Average Slope Calculator
Average slope is the steepness between two points with the bumps averaged out: take the elevation change between the start and the end, divide it by the horizontal distance between them, and you have the grade the whole stretch works out to. The average slope calculator below returns that one measurement in the three forms people actually use: percent grade, angle in degrees, and the “1 in X” gradient ratio used on drawings and road signs. Ten feet of rise over 200 feet of run, for example, is a 5.00% grade, an angle of 2.86 degrees, and a gradient of 1 in 20.
The average is the honest number for planning: a driveway, ramp, path or field drain is built and judged on its overall grade, not on its steepest metre. It is also the number standards are written in. Accessibility rules cap a ramp at 1 in 12, road designers keep interstates near 6%, and foundation grading asks for 2 to 5% away from the wall. Enter the elevation change and the horizontal distance, in feet or meters, and read your stretch against those benchmarks.
Enter the horizontal (map) distance, not the length measured along the slope. A negative elevation change returns a downhill grade. This tool measures ground slope between two points; for the slope of a graphed function between two x-values, the same rise-over-run idea applies with y-change over x-change, but the standards and gradient forms here are the ground-survey versions.
Quick Answer
Key takeaways
- Average slope is rise over run between two endpoints: local steep spots are averaged out, which is why standards and designs are written in average grade.
- Percent, degrees and 1-in-X are one measurement in three dialects: 5% = 2.86 degrees = 1 in 20, and 100% = 45 degrees, not vertical.
- The distance must be horizontal. A tape laid along the slope overstates the run and understates the grade.
- Benchmarks to read against: ADA ramps cap at 8.33% (1 in 12), interstates sit near 6%, foundation grading runs 2 to 5%.
- Quick Answer
- How to use the average slope calculator
- One slope, three expressions: percent, degrees, gradient
- Worked example: a 10 ft climb over 200 ft
- Grade standards worth reading your result against
- Measure horizontal distance, not slope distance
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the average slope calculator
Two measurements in, three expressions of the same slope out. The measurement steps are where accuracy is won or lost.
Get the elevation change. Subtract the start elevation from the end elevation. Endpoints at 1,240 ft and 1,250 ft give a change of +10 ft. Sources: a survey, a topo map, a phone altimeter for rough work, or a level and tape for short stretches. If the end is lower, the change is negative and the grade is downhill.
Get the horizontal distance. This is the flat distance between the points as a map sees them, not the distance walked or taped along the ground. Map tools and GPS tracks report horizontal distance by default; a tape on the ground does not.
Enter both in the same unit and calculate. Feet with feet, meters with meters. The unit picker only labels the basis line in the result, because a ratio of two lengths has no unit of its own. Chaining the endpoints into segments and measuring the average distance calculator style, segment by segment, gives the same total run if you need to build the distance up from parts.
One slope, three expressions: percent, degrees, gradient
The three outputs are conversions, not three different slopes. Percent grade is the surveyor's and road engineer's form. Degrees are the geologist's and hiker's form. The 1-in-X gradient is the form printed on drawings and written into accessibility standards, where "1 in 12" is faster to check against a built ramp than "8.33%".
A common misconception dies here: percent grade is not a share of vertical. Because the denominator is the horizontal run rather than the slope length, grades can exceed 100%. A 200% grade (63.4 degrees) exists on paper and on cliff faces; a vertical wall is not 100%, it is undefined, because its horizontal run is zero.
Worked example: a 10 ft climb over 200 ft
The calculator is pre-filled with this case, and it sits in a useful band: steeper than a drainage fall, gentler than a ramp limit. A path climbs 10 ft across a horizontal span of 200 ft.
| Output | Calculation | Result |
|---|---|---|
| Percent grade | (10 / 200) x 100 | 5.00% |
| Angle | arctan(10 / 200) | 2.86 degrees |
| Gradient ratio | 200 / 10 | 1 in 20.00 |
| Same stretch, downhill entry (-10 ft) | (-10 / 200) x 100 | -5.00% |
At 5%, this path sits exactly at the running-slope limit the ADA allows on an accessible route that is not a ramp, and it matches the top of the 2 to 5% band used for grading soil away from a foundation. It would feel like a steady, noticeable climb on foot and a gentle one in a car. For scale, the steepest residential streets in the world run near 35%, and a black-diamond ski run starts around 40%: the worked example is a working grade, not an extreme one.
Grade standards worth reading your result against
A percentage means little until it is compared with the standard for the job. The figures below come from the ADA Standards for Accessible Design, the US Access Board's ramp guidance, and standard highway and site-grading practice.
| Application | Grade | In the other forms |
|---|---|---|
| Wheelchair ramp maximum (ADA) | 8.33% | 1 in 12, 4.76 degrees |
| Accessible route running slope limit (not a ramp) | 5% | 1 in 20, 2.86 degrees |
| Sidewalk cross slope maximum | 2% | 1 in 50, 1.15 degrees |
| US interstate highway, typical maximum | 6% | 1 in 16.7, 3.43 degrees |
| Driveway drainage minimum | 1 to 2% | Enough fall for water to run off |
| Driveway practical maximum | about 15% | 1 in 6.7, 8.53 degrees |
| Grading away from a foundation, first 10 ft | 2 to 5% | 6 inches of fall in 10 ft is 5% |
| Residential roof, common 6:12 pitch | 50% | 26.57 degrees |
Standards are maximums or minimums for a specific build, not descriptions of the landscape: a trail at 12% breaks no rule, while a shop entrance ramp at 12% fails inspection. When checking your own measurement against a surveyed figure, remember the difference between horizontal distance and distance along the ground: the actual distance calculator covers that map-versus-ground distinction, and angle-based follow-ups such as arc length are handled by the arc length calculator.
Measure horizontal distance, not slope distance
The classic field error is stretching a tape along the ground and entering that length as the distance. The taped length is the hypotenuse: always longer than the horizontal run, so the computed grade comes out too low. On a 5% grade the error is tiny (the hypotenuse exceeds the run by about an eighth of a percent), which is why the mistake survives. On a 40% hillside the taped length overstates the run by about 7.7%, enough to turn a true 40.0% grade into a reported 37.1%.
What competing calculators miss
Winning move 1: all three forms, every time. The best-known hill-grade tool returns percent only. The flexible solver rivals return percent and degrees but no gradient ratio, which is the one form accessibility standards are written in. This calculator returns percent, degrees and 1-in-X from a single run, with the sign kept so downhill reads as downhill.
Winning move 2: the flat case handled, not crashed. A zero elevation change makes the gradient ratio a division by zero in naive tools. Here it returns "flat (no elevation change)" with 0.00% and 0.00 degrees, which is the correct survey answer for a level stretch.
Winning move 3: benchmarks attached to the number. Rival pages print a percentage and leave the reader to wonder whether it is steep. The verdict under this calculator reads the result against the ADA ramp maximum and driveway practice, and the standards table covers ramps, routes, highways, driveways, foundations and roofs in all three forms.
Frequently asked questions
Subtract the start elevation from the end elevation to get the rise, divide by the horizontal distance between the points, and multiply by 100 for percent grade. Ten feet of rise over 200 feet of horizontal distance is (10 / 200) x 100 = 5.00%. Using the endpoints is what makes it an average: steeper and flatter spots along the way are smoothed out.
Percent is rise over run times 100. Angle is the arctangent of rise over run, in degrees. They describe the same slope: 5% is 2.86 degrees, 8.33% is 4.76 degrees, and 100% is exactly 45 degrees. Small grades look deceptively similar in both forms, then diverge fast: doubling the percent from 50% to 100% moves the angle only from 26.57 to 45 degrees.
The ground rises 1 unit for every 20 units of horizontal distance. Compute X as horizontal distance divided by elevation change. A 1 in 20 gradient is a 5% grade. Smaller X means steeper: 1 in 12 (the ADA ramp maximum) is steeper than 1 in 20.
No. A 100% grade means the rise equals the horizontal run, which is a 45-degree angle. A vertical surface has zero horizontal run, so its percent grade is undefined (infinite), not 100%. Grades above 100% are real but rare: 200% is about 63.4 degrees.
Horizontal distance, always. The length measured along the ground is the hypotenuse and is longer than the run, so it understates the grade: slightly on gentle ground, by several percent of the value on steep ground. If only the slope distance is known, recover the run with Pythagoras: square root of (slope distance squared minus rise squared).
Under the ADA Standards, a ramp run may slope at most 1 in 12, which is 8.33% or 4.76 degrees, with level landings at the top and bottom and limits on the rise between landings. An existing-building alteration can allow slightly steeper short runs in narrow exceptions, but 1 in 12 is the design figure to work to.
Yes. Enter a negative elevation change when the end point is lower than the start, and the calculator returns a negative percent and angle with a downhill reading: -10 ft over 200 ft is -5.00%. The gradient ratio is reported as a positive 1 in 20.00, with the direction shown separately.
No. Slope is a ratio of two lengths in the same unit, so the units cancel: 10 ft over 200 ft and 10 m over 200 m are both 5.00%. The unit picker exists so the basis line in the result records which unit you measured in. Never mix units between the two inputs.
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References
- US Department of Justice, "2010 ADA Standards for Accessible Design" - section 405 sets ramp running slope at no steeper than 1 in 12, and section 403 sets accessible route running and cross slopes. ADA: 2010 Standards for Accessible Design. Accessed October 2026.
- US Access Board, "Guide to the ADA Standards: Ramps and Curb Ramps" - explains the 1 in 12 maximum, landings, and the exceptions for short rises in alterations. Access Board: Ramps and Curb Ramps Guide. Accessed October 2026.
- UK Department for Transport, "Inclusive Mobility: A Guide to Best Practice on Access to Pedestrian and Transport Infrastructure" - gradient recommendations for footways and ramps used outside the US system. GOV.UK: Inclusive Mobility. Accessed October 2026.
- Federal Highway Administration, "Designing Sidewalks and Trails for Access" - running slope and cross slope practice for shared-use paths and sidewalks. FHWA: Designing Sidewalks and Trails for Access. Accessed October 2026.
- US Geological Survey, "The National Map" - the elevation data source behind most US map-based rise and horizontal distance measurements. USGS: The National Map. Accessed October 2026.
- National Geodetic Survey, "Geodetic Tools and Surveys" - how horizontal distances and elevations are defined and measured in US surveying practice. NOAA: National Geodetic Survey. Accessed October 2026.