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) / 100

Slope Angle

angle_deg = round(57.2958 * (vertical_drop_ft / run_length_ft) * 100) / 100

Horizontal Distance

horizontal_dist = round(horizontal_ft)

Variables

VariableDescriptionDefault
vertical_drop_ftVertical Drop(ft)1500
run_length_ftRun Length (slope distance)(ft)5000
horizontal_ftDerived 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
  1. 01Horizontal distance = sqrt(5000^2 - 1500^2) = sqrt(25,000,000 - 2,250,000) = sqrt(22,750,000) = 4,770 ft.
  2. 02Grade = 1500 / 4770 x 100 = 31.4%.
  3. 03Angle = arcsin(1500/5000) x 57.3 = 17.5°.
  4. 04This slope would be rated blue (intermediate).

Ready to run the numbers?

Open Ski Slope Grade Calculator