MM to Degree Calculator
Convert linear movement in millimeters to angular rotation in degrees using radius or diameter. Essential calculator for CNC machining, mechanical engineering, and rotary motion design.
Convert between linear and angular measurements with geometric precision. Perfect for CNC programming, robotics, and mechanical linkage calculations.
Linear to Angular Converter
Linear distance or angular measurement
Radius or diameter of rotation
Angular Results
Enter distance and geometry
Convert Linear Motion Into Angular Rotation
Millimeters measure straight-line distance, while degrees measure rotation. A MM to Degree Calculator connects these two by using geometry, allowing you to convert linear movement into angular motion accurately.
This type of calculation is common in mechanical design, CNC machining, rotary systems, and engineering education.
Why MM Cannot Directly Convert to Degrees
Degrees describe rotation around a circle, not distance. To convert millimeters into degrees, you must know the radius of rotation. The same linear movement produces different angles depending on how large the circle is.
- 10 mm on a 50 mm radius circle = 11.46°
- 10 mm on a 100 mm radius circle = 5.73°
- Same distance, different angle due to circle size
Formula Used
The calculator is based on standard circular geometry:
Combined formula:
For reverse calculation:
Practical Conversion Examples
Here are common linear-to-angular conversions for different radii:
| Radius (mm) | Linear Travel (mm) | Degrees (°) | Application |
|---|---|---|---|
| 25 | 5 | 11.46° | Small rotary actuator |
| 25 | 10 | 22.92° | Quarter turn valve |
| 50 | 10 | 11.46° | Medium gear system |
| 50 | 25 | 28.65° | Robotic joint |
| 75 | 15 | 11.46° | Large pulley system |
| 100 | 10 | 5.73° | Precision positioning |
| 100 | 50 | 28.65° | CNC rotary table |
| 150 | 30 | 11.46° | Industrial conveyor |
| 200 | 20 | 5.73° | Large diameter wheel |
| 200 | 100 | 28.65° | Heavy machinery linkage |
| 10 | 3 | 34.38° | Small precision mechanism |
| 5 | 2 | 45.84° | Micro actuator |
| 300 | 60 | 11.46° | Large radius curve |
| 500 | 50 | 5.73° | Very large radius |
| 1 | 0.5 | 90.00° | Microscopic rotation |
| 1000 | 100 | 5.73° | Railway curve |
| 50 | 50 | 57.30° | Half circle arc |
| 25 | 15.7 | 36.00° | Quarter circle |
| 100 | 314.16 | 180.00° | Semicircle |
| 75 | 235.62 | 180.00° | Half circumference |
| 40 | 25.13 | 36.00° | 10% of circumference |
Always specify whether you're using radius or diameter in your calculations. This calculator automatically handles both, but manual calculations can go wrong if you're not clear about your geometry.