The gradient and gradient on the traffic signs indicate how much the road rises and falls. The information is not in degrees but in percent, which repeatedly leads to confusion.
A traffic sign with a gradient of 4% says that you have to overcome a height difference of 100 m over a distance of 4 m. If the road becomes steeper (e.g. 20% gradient), a height difference of 100 m must be overcome over a distance of 20 m.
The slope has nothing to do with degrees. The table below shows that a slope of 4% corresponds to an angle of 2,29 °. Even a relatively steep road with 20% is the equivalent of only 11,31 °:
| Slope in% | Incline in degrees |
|---|---|
| 1% | 0,57 |
| 2% | 1,15 |
| 3% | 1,72 |
| 4% | 2,29 |
| 5% | 2,86 |
| 6% | 3,43 |
| 7% | 4,00 |
| 8% | 4,57 |
| 9% | 5,14 |
| 10% | 5,71 |
| 11% | 6,28 |
| 12% | 6,84 |
| 13% | 7,41 |
| 14% | 7,97 |
| 15% | 8,53 |
| 16% | 9,09 |
| 17% | 9,65 |
| 18% | 10,20 |
| 19% | 10,76 |
| 20% | 11,31 |
| 21% | 11,86 |
| 22% | 12,41 |
| 23% | 12,95 |
| 24% | 13,50 |
| 25% | 14,04 |
| 26% | 14,57 |
| 27% | 15,11 |
| 28% | 15,64 |
| 29% | 16,17 |
| 30% | 16,70 |
| 31% | 17,22 |
| 32% | 17,74 |
| 33% | 18,26 |
| 34% | 18,78 |
| 35% | 19,29 |
| 36% | 19,80 |
| 37% | 20,30 |
| 38% | 20,81 |
| 39% | 21,31 |
| 40% | 21,80 |
| 41% | 22,29 |
| 42% | 22,78 |
| 43% | 23,27 |
| 44% | 23,75 |
| 45% | 24,23 |
| 46% | 24,70 |
| 47% | 25,17 |
| 48% | 25,64 |
| 49% | 26,10 |
| 50% | 26,57 |
| 51% | 27,02 |
| 52% | 27,47 |
| 53% | 27,92 |
| 54% | 28,37 |
| 55% | 28,81 |
| 56% | 29,25 |
| 57% | 29,68 |
| 58% | 30,11 |
| 59% | 30,54 |
| 60% | 30,96 |
| 61% | 31,38 |
| 62% | 31,80 |
| 63% | 32,21 |
| 64% | 32,62 |
| 65% | 33,02 |
| 66% | 33,42 |
| 67% | 33,82 |
| 68% | 34,22 |
| 69% | 34,61 |
| 70% | 34,99 |
| 71% | 35,37 |
| 72% | 35,75 |
| 73% | 36,13 |
| 74% | 36,50 |
| 75% | 36,87 |
| 76% | 37,23 |
| 77% | 37,60 |
| 78% | 37,95 |
| 79% | 38,31 |
| 80% | 38,66 |
| 81% | 39,01 |
| 82% | 39,35 |
| 83% | 39,69 |
| 84% | 40,03 |
| 85% | 40,36 |
| 86% | 40,70 |
| 87% | 41,02 |
| 88% | 41,35 |
| 89% | 41,67 |
| 90% | 41,99 |
| 91% | 42,30 |
| 92% | 42,61 |
| 93% | 42,92 |
| 94% | 43,23 |
| 95% | 43,53 |
| 96% | 43,83 |
| 97% | 44,13 |
| 98% | 44,42 |
| 99% | 44,71 |
| 100% | 45,00 |
Basics:
To convert the gradient in% to degrees, the arctan of the percentage value must be calculated. Example arctan (13%) = 7,41 °. If you want to check this in Excel, the value must also be converted so that the correct formula in Excel is as follows: = GRAD (ARCTAN (13%))
For example, if you want to convert 12 degrees to the slope in%, the formula in Excel is: = TAN (ARC (12))