When working with curved objects, circular arcs, or rotating components, it is often necessary to convert an angle (degrees) into a linear measurement (inches) along the arc. This conversion is useful in engineering, machining, carpentry, and metalworking to ensure precise cutting, bending, or positioning.

Understanding Arc Length

The arc length (linear distance along a curve) depends on the:

• Angle (θ in degrees) – The portion of the circle to be measured.
• Radius (r in inches) – The distance from the center of the circle to the curve.

Formula to Convert Degrees to Inches

The arc length (S) is calculated as:

$S = \frac{\theta}{360} \times 2\pi r$

Where:

• S = Arc length (in inches)
• θ = Angle in degrees
• r = Radius in inches
• π (Pi) = 3.1416
• 360 = Total degrees in a full circle

This formula helps find the actual curved distance covered by a given angle on a circular path.

Example Calculation

Let’s calculate the arc length for a 45° angle and a 10-inch radius.

Step 1: Identify Given Values

• θ = 45°
• r = 10 inches
• π = 3.1416

Step 2: Apply the Formula

$S = \frac{45}{360} \times 2\pi (10)$

$S = \frac{45}{360} \times 2 \times 3.1416 \times 10$

$S = 0.125 \times 62.832$

$S = 7.85 \text{ inches}$

Thus, a 45° angle on a 10-inch radius circle covers 7.85 inches along the curve.

Conclusion

A Degrees to Inches Calculator is an essential tool for anyone working with curved designs, circular paths, or rotational measurements. By simply entering the angle and radius, you can quickly determine the arc length in inches, ensuring precise fabrication and accurate positioning.