Elevation Grade Calculator — Slope & Angle
Enter the vertical rise and horizontal run of a road, trail or ramp to get the grade percentage, the angle in degrees and the slope distance — the three ways engineers and hikers describe steepness.
m
m
Percentage grade — rise divided by run, times 100
- 1
Slope ratio (rise ÷ run)
10 ÷ 100 = 0.1 - 2
Elevation grade
0.1 × 100 = 10
How does this calculator work?
Elevation grade = (rise ÷ run) × 100%. Enter the vertical rise and horizontal run of any slope to get the grade percentage (e.g. 10% means climbing 10 m for every 100 m horizontally), the angle in degrees via arctan(rise/run), and the actual slope distance.
Formula
How this is calculated
Elevation grade measures how steep a slope is by expressing vertical rise as a percentage of horizontal run. A 10% grade means the road climbs 10 metres for every 100 metres of horizontal distance — regardless of how long the actual road surface is. Engineers use percentage grade for roads and railways; hikers sometimes prefer the angle in degrees, while architects often quote a 1-in-X ratio (a 10% grade is 1:10).
This calculator converts between all three representations. The angle is derived via arctan(rise/run), which gives the true tilt in degrees. The slope distance (hypotenuse) is the actual path length an object travels along the incline, longer than the horizontal run whenever the grade is non-zero.
Assumptions: the run you enter is the horizontal projection of the distance, not the slope distance itself. If you measured along the road surface instead, the true horizontal run is slightly shorter, so the computed grade will be a small underestimate for very steep slopes.
Frequently asked questions
Most highways are designed for grades below 6%. Grades of 8–10% are considered steep and uncommon on main roads. Mountain roads and switchbacks can reach 12–15%, and some off-road tracks exceed 20%. Cyclists generally consider anything above 8% a serious climb.
Use the formula: angle = arctan(grade% ÷ 100). For example, a 10% grade gives arctan(0.10) ≈ 5.7°. The calculator does this automatically. Note that a 45° angle equals a 100% grade, not 45%.
Grade (or gradient) expresses rise over horizontal run as a percentage and is used for roads, trails and railways. Pitch is the same concept applied to roofs, usually expressed as a ratio of rise per 12 inches of run (e.g. 4:12 pitch). Both measure steepness — they just use different conventions for the denominator.
Also known as
TG we-Calculate Editorial Team. (2026). Elevation Grade Calculator — Slope & Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/elevation-grade-calculator
TG we-Calculate Editorial Team. "Elevation Grade Calculator — Slope & Angle." TG we-Calculate. 2026. https://we-calculate.com/calculator/elevation-grade-calculator.
TG we-Calculate Editorial Team, "Elevation Grade Calculator — Slope & Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/elevation-grade-calculator
@misc{wecalculate_elevation_grade_calculator, title = {Elevation Grade Calculator — Slope & Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/elevation-grade-calculator}}, year = {2026}, note = {TG we-Calculate} }
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