Percent versus degrees
Slopes are described in two ways:
- Percent grade: rise ÷ run × 100. A 100% slope rises 1 m for every 1 m horizontally.
- Degrees: the angle with the horizontal. Angle = arctan(grade ÷ 100).
They are easy to confuse: a 100% slope is only 45°, and a 40% slope is 21.8°.
| Grade | Angle |
|---|---|
| 10% | 5.7° |
| 25% | 14.0° |
| 40% | 21.8° |
| 58% | 30° |
| 70% | 35° |
| 84% | 40° |
| 100% | 45° |
From a map or a trail profile
If you know the vertical drop and horizontal distance, the grade is drop ÷ distance. If you know the drop and the length along the slope, as on a ski run’s published length, the angle is arcsin(drop ÷ length). A run dropping 1,000 ft over 2,500 ft horizontally averages 40%, but its steepest pitch can be much steeper.
Ski run ratings
| Rating (North America) | Typical steepest grade |
|---|---|
| Green circle | under about 25% |
| Blue square | about 25 to 40% |
| Black diamond | 40% and more |
Ratings are set by each resort relative to its own terrain and also reflect width, grooming and hazards, so a black run at one area may be a blue at another. European resorts use blue, red and black, and French resorts add green.
Avalanche terrain
Most slab avalanches start on slopes of 30 to 45°, with a peak around 38°. Slopes under 30° rarely release but can be hit by avalanches from steeper slopes above. Before skiing off-piste or in the backcountry, check the local avalanche forecast, carry a beacon, shovel and probe, and travel with trained partners. An inclinometer or phone app measures slope angle on the spot.
Other uses
The same conversion applies to roads (a 6% grade is 3.4°), hiking trails, wheelchair ramps (ADA maximum 8.33%, a 1:12 ratio) and roofs.