CM to Degrees Calculator

Convert arc length in centimeters to degrees using circle geometry. Perfect for engineers, architects, students, and designers.

Geometry Calculator:

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

Angle Result

--
degrees

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:

Step 1: Calculate Angle in Radians
θ = Arc Length ÷ Radius
Step 2: Convert to Degrees
Degrees = θ × (180 ÷ π)
Combined Formula
Degrees = (Arc Length ÷ Radius) × (180 ÷ π)
π ≈ 3.14159
Example: Arc Length = 10 cm, Radius = 5 cm
θ = 10 ÷ 5 = 2 radians
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°
Why This Conversion Matters:

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.