Angle and Slope Conversion
Quick answer: A 100 % slope = 45°, 10 % ≈ 5.71°, 1:12 ≈ 4.76° (8.33 %); 1 rad ≈ 57.2958°, 1 gon = 0.9° and a 6/12 roof = 50 % ≈ 26.57°.
Degrees, radians, gon, arcminutes and arcseconds, and slope in percent, per mille, 1:x ratio and roof pitch x/12 – via the tangent.
How the calculation works
Enter an angle or slope and choose the unit. The table shows the same angle in degrees, minutes and seconds, radians, gons, turns and mils, and as a slope in %, ‰, a 1:x ratio and inches per foot (x/12).
Formula and assumptions
The base unit is the radian; 1° = π/180 rad, 1 gon = π/200 rad. Slope is not linear with the angle: slope = tan(angle). So 100 % = tan 45°, and 200 % ≈ 63.4°, not 90°. A 1:x ratio means a rise of 1 over a run of x, so angle = arctan(1/x); a roof pitch x/12 is arctan(x/12).
More worked examples
- A 1:12 ramp (accessibility): arctan(1/12) ≈ 4.76° = 8.33 %.
- A 30° roof: tan 30° ≈ 57.7 % ≈ 6.93/12.
- A 2 % drainage fall: arctan(0.02) ≈ 1.15°.
- Stairs 17/29 cm: arctan(17/29) ≈ 30.4° ≈ 58.6 %.
Slope and angle
| Slope % | Angle | Ratio |
|---|---|---|
| 1 % | 0.573° | 1:100 |
| 2 % | 1.146° | 1:50 |
| 8.33 % | 4.76° | 1:12 |
| 25 % | 14.04° | 1:4 |
| 50 % | 26.57° | 1:2 |
| 100 % | 45° | 1:1 |
Common mistakes
- Converting percent to degrees by division (100 % is not 90°).
- Confusing a 1:x ratio (rise:run) with x:1.
- Mixing degrees and gons (100 gon = 90°).
Frequently asked questions
How many degrees is a 100 % slope?
100 % means the rise equals the run, which is an angle of 45°.
How do I convert slope percent to degrees?
Angle = arctan(percent/100). For 15 %: arctan(0.15) ≈ 8.53°.
How many degrees is a 4/12 roof pitch?
arctan(4/12) ≈ 18.43°, i.e. a 33.3 % slope.
How many degrees are in one radian?
1 rad = 180°/π ≈ 57.2958°.
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