the arc length.
- View the result displayed below the calculator.
The calculator will show you the arc length in the same units as the radius you entered. For example, if you enter the radius in centimeters, the arc length will also be in centimeters.
Arc Length Formula
The arc length (L) of a circle can be calculated using the following formula:
L = (θ/360) × 2πr
Where:
- L = Arc length
- θ = Central angle in degrees
- r = Radius of the circle
- π ≈ 3.141592653589793
This formula calculates the fraction of the circumference that corresponds to the given angle in degrees. The result is the length of the arc along the circumference of the circle.
Example Calculation
Let's say you have a circle with a radius of 10 units and you want to find the arc length for a 90-degree angle. Here's how you would calculate it:
Example:
Given:
- Radius (r) = 10 units
- Angle (θ) = 90 degrees
Calculation:
L = (90/360) × 2π × 10
L = (0.25) × 20π
L ≈ 15.7079632679 units
So, the arc length is approximately 15.71 units.
You can verify this result using our arc length degrees calculator by entering 10 for the radius and 90 for the angle.
Frequently Asked Questions
What is arc length?
Arc length is the distance along the circumference of a circle between two points. It is a portion of the circle's total circumference.
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 π/2 radians.
What units should I use for the radius?
The arc length will be in the same units as the radius. For example, if you enter the radius in meters, the arc length will be in meters.
Can I use this calculator for partial circles?
Yes, this calculator works for any angle between 0 and 360 degrees. It calculates the arc length for any portion of the circle's circumference.