Arc Length Calculator
Convert between angle and arc length using radius. Bidirectional arc length calculator for machining, construction, and engineering applications.
Essential for machinists, engineers, and construction professionals. Converts rotational angles to linear distances using arc length formulas.
Arc Length Calculator
Calculation Results
Enter values and click Calculate for arc length conversion
Arc Length Calculator
Angles and distances describe different kinds of measurement. Degrees tell you how far something rotates, while inches describe how far it moves in a straight line. An **Arc Length Calculator** bridges this gap by converting rotational movement into linear distance using a known radius or diameter.
Formula Used in the Calculator
The calculator uses the arc length formula:
Example Conversion Table
Here are examples of angle to distance conversions using different radii:
| Degrees | Radius (in) | Arc Length (in) | Application |
|---|---|---|---|
| 30° | 5 | 2.62 | Small gear rotation |
| 45° | 10 | 7.85 | Large pulley turn |
| 90° | 4 | 6.28 | Quarter circle arc |
| 120° | 6 | 12.57 | Third circle arc |
| 180° | 8 | 25.13 | Semicircle distance |
| 270° | 3 | 14.14 | Three-quarter circle |
| 360° | 12 | 75.40 | Full circle circumference |
| 15° | 3 | 0.79 | Small angle rotation |
| 25° | 8 | 3.49 | Camshaft timing |
| 35° | 6 | 3.67 | Valve opening |
| 50° | 12 | 10.47 | Large gear segment |
| 65° | 7 | 8.01 | Pulley wrap angle |
| 75° | 9 | 11.78 | Quarter circle plus |
| 85° | 2 | 2.97 | Small radius arc |
| 95° | 15 | 24.87 | Large radius segment |
| 105° | 5 | 9.16 | Fan blade sweep |
| 115° | 11 | 21.85 | Propeller section |
| 125° | 4 | 8.72 | Crankshaft throw |
| 135° | 13 | 30.63 | Three-quarter circle |
| 145° | 3.5 | 8.84 | Blade angle |
| 155° | 14 | 37.68 | Almost full semicircle |
| 165° | 2.5 | 7.22 | Small diameter arc |
| 175° | 16 | 48.69 | Near full circle |
| 185° | 1.8 | 5.83 | Very small radius |
| 195° | 17 | 58.08 | Over semicircle |
| 205° | 4.2 | 15.07 | Extended arc |
| 215° | 18 | 67.54 | Two-thirds circle |
| 225° | 3.8 | 14.84 | Five-eighths circle |
The table above demonstrates how arc length increases with both angle and radius. A 90° turn of a 4-inch radius wheel covers 6.28 inches, while the same angle on a 12-inch radius would cover 18.84 inches.
By combining clear inputs with accurate formulas, the Arc Length Calculator makes rotational measurements easier to understand and apply in practical engineering situations.
For precise measurements, always measure the actual radius or diameter of your rotating component. Manufacturing tolerances can affect final dimensions.