Degrees Into Inches Calculator
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Reviewed by Calculator Editorial Team
Convert angles in degrees to linear measurements in inches using our precise degrees into inches calculator. This tool helps you determine the length of an arc or chord when you know the angle and radius in inches.
How to Use This Calculator
To convert degrees to inches, follow these simple steps:
- Enter the angle in degrees in the first input field.
- Enter the radius in inches in the second input field.
- Select whether you want to calculate the arc length or chord length.
- Click the "Calculate" button to get the result.
- Review the result and use the "Reset" button to clear the inputs if needed.
This calculator assumes you're working with a circle. For non-circular shapes, additional factors may apply.
Formula Explained
The conversion from degrees to inches depends on whether you're calculating arc length or chord length:
Arc Length Formula
Arc Length (inches) = (θ/360) × 2πr
Where:
- θ = angle in degrees
- r = radius in inches
- π ≈ 3.141592653589793
Chord Length Formula
Chord Length (inches) = 2r × sin(θ/2)
Where:
- θ = angle in degrees
- r = radius in inches
The calculator uses these formulas to provide accurate results based on your inputs.
Worked Examples
Let's look at two practical examples to understand how the conversion works.
Example 1: Arc Length Calculation
Problem: What is the arc length of a 90-degree angle with a radius of 5 inches?
Solution:
Arc Length = (90/360) × 2π × 5 ≈ 8.7266 inches
This means a 90-degree arc with a 5-inch radius spans approximately 8.73 inches.
Example 2: Chord Length Calculation
Problem: What is the chord length of a 60-degree angle with a radius of 10 inches?
Solution:
Chord Length = 2 × 10 × sin(60/2) ≈ 17.3205 inches
This means a 60-degree chord with a 10-inch radius is approximately 17.32 inches long.
Comparison Table
Here's a comparison of arc length and chord length for different angles with a fixed radius of 10 inches:
| Angle (degrees) | Arc Length (inches) | Chord Length (inches) |
|---|---|---|
| 30 | 2.6179 | 5.1764 |
| 45 | 3.9269 | 7.0711 |
| 60 | 5.2359 | 8.6603 |
| 90 | 8.7266 | 10.0000 |
| 120 | 11.3446 | 10.3528 |
Notice how the chord length approaches the diameter (20 inches) as the angle approaches 180 degrees.
Frequently Asked Questions
What is the difference between arc length and chord length?
Arc length is the distance along the curve of the circle, while chord length is the straight-line distance between the two endpoints of the arc. For small angles, these values are similar, but they diverge as the angle increases.
Can I use this calculator for non-circular shapes?
This calculator is specifically designed for circular measurements. For other shapes, you would need to use different formulas appropriate for those geometric forms.
What units should I use for the radius?
The calculator expects the radius to be in inches. If you're working with a different unit, you'll need to convert it to inches before using this tool.
Is there a limit to the angle I can enter?
The calculator accepts angles from 0 to 360 degrees. Angles outside this range will not produce meaningful results.