A Degrees to Inches Calculator converts an angular measurement in degrees into a linear distance in inches along a circular arc. This conversion is essential in engineering, construction, machining, and automotive design, where precise curved measurements are needed.
Importance of Degrees to Inches Conversion:
- Used in Engineering & Machining: Helps in cutting and shaping curved materials.
- Essential for Construction & Roadway Design: Converts angular measurements into real-world distances.
- Important in Automotive & Aerospace: Determines curved surface dimensions accurately.
- Applied in Robotics & Motion Control: Ensures precision in rotational movements.
Formula of Degrees to Inches Calculator
The conversion from degrees to inches depends on the radius (r) of the circular arc and follows this formula:
Inches = (Degrees / 360) × (2πr)
Where:
- Degrees = Angle in degrees.
- r = Radius in inches.
- π ≈ 3.1416.
- 360° represents a full circle.
This formula calculates the arc length, which is the linear distance covered along a circular path.
Degrees to Inches Reference Table
The table below provides pre-calculated values for common degree-to-inch conversions with a 10-inch radius:
| Degrees | Arc Length (Inches) (r = 10") |
|---|---|
| 1° | 0.1745" |
| 5° | 0.8727" |
| 10° | 1.7453" |
| 15° | 2.6180" |
| 30° | 5.2360" |
| 45° | 7.8540" |
| 60° | 10.4720" |
| 90° | 15.7080" |
| 180° | 31.4160" |
| 360° | 62.8320" |
This table allows for quick reference and application in real-world scenarios.
Example of Degrees to Inches Calculator
Suppose an automotive engineer needs to calculate the arc length of a 60-degree turn on a steering wheel with a radius of 15 inches.
Step 1: Apply the Formula
Inches = (60 / 360) × (2 × 3.1416 × 15)
Step 2: Solve the Equation
Inches = (60 / 360) × (94.2480)
Inches = 0.1667 × 94.2480 = 15.71 inches
Thus, a 60-degree rotation on a 15-inch radius results in an arc length of 15.71 inches.
Most Common FAQs
This conversion is essential in design, engineering, and construction, where curved distances must be measured precisely.
The radius depends on the circular path of motion, such as wheel diameter, curved roads, or machining operations.
Yes, astronomers and physicists use similar formulas to calculate arc distances on celestial bodies.