👤 By whycalculator Team 📅 Last Updated April 09, 2026
Cm to Degree Calculator
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This calculator converts arc length or deflection in centimeters to degrees based on the radius or width. Simply enter the values, choose the desired units, and get accurate results instantly. Perfect for engineering, geometry, and construction applications.
How to Convert Cm to Degree?
To convert centimeters to degrees, first understand how arc length and the circle's radius relate to each other. Then calculate the angle in degrees by finding out what portion of the circle's circumference the arc length covers.
Formula:
θ = (L/2πR) × 360
Where:
- θ = Angle in degrees
- L = Arc length (in cm)
- R = Radius (in cm)
Example 1:
Arc length L = 31.4 cm, Radius R =10 cm
θ = (31.4/2π×10) × 360 = 180°
θ = [31.4/2(3.14)×10] × 360 = 180°
θ = [31.4/6.28×10] × 360 = 180°
θ = (31.4/62.8) × 360 = 180°
θ = 0.5 × 360 = 180°
Example 2:
Arc length L = 15.7 cm, Radius R = 10 cm
θ = (15.7/2π×10) × 360 = 90°
Can Cm be changed into degrees directly?
No, cm cannot be directly converted into degrees because they are different quantities. Centimeters measure length or distance, while degrees measure angles.
However, we can calculate the angle in degrees from a length (such as arc length) if we know the radius of the circle.
To convert arc length to degrees, apply the formula:
θ = (L/2πR) × 360
| Arc Length (cm) | Radius (cm) | Angle (Degrees) |
|---|---|---|
| 5 | 10 | 28.65° |
| 7 | 10 | 40.11° |
| 10 | 15 | 38.20° |
| 12 | 15 | 45.84° |
| 15 | 20 | 42.92° |
| 18 | 25 | 41.31° |
| 20 | 30 | 38.20° |
| 25 | 30 | 47.75° |
| 30 | 40 | 42.92° |
| 35 | 45 | 44.49° |
| 40 | 50 | 45.84° |
| 45 | 55 | 46.90° |
| 50 | 60 | 47.75° |
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FAQs:
Why do I need the radius to convert cm to degrees?
The radius is essential because the angle formed by an arc depends on the circle's size. Larger circles need longer arcs to create the same angle. That's why the radius is a crucial part of the calculation.