👤 By whycalculator Team 📅 Last Updated April 09, 2026
Degree to mm Calculator
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Effortlessly convert angles to linear measurements with this Degree to mm Calculator! Enter the angle and radius, and let the calculator handle the rest. No need to worry about unit conversions – the results are instantly displayed in millimeters with precision.
Whether you're designing, engineering, or just curious, this calculator makes complex calculations simple and quick!
How to convert degrees to mm?
To convert degrees to millimeters (mm), we need to know the radius or distance from the center of the circle. Then use the formula:
S = θ × π/180 × r
Where:
- S = Arc length (in mm)
- θ = Angle (in degrees)
- r = Radius of the circle (in mm)
- π = 3.1416
Example 1: Arc Length for 45 Degrees
- Angle (θ) = 45°
- Radius (r) = 100 mm
S = 45 × π/180 ×100
S = 78.54 mm
Result: The arc length for 45 degrees is 78.54 mm.
Example 2: Arc Length for 90 Degrees
- Angle (θ) = 90°
- Radius (r) = 200 mm
S = 90 × π/180 × 200
S = 314.16 mm
Result: The arc length for 90 degrees is 314.16 mm.
Convert 75 degrees to mm, if the radius is 5 inches:
To convert 75 degrees to millimeters with a radius of 5 inches, follow these steps:
Step 1: Formula for Arc Length
S = θ × π/180 × r
Step 2: Convert Radius to mm
1 inch = 25.4 mm
5 × 25.4 = 127 mm
Step 3: Apply Values to the Formula
- θ = 75°
- r = 127 mm
S = 75 × π/180 × 127
S = 75 × 0.01745 × 127
S = 166.21 mm
Result: The arc length for 75 degrees with a 5-inch radius is 166.21 mm.
This table shows the calculated arc lengths for various angles and radius values:
| Angle (°) | Radius (inches) | Radius (mm) | Arc Length (mm) |
|---|---|---|---|
| 15 | 5 | 127 | 39.27 |
| 30 | 5 | 127 | 78.54 |
| 45 | 5 | 127 | 117.81 |
| 60 | 5 | 127 | 157.08 |
| 75 | 5 | 127 | 196.35 |
| 90 | 5 | 127 | 235.62 |
| 45 | 6 | 152.4 | 141.37 |
| 60 | 6 | 152.4 | 188.82 |
| 75 | 6 | 152.4 | 236.27 |
| 90 | 6 | 152.4 | 283.72 |
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FAQs:
Can this calculator be used for both small and large angles?
Yes, the calculator works for both small and large angles, whether you're working with angles less than 90° or more than 180°. The formula applies universally for any angle, as long as the radius is known.
What is the difference between radians and degrees in this calculation?
Radians and degrees are two different units for measuring angles. The formula used here works for both methods.