Degrees to Inches Calculator

Convert degrees to inches using radius. Bidirectional arc length calculator for machining, construction, and engineering applications.

Technical Calculator:

Essential for machinists, engineers, and construction professionals. Converts rotational angles to linear distances using arc length formulas.

Arc Length Calculator

Calculation Mode
degrees

Calculation Results

Enter values and click Calculate for arc length conversion

Degrees to Inches 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. A **Degrees to Inches 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:

For Degrees to Inches (Angle → Distance):
Radians = Degrees × (π ÷ 180)
Arc Length (inches) = Radius × Radians
For Inches to Degrees (Distance → Angle):
Degrees = (Arc Length ÷ Radius) × (180 ÷ π)

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 Degrees to Inches Calculator makes rotational measurements easier to understand and apply in practical engineering situations.

Engineering Tip:

For precise measurements, always measure the actual radius or diameter of your rotating component. Manufacturing tolerances can affect final dimensions.