Ski Slope Grade Calculator Formula
Understand the math behind the ski slope grade calculator. Each variable explained with a worked example.
Formulas Used
Grade (%)
grade_pct = round(vertical_drop_ft / horizontal_ft * 10000) / 100Slope Angle
angle_deg = round(57.2958 * (vertical_drop_ft / run_length_ft) * 100) / 100Horizontal Distance
horizontal_dist = round(horizontal_ft)Variables
| Variable | Description | Default |
|---|---|---|
vertical_drop_ft | Vertical Drop(ft) | 1500 |
run_length_ft | Run Length (slope distance)(ft) | 5000 |
horizontal_ft | Derived value= sqrt(pow(run_length_ft, 2) - pow(vertical_drop_ft, 2)) | calculated |
How It Works
How Ski Slope Grade Is Calculated
Formulas
Grade (%) = Vertical Drop / Horizontal Distance x 100
Horizontal Distance = sqrt(Run Length^2 - Vertical Drop^2)
Angle (degrees) = arcsin(Vertical Drop / Run Length) x 57.2958
Ski Trail Ratings by Steepness
| Rating | Grade | Angle | |--------|-------|-------| | Green (Beginner) | 6-25% | 3-14° | | Blue (Intermediate) | 25-40% | 14-22° | | Black (Advanced) | 40-80% | 22-39° | | Double Black (Expert) | 80%+ | 39°+ |
Worked Example
A run with 1,500 ft vertical drop and 5,000 ft slope length.
vertical_drop_ft = 1500run_length_ft = 5000
- 01Horizontal distance = sqrt(5000^2 - 1500^2) = sqrt(25,000,000 - 2,250,000) = sqrt(22,750,000) = 4,770 ft.
- 02Grade = 1500 / 4770 x 100 = 31.4%.
- 03Angle = arcsin(1500/5000) x 57.3 = 17.5°.
- 04This slope would be rated blue (intermediate).
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