Convert Feet to Degrees Calculator
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Reviewed by Calculator Editorial Team
Convert feet to degrees with our precise calculator. Learn how to convert linear measurements to angular measurements and understand the conversion formula.
What is Feet to Degrees Conversion?
Converting feet to degrees involves transforming a linear measurement (feet) into an angular measurement (degrees). This conversion is commonly used in fields like astronomy, engineering, and navigation where both linear and angular measurements are important.
The conversion is based on the relationship between the length of an arc and the angle it subtends at the center of a circle. The key factor is the radius of the circle, as the length of an arc depends on both the angle and the radius.
How to Convert Feet to Degrees
To convert feet to degrees, you need to know the radius of the circle in which the arc length is measured. Here are the steps:
- Measure the arc length in feet.
- Determine the radius of the circle in feet.
- Use the formula: degrees = (arc length / radius) × (180/π).
- Calculate the result to get the angle in degrees.
This formula converts the arc length to radians first (arc length / radius), then converts radians to degrees by multiplying by (180/π).
Feet to Degrees Formula
Where:
- degrees is the angular measurement in degrees
- arc length is the linear measurement in feet
- radius is the distance from the center to the arc in feet
- π (pi) is approximately 3.14159265359
This formula is derived from the relationship between arc length, radius, and angle in a circle.
Feet to Degrees Conversion Table
Here's a table showing common arc lengths and their corresponding angles for a circle with a radius of 1 foot:
| Arc Length (feet) | Angle (degrees) |
|---|---|
| 0.1 | 5.73 |
| 0.5 | 28.65 |
| 1 | 57.29 |
| 2 | 114.59 |
| 3 | 171.89 |
| 4 | 229.18 |
| 5 | 286.48 |
Note: These values are based on a radius of 1 foot. For different radii, the angle will change proportionally.
Feet to Degrees FAQ
What is the difference between arc length and angle?
Arc length is a linear measurement along the curve of a circle, while angle is a measurement of rotation. The relationship between them depends on the radius of the circle.
Can I convert degrees to feet using the same formula?
No, the formula works only for converting feet to degrees. To convert degrees to feet, you would use the inverse formula: arc length = (angle × π/180) × radius.
What units should I use for the radius?
The radius should be in the same units as the arc length. If your arc length is in feet, the radius should also be in feet for consistent results.