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Slope Percentage Calculator

Calculate slope percentage from rise and run, convert grade percent to angle, or solve rise when you know angle and horizontal distance. Built for construction grading, road design, roofing, trails, surveying, and math homework.

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Lab worksheet

Use the same units for rise and run. Decimals are fine. Results update in your browser only.

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Angle

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Slope percent

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Using this calculator

  1. Enter rise and run: slope percent and angle update instantly.
  2. To start from angle, enter run first, then change angle. Rise recalculates with tan(angle) x run.
  3. Scroll down for formulas, examples, and grade conversion notes.

What Is Slope Percentage?

Slope percentage (grade percent) expresses vertical change compared with horizontal distance. The core idea is rise over run: how much you go up or down for each unit you travel across level ground, scaled to 100.

It is not the same as slope angle, though the two convert cleanly. Percent answers how steep in parts per hundred of run; angle answers how steep in degrees. Construction codes, ADA ramp guides, and trail signs may use either format.

A positive slope climbs in the direction of measurement; a negative slope drops. Sign matters for drainage, accessibility, and machine direction, even though the absolute percent is what most maximum-grade tables list.

  • Definition

    Slope % = (rise / run) x 100 when rise and run use the same length units.

  • Rise over run

    Rise is vertical change. Run is horizontal plan distance, not surface length along the slope unless you convert it.

  • Real-world uses

    Roads, roofs, ramps, trails, land grading, rail grades, and coordinate geometry all rely on the same triangle.

Slope Percentage Formula

m = (rise / run) x 100

Angle (degrees) = arctan(rise / run)

rise = run x tan(angle in radians)

Positive slope: rise and run share the same sign convention.

Negative slope: rise is below the starting level while run stays forward.

The grade percentage formula is linear in rise when run is fixed. Double the rise and you double the percent. That is why small measurement errors in rise matter on long runs.

For a deeper walkthrough with sign rules and unit checks, see our <a href="/blog/slope-percentage-formula/" class="text-link underline">slope percentage formula</a> article.

How to Calculate Slope Percentage

You can calculate slope percentage by hand, in a spreadsheet, or with the tool at the top of this page. The method is the same: measure, divide, multiply by 100, then convert to angle if needed.

  1. Measure rise and run: Use consistent units. Record vertical change (rise) and level horizontal distance (run).
  2. Divide rise by run: This ratio is the tangent of the slope angle when both are perpendicular.
  3. Multiply by 100: The product is slope percentage. Example: 3 ft rise over 20 ft run gives 15%.
  4. Optional angle: Use arctan(rise / run) and convert to degrees for equipment or drawings.
  5. Check with the calculator: Enter the same numbers in the panel above to confirm rounding and sign.

Spreadsheet users can place rise in one cell and run in another, then use =(rise/run)*100. See slope percentage in Excel for layout tips.

Step-by-step detail lives in how to calculate slope percentage.

Slope Percentage Examples

Five common situations. Each uses slope % = (rise / run) x 100. Try the numbers in the calculator at the top.

Road slope example

A county road gains 42 ft over 1,400 ft of horizontal run.

  1. Percent: (42 / 1400) x 100 = 3% grade.
  2. Angle: arctan(42/1400) is about 1.72 degrees.

Result: 3% road grade, about 1.72 degrees.

Roof pitch example

Rise is 9 ft over 12 ft run (common pitch language).

  1. Percent: (9 / 12) x 100 = 75% slope on the plan triangle.
  2. Angle: arctan(9/12) is about 36.87 degrees.

Result: 75% slope, about 36.87 degrees. See roof pitch article on the blog.

Wheelchair ramp example

Ramp rises 30 in over 360 in of run (design check).

  1. Percent: (30 / 360) x 100 = 8.33%.
  2. Compare: Many accessibility tables cite maximum running slopes near 8.33% for new ramps (verify local code).

Result: 8.33% grade.

Hiking trail example

Trail climbs 450 m over 3,000 m map distance.

  1. Percent: (450 / 3000) x 100 = 15%.
  2. Angle: arctan(0.15) is about 8.53 degrees.

Result: 15% average grade, about 8.53 degrees.

Land grading example

Pad must fall 1.2 ft across 40 ft for drainage.

  1. Percent: (1.2 / 40) x 100 = 3% away from structure.
  2. Sign: Negative rise if you measure drop in the flow direction.

Result: 3% drainage slope (confirm direction and local spec).

Slope Percentage vs Degrees

Percentage grade and angle describe the same incline with different units. Percent scales rise per hundred units of run; angle reports rotation from horizontal.

Use percent when codes, cut sheets, or ADA tables quote limits as grade. Use degrees when setting rotary lasers, tilt sensors, or discussing roof pitch with trades.

Conversion is trigonometry, not a separate slope type: percent = tan(angle) x 100 when angle is in degrees inside the tangent function.

Slope % = tan(angle) x 100

angle = arctan(slope % / 100)

Grade Percentage Calculator

Grade percentage is another name for slope percentage on roads, rails, and site plans. The calculator at the top of this page is a grade percentage calculator: enter rise and run to read percent and angle together.

Highway engineers watch maximum grades for trucks; trail planners watch average and peak grades for users. Elevation change over plan distance always returns to rise over run.

Read grade percentage calculator for road and terrain examples.

Roof Pitch to Percentage

Roof pitch is often spoken as rise-in-12 run (for example 6:12). Convert to percent with (rise / run) x 100, so 6:12 becomes 50% on the right triangle.

Building standards may list minimum slopes for drainage. Contractors still verify with field measurements because truss layout and crickets change local rise.

Our roof pitch to percentage guide covers common pitches and checks.

Rise Over Run Calculator

Rise over run is the raw ratio behind every slope percent. This page keeps rise, run, angle, and percent synchronized so you can start from whichever field you measured first.

Surveyors and mappers extract rise from elevation data and run from horizontal distance. Engineers label the same legs on section views.

See rise over run calculator for horizontal vs vertical measurement notes.

Slope Percentage Calculator

The interactive tool stays at the top of this page in the lab panel. Enter rise and run for instant slope percent and angle, or enter angle and run to solve rise.

Use it for quick checks before you commit stakes, pour concrete, or sign a grading sheet. No account is required and values do not leave your browser.

Back to the calculator

Common Slope Percentage Mistakes

Most errors are measurement or unit problems, not arithmetic.

Slope Percentage vs Angle

Slope percentage and angle are interchangeable through tan() but they do not grow at the same rate. Near level grades, a small percent change is a tiny angle change; near 45 degrees, percent and angle both climb quickly.

Reports should state which unit was used. Saying a ramp is 8 degrees when the permit expects 8% has very different implications.

For comparison tables and surveying notes, read slope percentage vs degrees.

FAQs About Slope Percentage

What is the slope percentage formula?

Slope percentage = (rise / run) x 100. Rise and run must share the same units and run must not be zero.

How do you convert slope percent to degrees?

Take arctan(slope percent / 100) and express the result in degrees. The calculator does this when rise and run are filled in.

Is grade percent the same as slope percent?

Yes for road and site work. Grade percent, incline percent, and slope percent usually mean rise over run times 100.

What is a 10% slope?

Ten feet (or any unit) of rise for each 100 units of horizontal run. The angle is about 5.71 degrees.

Can slope percent be negative?

Yes when measuring drop in the forward direction. Codes still cite maximum steepness using the absolute value.

Does the calculator send data to a server?

No. All math runs locally in your browser.