Calculate feet from degrees using angle and radius, or solve chord length, field-of-view width, and slope rise from related measurements.
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Degrees to Feet Formula
For a circular arc, the following formula converts a nonnegative central angle in degrees to arc length in feet when the radius is known. An angle alone does not determine a length.
- Where L is the length in feet
- a is the angle in degrees
- r is the radius of the circle in feet
To calculate feet from degrees, divide the angle by 360, multiply by 2 times pi, then finally, multiply by the radius.
| Angle (°) | Arc @ 1 ft r (ft) | Arc @ 10 ft r (ft) | Arc @ 50 ft r (ft) | Arc @ 100 ft r (ft) |
|---|---|---|---|---|
| 0.5 | 0.009 | 0.087 | 0.436 | 0.873 |
| 1 | 0.017 | 0.175 | 0.873 | 1.745 |
| 2 | 0.035 | 0.349 | 1.745 | 3.491 |
| 3 | 0.052 | 0.524 | 2.618 | 5.236 |
| 5 | 0.087 | 0.873 | 4.363 | 8.727 |
| 7.5 | 0.131 | 1.309 | 6.545 | 13.090 |
| 10 | 0.175 | 1.745 | 8.727 | 17.453 |
| 12 | 0.209 | 2.094 | 10.472 | 20.944 |
| 15 | 0.262 | 2.618 | 13.090 | 26.180 |
| 20 | 0.349 | 3.491 | 17.453 | 34.907 |
| 22.5 | 0.393 | 3.927 | 19.635 | 39.270 |
| 30 | 0.524 | 5.236 | 26.180 | 52.360 |
| 45 | 0.785 | 7.854 | 39.270 | 78.540 |
| 60 | 1.047 | 10.472 | 52.360 | 104.720 |
| 75 | 1.309 | 13.090 | 65.450 | 130.900 |
| 90 | 1.571 | 15.708 | 78.540 | 157.080 |
| 120 | 2.094 | 20.944 | 104.720 | 209.440 |
| 135 | 2.356 | 23.562 | 117.810 | 235.619 |
| 180 | 3.142 | 31.416 | 157.080 | 314.159 |
| 360 | 6.283 | 62.832 | 314.159 | 628.319 |
| * Rounded to 3 decimals. Arc length s = r × θ, with θ in radians. Conversion: 1° ≈ 0.017453 rad, so per 1 ft radius: 1° ≈ 0.017 ft. | ||||
Degrees to Feet Conversion
What is a conversion between degrees and feet?
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. For geographic latitude and longitude, select an appropriate Earth model; a longitude degree does not represent a constant surface distance at every latitude.
Example Problem
How to convert degrees to feet?
First, determine the total angle in degrees.
For this example, the angle is found to be 50 degrees.
Next, determine the radius of the circle that contains the angle.
In this case, the radius of the circle is measured to be 50 feet.
Finally, calculate the arc length in feet using the formula above:
L = (a/360)*2*pi*r
L = (50/360)*2*pi*50
L ≈ 43.633 feet
