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Degrees to Feet Conversion Calculator

Formula

To convert an angle in degrees to length in feet:

$L = \left(\frac{a}{360}\right) \times 2 \pi r$

Where:

$L$ is the length in feet
$a$ is the angle in degrees
$r$ is the radius of the circle in feet

Degrees to Feet Conversion

Converting degrees to feet is typically talked about when looking at a circle and converting an angle to the corresponding length of the arc of that angle. Often times that circle is the earth when talking about latitude and longitude.

Example Calculation

Let's assume the following values:

Angle in Degrees $a$ = 45 degrees
Radius of the Circle $r$ = 10 feet

Step 1: Divide the angle by 360:

$\frac{a}{360} = \frac{45}{360} = 0.125$

Step 2: Multiply by 2π:

$0.125 \times 2 \pi \approx 0.125 \times 6.2832 = 0.7854$

Step 3: Multiply by the radius:

$L = 0.7854 \times 10 = 7.85 \text{ feet}$