Slope Gradient Calculator
Calculate slope gradient as percent grade, angle, ratio, rise, run, or slope length using construction, grading, and geometry inputs.
Calculator is for informational purposes only. Terms and Conditions
Choose what to solve for
Select the unknown and the known slope format. The required inputs update automatically.
Enter the known values
Percent grade uses horizontal run, not diagonal slope length.
Visual Check
Confirm the rise, horizontal run, slope length, angle, and grade relationship.
Solution
Live result, slope conversions, warnings, and full solution steps.
Quick checks
- Check—
Show solution steps See unit conversions, substitutions, assumptions, and slope checks
- Enter values to see the full solution steps and checks.
Source, Standards, and Assumptions
Calculation basis, constants, assumptions, and limitations.
Source/standard information updates after a valid calculation.
- Assumptions will appear after a valid calculation.
Calculator guide
How the Slope Gradient Calculator Works
The Slope Gradient Calculator above—also useful as a slope calculator, percent grade calculator, and rise-over-run calculator—converts slope between rise and horizontal run, decimal slope, percent grade, angle, rise:run ratio, and diagonal slope length.
The core relationship is simple: slope equals vertical rise divided by horizontal run. The calculator is most useful because it keeps the equivalent slope formats together, handles mixed length units, and lets you work backward when rise, run, grade, or angle is the unknown.
- Best for
- Grade, drainage, ramps, roads, site work, surveying, roofs, trails, landscaping, and geometry checks
- Main conversions
- Rise/run, percent grade, degrees, decimal slope, ratio, and slope length
- Most important rule
- Percent grade uses horizontal run—not the diagonal distance along the slope
How to Calculate Slope, Grade, or Angle
Choose the unknown first, then use the slope representation that matches the measurements you already have.
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Choose what you need to solve for
Select slope or percent grade, rise, horizontal run, angle, or slope length depending on the calculator mode available.
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Use horizontal distance for the run
The run is the plan-view horizontal distance between the two points. Do not substitute the diagonal distance measured along the sloped surface.
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Match or select the correct units
Rise and run may use different units if the calculator converts them, but a manual calculation must convert both distances to the same length unit before division.
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Keep the sign when direction matters
A positive rise describes an uphill grade in the chosen direction; a negative rise describes a downhill grade. Use the absolute value when you only need steepness.
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Check an equivalent result
Compare the percent grade with the displayed angle or ratio. For example, 5% should be about 2.86° and approximately 1:20.
Slope Calculator Inputs and Outputs
Slope can be represented several ways. The calculator converts between the formats used in grading, civil engineering, construction, surveying, roofing, and general geometry.
| Quantity | Meaning | Typical Format |
|---|---|---|
| Rise | Vertical elevation change between the start and end points | in, ft, yd, mm, cm, m |
| Horizontal run | Horizontal plan distance over which the elevation changes | in, ft, yd, mm, cm, m |
| Decimal slope | Rise divided by horizontal run | 0.05 |
| Percent grade | Decimal slope multiplied by 100 | 5% |
| Slope angle | Incline angle measured from horizontal | 2.86° |
| Rise:run ratio | Vertical change compared with horizontal distance | 1:20 |
| Slope length | Diagonal distance along the incline | Length unit |
Slope Gradient Formulas
USGS describes percent slope and slope angle from the same rise-over-run geometry: percent slope is rise divided by run times 100, while angle is the inverse tangent of rise divided by run.
Decimal slope
The result is dimensionless after rise and run are expressed in compatible length units.
Percent grade or percent slope
A 5% grade means 5 units of vertical change for every 100 units of horizontal run.
Slope angle
The angle is measured from horizontal.
Convert angle to percent grade
Degrees and percent grade are different representations; a 5° slope is about 8.75%, not 5%.
Slope length
This is the diagonal distance along a straight slope.
Worked Example: 5% Grade
A surface rises 5 ft over a horizontal run of 100 ft. Find the percent grade, angle, rise:run ratio, and diagonal slope length.
Percent grade
Slope angle
Rise:run ratio
Slope length
Result
5% grade = 2.86° = 1:20 rise:run
The diagonal slope length is approximately 100.12 ft.
Percent Grade, Degrees, and Ratio
Grade, angle, and ratio describe the same incline but are not numerically interchangeable. This distinction is one of the most common reasons users get unexpected slope results.
Percent grade
Percent grade equals 100 times rise/run. A 10% grade has a decimal slope of 0.10.
Degrees
Angle is calculated with arctangent. A 10% grade is approximately 5.71°, not 10°.
Rise:run ratio
A 1:20 slope means one unit of rise for 20 units of horizontal run, which equals 5%.
Common Slope Conversion Table
Use these mathematically equivalent values as a fast reasonableness check. They are conversion references, not universal design limits.
| Rise:Run | Decimal Slope | Percent Grade | Angle |
|---|---|---|---|
| 1:100 | 0.0100 | 1.00% | 0.57° |
| 1:50 | 0.0200 | 2.00% | 1.15° |
| 1:20 | 0.0500 | 5.00% | 2.86° |
| 1:12 | 0.0833 | 8.33% | 4.76° |
| 1:10 | 0.1000 | 10.00% | 5.71° |
| 1:4 | 0.2500 | 25.00% | 14.04° |
| 1:2 | 0.5000 | 50.00% | 26.57° |
| 1:1 | 1.0000 | 100.00% | 45.00° |
Horizontal Run vs Slope Length
Percent grade is based on horizontal run. The diagonal distance along the surface is a different quantity called slope length.
| Distance | Definition | Use in Percent Grade? |
|---|---|---|
| Horizontal run | Plan-view horizontal distance between endpoints | Yes |
| Slope length | Diagonal distance along the incline | No |
USGS defines the run for slope angle as the idealized horizontal distance. Using diagonal length instead of horizontal run makes the calculated percent grade too low, with the error becoming more significant as the slope gets steeper.
Slope Applications and Design Context
The same geometry appears in many fields, but the acceptable slope is controlled by the application. Use the calculator for the number; use the governing design criteria for acceptance.
| Application | Why Slope Matters | What to Verify After Calculating |
|---|---|---|
| Drainage and site grading | Controls fall, runoff direction, ponding risk, and erosion potential | Plans, drainage criteria, surface tolerances, outlet elevations, and erosion protection |
| Accessible ramps | Running slope affects accessibility and usability | Applicable ADA/ABA requirements, landings, cross slope, rise limits, handrails, and project conditions |
| Roads and driveways | Grade affects vehicle operation, drainage, transitions, and traction | Agency or local roadway criteria, vertical curves, drainage, and site conditions |
| Roofs | Controls drainage and roof geometry | Roof pitch convention, roofing-system requirements, drainage, and manufacturer limits |
| Trails and landscapes | Affects comfort, erosion, maintenance, and runoff | Surface type, accessibility goals, erosion controls, and local trail/site standards |
| Surveying and terrain | Converts elevation change and horizontal distance into gradient | Measurement method, coordinate basis, stationing, and whether distance is horizontal or slope distance |
How to Interpret the Result
A slope result tells you the rate of elevation change relative to horizontal distance. The equivalent formats help communicate the same geometry to different audiences.
Percent grade
A 5% grade means the elevation changes 5 units vertically for each 100 units of horizontal run.
Angle
A 5% grade is only about 2.86°. Degrees become much different from percent grade as the slope gets steeper.
Direction
The sign tells you whether elevation rises or falls in the selected direction. The absolute value describes steepness.
Units and Measurement Checks
Slope is dimensionless only after rise and run are expressed in the same length basis. Most large errors come from measurement definition or unit mismatch.
Inches and feet
\(12\ \mathrm{in}=1\ \mathrm{ft}\). A 6 in rise over 10 ft is 6/120, not 6/10.
Millimeters and meters
\(1000\ \mathrm{mm}=1\ \mathrm{m}\). A 20 mm fall over 2 m is \(20/2000=0.01=1\%\).
Horizontal distance
Surveyed slope distance or tape distance along the surface is not the horizontal run unless the slope is negligible or the value has been reduced to horizontal.
Ratio order
This article uses rise:run. A 1:12 ratio therefore means one unit vertical for twelve units horizontal.
Negative values
A negative rise produces a negative grade and angle in the chosen direction. Avoid discarding the sign when drainage or profile direction matters.
Vertical lines
When horizontal run is zero, rise/run is undefined. A vertical line is 90° but has no finite percent grade.
Common Slope Calculation Mistakes
The equation is straightforward. The most common failures come from using the wrong distance, mixing units, or confusing slope representations.
Using slope length as run
Percent grade requires horizontal run. Using the diagonal distance understates the grade.
Mixing inches and feet
Convert both measurements first or use the calculator’s unit selectors.
Confusing percent with degrees
5% is about 2.86°, while 5° is about 8.75%.
Assuming 100% means vertical
100% means rise equals run, giving a 45° angle.
Reversing a ratio
1:12 and 12:1 describe radically different slopes. Confirm whether the source uses rise:run, run:rise, H:V, or V:H notation.
Applying one design limit everywhere
A mathematically equivalent ratio may have different acceptability depending on whether the surface is a ramp, roadway, drain, roof, trail, or site grade.
Assumptions and Limitations
The calculator uses straight-line right-triangle geometry between two points. That is appropriate for a basic slope conversion but does not represent every design problem.
Straight slope between endpoints
The calculation assumes one constant average rise/run relationship. Curved profiles and vertical curves require more detailed geometry.
No surface-performance model
The calculator does not predict drainage capacity, erosion, traction, structural behavior, or accessibility compliance.
No measurement uncertainty
Survey, level, tape, digital level, and elevation-data errors are not propagated into the result.
No project-specific code check
Acceptable slopes depend on the governing jurisdiction, standard, facility type, surface, and design purpose.
Sources and Calculation Basis
The formula and application notes were checked against current U.S. Geological Survey and U.S. Access Board guidance.
- U.S. Geological Survey — Determine Percent of Slope and Angle of Slope — supports rise/run percent-slope calculations and inverse-tangent conversion from rise/run to slope angle.
- U.S. Geological Survey — Slope Conversions — documents gradient as rise/run, slope percent as gradient × 100, and angle as another equivalent slope metric.
- U.S. Access Board — Ramps and Curb Ramps — supports the 1:12 (8.33%) maximum running-slope context for ADA ramp runs and explains why accessibility design requires more than one slope number.
The 5 ft rise / 100 ft run worked example was independently verified: grade = 5%, angle = 2.8624°, ratio = 1:20, and diagonal length = 100.1249 ft.
Slope Gradient Calculator FAQ
These are the slope-conversion questions most likely to cause an incorrect result or interpretation.
What is the formula for slope gradient?
Slope gradient is rise divided by horizontal run: \(m=\mathrm{rise}/\mathrm{run}\). Multiply by 100 to express the same gradient as percent grade.
How do I calculate percent grade from rise and run?
Convert rise and run to the same length unit, divide rise by horizontal run, then multiply by 100. A 5 ft rise over 100 ft is \(5/100\times100=5\%\).
How do you convert percent grade to degrees?
Use \(\theta=\tan^{-1}(G/100)\), where \(G\) is percent grade. A 5% grade is approximately 2.86°.
Is a 100% slope vertical?
No. A 100% slope means rise equals horizontal run, which gives a 45° angle. A vertical line has zero horizontal run and therefore no finite percent grade.
What does a 1:12 slope mean?
Using rise:run notation, 1:12 means 1 unit of vertical rise for every 12 units of horizontal run. It equals 8.33% and approximately 4.76°. In U.S. accessibility design, 1:12 is also the general maximum running slope for ADA ramp runs, subject to the rest of the applicable ramp requirements.
Should percent grade use horizontal run or slope length?
Use horizontal run. Slope length is the diagonal distance along the incline and is calculated separately with the Pythagorean theorem.
What is the difference between 5% slope and 5° slope?
A 5% slope is about 2.86°. A 5° slope is \(100\tan(5^\circ)\approx8.75\%\). Percent and degrees are not numerically equivalent.
How do I calculate fall over a known distance?
Rearrange the grade equation: \(\mathrm{rise}=(G/100)\times\mathrm{run}\). For a 2% downward grade over 50 ft, the magnitude of the fall is \(0.02\times50=1\) ft.