Convert circular arc length and radius to a central angle, or solve for arc length or radius. Slope mode finds an angle and percent grade from inches of rise over a 12-inch horizontal run.
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Inches To Degrees Formula
The following formula converts circular arc length I and positive circle radius R, both in inches, to a central angle D in degrees. Inches alone do not determine an angle.
Variables:
- D is the central angle in degrees; I is the circular arc length in inches.
- R is the positive circle radius in inches; ฯ is the mathematical constant, approximately 3.14159.
To calculate the angle in degrees, divide the length in inches by the product of 2, ฯ, and the radius of the circle in inches. Multiply the result by 360 to get the equivalent value in degrees.
| Inches (arc length) | Degrees (deg) |
|---|---|
| โ | 0.597 |
| ยผ | 1.194 |
| โ | 1.790 |
| ยฝ | 2.387 |
| โ | 2.984 |
| ยพ | 3.581 |
| โ | 4.178 |
| 1 | 4.775 |
| 1ยผ | 5.968 |
| 1ยฝ | 7.162 |
| 2 | 9.549 |
| 3 | 14.324 |
| 4 | 19.099 |
| 6 | 28.648 |
| 8 | 38.197 |
| 10 | 47.746 |
| 12 | 57.296 |
| 16 | 76.394 |
| 18 | 85.944 |
| 24 | 114.592 |
| * Rounded to 3 decimals. Assumes circular arc with radius 12 in. Conversion: ฮธ(deg) = (L/R) ร 180/ฯ; at R = 12 in, 1 in arc โ 4.775ยฐ. | |
What is Inches To Degrees?
Inches to degrees is a conversion method used in various fields such as mathematics, engineering, and physics. It involves converting a measurement given in inches into an equivalent value in degrees, typically used in the context of angles or rotations. This conversion is not straightforward as inches are units of length and degrees are units of angle. For a circular arc, both its length and the positive circle radius are needed. Arc length is measured along the circle, not across its chord. Zero length gives zero angle; zero length and zero angle do not identify a unique radius. Nonnegative arc angles may exceed one turn. Slope mode uses a different relation: angle = atan(rise / 12), with rise in inches over a 12-inch horizontal run; percent grade = (rise / 12) ร 100. A negative rise indicates a downward slope.
How to Calculate Inches To Degrees?
The following steps outline how to calculate the Inches To Degrees using the formula: D = (I / (2ฯR)) * 360
- First, determine the length in inches (I).
- Next, determine the radius of the circle in inches (R).
- Next, calculate the value of 2ฯR.
- Then, divide the length in inches (I) by the value of 2ฯR.
- Next, multiply the result by 360.
- Finally, calculate the angle in degrees (D).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
length in inches (I) = 10
radius of the circle in inches (R) = 5
Using ฯ, the 10-inch arc on a 5-inch radius has central angle D = (10 / (2ฯ ร 5)) ร 360 โ 114.592ยฐ. In slope mode, a 3-inch rise over a 12-inch horizontal run gives atan(3 / 12) โ 14.036ยฐ and 25% grade.
