Calculator Degrees to Meters
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Reviewed by Calculator Editorial Team
This calculator converts an angle in degrees to the length of an arc in meters. It's useful for geometry, engineering, and navigation applications where you need to calculate the distance along a curve based on an angle.
How to Use This Calculator
To convert degrees to meters using this calculator:
- Enter the angle in degrees in the first input field
- Enter the radius of the circle in meters in the second input field
- Click the "Calculate" button
- The calculator will display the arc length in meters
The calculator uses the standard formula for arc length calculation. You can also view a visual representation of the calculation with the interactive chart.
Formula Explained
The arc length (L) in meters is calculated using the formula:
Arc Length Formula
L = (θ × π × r) / 180
Where:
- L = Arc length in meters
- θ = Angle in degrees
- π = Pi (approximately 3.14159)
- r = Radius in meters
This formula converts the angle from degrees to radians (by dividing by 180) and then multiplies by the radius to get the arc length. The result is in meters if the radius is in meters.
Worked Examples
Example 1: Small Angle
If you have a 30-degree angle and a radius of 5 meters:
Calculation
L = (30 × π × 5) / 180
L = (150π) / 180
L ≈ 2.61799 meters
Example 2: Large Angle
If you have a 90-degree angle and a radius of 10 meters:
Calculation
L = (90 × π × 10) / 180
L = (900π) / 180
L ≈ 15.70796 meters
Example 3: Full Circle
If you have a 360-degree angle and a radius of 1 meter:
Calculation
L = (360 × π × 1) / 180
L = 360π / 180
L ≈ 6.28319 meters (which is the circumference of a circle with radius 1 meter)
Frequently Asked Questions
What is the difference between degrees and radians?
A full circle is 360 degrees or 2π radians. To convert degrees to radians, multiply by π/180. This calculator uses degrees directly in the formula.
Can I use this calculator for partial circles?
Yes, this calculator works for any angle from 0 to 360 degrees. It calculates the arc length for any portion of a circle.
What if I enter a negative angle?
The calculator will use the absolute value of the angle, so negative angles will be treated as positive. This is because arc length is always positive.
Is the result accurate for very small angles?
Yes, the formula works for very small angles. The calculator uses JavaScript's Math.PI for precise calculations.