Degrees to Millimeters Calculator
Our degrees to millimeters (mm) calculator helps transforming angular measurements into linear distances and calculating accurate arc lengths.
0.1° = (0.1 × 2π/360) × 1000 = 1.745 mm
0.2° = (0.2 × 2π/360) × 1000 = 3.491 mm
0.5° = (0.5 × 2π/360) × 1000 = 8.727 mm
Converting Degrees to Millimeters Formula
The conversion formula from degrees to millimeters along an arc is:
Arc Length (mm) = (2 × π × radius × angle) / 360Where:
- π (pi) represents approximately 3.14159
- radius is measured in millimeters
- angle is measured in degrees
Calculating the arc length for a 45-degree angle on a circle with a 100mm radius:
Arc Length = (2 × 3.14159 × 100 × 45) / 360 = 78.54 mmFor a 30-degree angle with a radius of 50mm:
Arc Length = (2 × 3.14159 × 50 × 30) / 360 = 26.18 mmFor a 90-degree angle with a radius of 75mm:
Arc Length = (2 × 3.14159 × 75 × 90) / 360 = 117.81 mmDegrees to MM Conversion Table
| Degrees (°) | Arc Length (mm) |
|---|---|
| 1 | 1.745 |
| 2 | 3.491 |
| 3 | 5.236 |
| 4 | 6.981 |
| 5 | 8.727 |
| 6 | 10.472 |
| 7 | 12.217 |
| 8 | 13.963 |
| 9 | 15.708 |
| 10 | 17.453 |
| 11 | 19.199 |
| 12 | 20.944 |
| 13 | 22.689 |
| 14 | 24.435 |
| 15 | 26.180 |
| 16 | 27.925 |
| 17 | 29.671 |
| 18 | 31.416 |
| 19 | 33.161 |
| 20 | 34.907 |
| 21 | 36.652 |
| 22 | 38.397 |
| 23 | 40.143 |
| 24 | 41.888 |
| 25 | 43.633 |
| 26 | 45.379 |
| 27 | 47.124 |
| 28 | 48.869 |
| 29 | 50.615 |
| 30 | 52.360 |
| 31 | 54.105 |
| 32 | 55.851 |
| 33 | 57.596 |
| 34 | 59.341 |
| 35 | 61.087 |
| 36 | 62.832 |
| 37 | 64.577 |
| 38 | 66.323 |
| 39 | 68.068 |
| 40 | 69.813 |
| 41 | 71.559 |
| 42 | 73.304 |
| 43 | 75.049 |
| 44 | 76.794 |
| 45 | 78.540 |
| 46 | 80.285 |
| 47 | 82.030 |
| 48 | 83.776 |
| 49 | 85.521 |
| 50 | 87.266 |
| 55 | 96.993 |
| 60 | 104.720 |
| 65 | 113.447 |
| 70 | 122.173 |
| 75 | 130.900 |
| 80 | 139.626 |
| 85 | 148.353 |
| 90 | 157.080 |
| 95 | 165.806 |
| 100 | 174.533 |
How to Convert Angle Degree to Millimeters
- Measure the exact radius of your circle in millimeters
- Determine the precise angle measurement in degrees
- Apply the conversion formula: Arc Length (mm) = (2 × π × radius × angle) / 360
- Round the final result to your desired precision level
Converting a 60-degree angle with a 200mm radius:
- Insert values into formula: (2 × 3.14159 × 200 × 60) / 360
- Calculate: 209.44 mm
What is Degrees and Millimeters?
Degrees represent angular measurement, with 360 degrees making a complete circle. This ancient system remains vital in modern applications, from basic geometry to complex navigation. Engineers, architects, and scientists rely on degrees to measure angles, calculate rotations, and design structures. The versatility of degrees makes them essential in fields ranging from astronomy to robotics, where precise measurements are crucial.
Millimeters are metric units of length, with one millimeter equaling 1/1000 of a meter. This precise measurement unit is fundamental in manufacturing, engineering, and medical fields where accuracy is paramount. Industries worldwide use millimeters for precision engineering, component manufacturing, and technical work, making it the standard unit for small-scale measurements in most countries.