Enter the degrees or a circle into the calculator and the radius of the circle in feet to calculate the feet of the arc. This calculator can also determine the degrees or radius given the other variables are known.
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Degrees to Feet Formula
The following formula is used to convert an angle in degrees to length in feet.
L = (a/360)*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
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. Often times that circle is the earth when talking about latitude and longitude.
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*3.14149*50
L = 43.631
