Slope grade calculator: percent, angle, rise, and run

Calculate slope grade, angle, rise, run, and slope distance from rise over run or from two elevations. Use it for roads, trails, ramps, drainage, and line-of-sight checks.

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Example presets

Choose a preset to fill the form and show results right away. Presets are examples.

Inputs

Reverse calculations and extra outputs

Reverse calculations

Need rise from grade, or run from grade? Open this panel and solve the missing value.

Results update automatically as you type and can be restored from a share URL.

Results

Gradient (%)
—
Gradient (‰)
—
Angle (°)
—
Height difference (m) —
Slope distance (m) —
Gradient ratio (1:n) —
Up/down per 100m (m/100m) —

Right-triangle diagram

The figure is schematic. Scale changes automatically to keep the shape readable.

Formulas and conversion table

Show formulas

Slope ratio: r = rise / run = Δz / d

Gradient (% / ‰): grade_% = 100r, grade_‰ = 1000r

Angle: θ = atan(r)

Slope distance: L = sqrt(d² + Δz²)

Show conversion table (% grade ↔ angle)
Gradient (%) Angle (°) Per 100m (m)
0%0.00°0
5%2.86°5
10%5.71°10
15%8.53°15
20%11.31°20
30%16.70°30
50%26.57°50
100%45.00°100
Reference values using angle = atan(grade / 100).

Slope, grade, rise, and run: quick definitions

Use this page when you need to convert between rise over run, percent grade, angle in degrees, and slope distance. It is useful for roads, ramps, trails, drainage, and classroom checks where you want a fast, consistent answer.

What each term means

Which mode to choose

Common mistakes to avoid

See also

Frequently asked questions

What is the difference between horizontal distance and slope distance?
Horizontal distance is the run measured on a flat plan view. Slope distance is the actual sloped length along the surface, which is always longer than the run unless the terrain is perfectly flat.
What is the relationship between slope (%) and angle (°)?
Grade is rise / run × 100. Angle is atan(rise / run). For example, a 10% grade is about 5.71°.
What is line of sight gradient?
It is the grade of the straight line between observer and target, including observer height and target height above ground. Earth curvature and refraction are ignored in this mode.
Can it be used over long distances (several tens of kilometers or more)?
Use it only as a rough approximation. Over long distances, mapped run, Earth curvature, and refraction matter more. For those cases, combine ES-001 for distance and ES-014 for horizon or curvature checks.
What should I do first on this page?

Start with the simplest known pair: run + rise or run + start/end elevation. Check that the units match, run one baseline case, and then compare grade, angle, and slope distance before trying line-of-sight mode or reverse calculations.

Worked examples: rise over run, percent grade, and angle

Example 1: 100 m rise over 1 km run

A rise of 100 m over a run of 1,000 m gives a 10% grade, about 5.71°, and a slope distance just over 1,004.99 m. This is a useful sanity check for roads, hiking profiles, and earthworks.

Example 2: checking a 12% driveway

If a driveway is limited to 12% and you know the rise is 1.8 m, use the reverse calculation to find the minimum run. This is often easier than converting from angle first.

When to use line-of-sight mode

Use line-of-sight mode when the observer and target are above the ground, such as signage, cameras, or sightlines. It answers a different question from terrain grade because it follows the straight view line rather than the ground surface.

What to check if the result looks wrong

Most unexpected results come from confusing run with slope distance, switching between percent and degrees, or mixing meters and kilometers across runs. Recheck the run first, then the rise, then the mode.

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