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
Worked Example
A run with 1,500 ft vertical drop and 5,000 ft slope length.
- 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).
Frequently Asked Questions
What is considered a steep ski slope?
Slopes above 40% grade (22 degrees) are considered steep and rated black diamond. Expert-only slopes can exceed 80% grade (39 degrees). Most groomed runs are 15-35% grade.
Is grade the same as degrees?
No. Grade is rise over run (percentage). Degrees measure the angle from horizontal. A 100% grade equals 45 degrees. A 50% grade equals about 27 degrees. They are related but not the same.
Does grade affect ski speed?
Steeper slopes allow faster speeds due to greater gravitational force component along the slope. However, grooming, snow conditions, and skier technique also significantly affect speed.
Ready to run the numbers?
Open Ski Slope Grade Calculator