Elevation Grade Calculator
Find the grade (percent slope), angle, ratio and slope length of a road, trail or route from rise and run, start and end elevations, distance along the path or a whole elevation profile — with total ascent and descent, steepest section, a profile chart, climb difficulty and optional walking time.
How it works
grade % = (rise ÷ horizontal run) × 100 · angle = atan(rise ÷ run) · slope length = √(rise² + run²) · from a path (odometer) distance d: run = √(d² − rise²) · profile: average grade = (last elevation − first) ÷ total horizontal distance; ascent and descent are the sums of the rises and drops between points · climb score = distance along the climb (m) × average grade (%) · Tobler walking speed = 6 × e^(−3.5 × |grade/100 + 0.05|) km/h · Naismith time = distance ÷ 5 km/h + ascent ÷ 600 m/h
Grade expresses steepness as the vertical rise per 100 units of horizontal distance — the number on road signs and in cycling and hiking guides. A 100% grade is a 45° angle, not vertical, a common surprise. You can enter the rise and horizontal distance, two elevations (from a map, an altimeter or a GPS) and the distance between them, or the distance travelled along the slope, which the calculator converts to horizontal run. For a real route, paste an elevation profile — distance and elevation at several points — to get the average grade, the steepest climbing and descending sections, total ascent and descent, a profile chart and a segment-by-segment table: averages hide short steep pitches. Results include the angle, slope length, rise:run ratio, a steepness class and a climb score (distance × grade) with the cycling-style category it would earn, and you can switch on walking-time estimates from Tobler’s hiking function and Naismith’s rule.
Worked example
Climbing 120 m over 2,000 m of horizontal distance: grade = 120 ÷ 2,000 × 100 = 6%, angle = atan(0.06) ≈ 3.43°, slope length = √(120² + 2,000²) ≈ 2,003.6 m, a ratio of 1 : 16.7. The climb score is 2,003.6 × 6 ≈ 12,022, a category 4 climb. If you measured 2,003.6 m along the road instead, the calculator recovers the same 2,000 m of run. The default profile (350, 372, 410, 395 and 470 m every 500 m) averages the same 6% but climbs 135 m and drops 15 m, with a steepest section of 15% between 1,500 and 2,000 m.
Sources: Grade (slope) — Wikipedia · Tobler, W. (1993) Three presentations on geographical analysis and modeling — hiking function · US Access Board — ADA Standards 405.2 ramp slope (1:12)
Frequently asked questions
Is grade the same as the angle?
No. Grade is a percentage (rise ÷ run × 100); the angle is its arctangent. A 10% grade is about 5.7°, and a 100% grade is 45°.
Should run be horizontal or along the slope?
Grade uses the horizontal distance. If you only know the distance along the road or trail (from an odometer or a GPS track), choose “Rise and distance along the path” and the calculator works out the horizontal run. Below about 10% the difference is under half a percent.
What grade is considered steep for a road?
Highway grades rarely exceed 6–7%. Grades above 10–12% are steep and often signposted; mountain roads occasionally reach 15% or more, and a few city streets exceed 30%.
How do I find the grade of a route with ups and downs?
Choose “Elevation profile” and paste distance and elevation pairs from a map or GPS app, one per line. You get the average grade, the steepest climb and descent, total ascent and descent, and a chart of the profile.
What do the climb categories mean?
They follow the common cycling rule of thumb used by apps such as Strava: distance in metres × average grade in percent. About 8,000 is category 4, 16,000 category 3, 32,000 category 2, 64,000 category 1 and 80,000 or more “hors catégorie”. Race organisers set official categories their own way.
Related calculators
Educational estimate. Uses a spherical-Earth model; results differ slightly from ellipsoidal (WGS84) calculations.