CM to Degrees Calculator
Convert arc length in centimeters to degrees using circle geometry. Perfect for engineers, architects, students, and designers.
Converts arc length to angle using: Degrees = (Arc Length ÷ Radius) × (180 ÷ π)
Arc Length to Angle Converter
Length of the arc on the circle
Distance from center to edge
Advanced Settings
Angle Result
Enter arc length and radius
then click "Calculate" for angle
CM to Degrees: How Arc Length Converts to Angle
Centimeters measure distance, while degrees measure angles. To convert cm into degrees, the length must represent an arc on a circle. This conversion is essential in engineering, architecture, and design work.
The Formula Used
The relationship between arc length and angle depends on the radius of the circle:
Degrees = 2 × (180 ÷ 3.1416)
Result: ≈ 114.59°
Arc Length to Degrees Conversion Table
Quick reference for common arc lengths and radii:
| Arc Length (cm) | Radius (cm) | Degrees | Radians |
|---|---|---|---|
| 1 | 5 | 11.46° | 0.20 |
| 3 | 5 | 34.38° | 0.60 |
| 5 | 5 | 57.30° | 1.00 |
| 7 | 5 | 80.21° | 1.40 |
| 10 | 5 | 114.59° | 2.00 |
| 15 | 5 | 171.89° | 3.00 |
| 5 | 10 | 28.65° | 0.50 |
| 10 | 10 | 57.30° | 1.00 |
| 15 | 10 | 85.94° | 1.50 |
| 20 | 10 | 114.59° | 2.00 |
| 25 | 10 | 143.24° | 2.50 |
| 10 | 8 | 71.62° | 1.25 |
| 20 | 8 | 143.24° | 2.50 |
| 15 | 12 | 71.62° | 1.25 |
| 30 | 12 | 143.24° | 2.50 |
| 20 | 15 | 76.39° | 1.33 |
| 40 | 15 | 152.79° | 2.67 |
| 25 | 20 | 71.62° | 1.25 |
| 50 | 20 | 143.24° | 2.50 |
| 31.42 | 10 | 180.00° | π |
| 62.83 | 10 | 360.00° | 2π |
Engineers and designers use arc-to-angle conversion when drafting curves, building circular structures, or designing mechanical components. Without radius information, converting cm to degrees is mathematically impossible — the radius defines how "curved" the arc is.