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FigureCalc

Rise Over Run Calculator

By Uzair Arshad , Senior Civil and Structural Engineer

Last updated: June 6, 2026

An 8 ft rise over a 20 ft run is a 40 percent slope, 21.8 degrees, or a 4.8/12 roof pitch. That same ratio works as a stair stringer angle or driveway grade — but ADA caps wheelchair ramps at 1:12 (8.3 percent). This calculator returns slope, percent grade, angle in degrees, roof pitch in /12, and the actual ramp length from your rise and run. Common pitfall: confusing the rise/run ratio (8/20 = 0.40) with the slope-distance ratio (8/21.5 = 0.37) — they are not the same.

How to use this calculator

This rise over run calculator converts measured rise and run into slope, angle, percent grade, and roof pitch in one step. Choose your input method, enter your numbers, and read all conversion results at once.

  1. Select your input method. Choose "Rise and run" if you measured vertical and horizontal distances. Use "Two points" for graph or survey coordinates. Choose "Known angle" or "Known grade" to reverse-calculate rise and run from an existing measurement.
  2. Enter rise and run using the same real-world unit. If your rise is in inches, your run should be in inches too. Mixed units produce incorrect slope results.
  3. For graph problems, enter the coordinates of two points (X1, Y1) and (X2, Y2). The calculator finds rise as Y2 minus Y1 and run as X2 minus X1 automatically.
  4. Click "Calculate slope" to see the slope ratio, decimal slope, percent grade, angle in degrees, and pitch in 12.
  5. Use percent grade for roads and ramps. Use pitch in 12 for roof framing. Use angle in degrees for saw cuts and layout angles.

Pro tip: always measure horizontal run, not the diagonal board length. Measuring along the slope instead of the level ground is one of the most common field mistakes and changes the slope result significantly.

Common slope quick reference

Use this table to sanity-check your rise over run calculation. It covers typical slopes for roofs, stairs, and ramps.

Rise : Run Slope Grade Angle Typical use
1 : 120.0838.3%4.76°ADA ramp maximum slope
4 : 120.33333.3%18.43°Low-slope shingle roof
6 : 120.50050.0%26.57°Common residential roof
7 : 100.70070.0%34.99°Typical residential stair
10 : 120.83383.3%39.81°Steep residential roof

How the calculation works 

Core:
Slope = Rise / Run
Percent grade = Slope × 100
Angle (degrees) = atan(Slope) × (180 / π)
Pitch in 12 = Slope × 12

Two points:
Rise = Y2 - Y1
Run = X2 - X1
Slope = Rise / Run

Reverse from angle:
Slope = tan(Angle × π / 180)

Reverse from percent grade:
Slope = Percent grade / 100
Rise
Vertical change between two points or heights
Run
Horizontal distance between the same two points
Slope
Rise divided by run, expressed as a decimal
Percent grade
Slope multiplied by 100, common for roads and ramps
Angle
Incline angle in degrees, used for cutting and layout
Pitch in 12
Inches of rise per 12 inches of run, standard roof notation

The rise over run formula divides vertical change (rise) by horizontal change (run) to produce slope. From that single number, the calculator converts to every other format you might need for construction, grading, or graphing.

Slope = Rise / Run. Both measurements must use the same unit. This rise over run calculator works in feet, inches, or any consistent unit. If rise is 6 inches and run is 24 inches, slope = 6 / 24 = 0.25.

Percent grade = Slope × 100. A 0.25 slope is a 25% grade. Roads and ramps commonly use percent grade for specifications.

Angle = atan(Slope) × (180 / π). A 0.25 slope converts to about 14.04 degrees. Use degrees to convert rise over run into saw cuts, layout angles, and CAD work.

Pitch in 12 = Slope × 12. A 0.25 slope is a 3 in 12 pitch. Roofers and framers read pitch as inches of rise per 12 inches of horizontal run.

Worked example

Given: 6 inches of rise over 24 inches of run.

  • Slope = 6 / 24 = 0.25
  • Percent grade = 0.25 × 100 = 25%
  • Angle = atan(0.25) × (180 / π) = 14.04 degrees
  • Pitch in 12 = 0.25 × 12 = 3 in 12

This means the surface rises 3 inches for every 12 inches of horizontal distance. For a roof, that's a relatively gentle slope. For a ramp, it's much steeper than ADA's maximum 1:12 (8.3%) guideline.

Quick rule

  • Slope = Rise / Run (same units required)
  • Multiply slope by 100 for percent grade
  • Multiply slope by 12 for roof pitch in 12

Two-point method (graph use)

For coordinates, rise = Y2 minus Y1 and run = X2 minus X1. Points (3, 2) and (7, 5) give rise = 3 and run = 4, so slope = 3 / 4 = 0.75. Keep the sign consistent: always subtract in the same direction to avoid flipping the slope. Note that run over rise gives the inverse (4 / 3 = 1.33), which some graphing problems use for horizontal distance per unit of vertical change.

Common mistakes this calculator helps prevent

Measuring the diagonal board length instead of the horizontal run is the most common field error. The diagonal is always longer than the run, so using it gives a slope that's lower than the actual incline.

Mixing units is another frequent mistake. If rise is in inches and run is in feet, your slope will be off by a factor of 12. Convert both to the same unit before dividing.

For stairs, total rise and total run give the overall pitch, but individual riser height and tread depth still need separate checks against local building codes.

Assumptions and limitations

This rise over run calculator assumes a straight-line slope. It does not account for curves, transitions, or compound angles. Roof pitch results use standard X in 12 notation and assume a uniform slope. For ramp projects, percent grade helps compare incline, but accessibility compliance requires project-specific code review. Always verify field measurements before cutting or building.

Frequently Asked Questions

How do you calculate rise over run?

Divide rise by run with both measurements in the same unit. A 6 in rise over a 24 in run = 6 / 24 = 0.25, which is a 25 percent grade and about 14.04 degrees. Multiply the decimal result by 100 to convert to percent grade, or take arctan(rise/run) in degrees for the angle. Roof pitch is expressed as rise per 12 in of run, so 0.25 × 12 = 3 in 12 pitch. Worked example: a wheelchair ramp that rises 24 in over a 288 in run (24 ft) = 0.083, or 8.3 percent, or 1:12 — exactly the ADA maximum slope. Common mistake: using different units for rise and run without converting — 6 in over 2 ft accidentally entered as 6/2 = 3.0 (a 300 percent grade, near-vertical) instead of the correct 6/24 = 0.25. Always convert both numbers to the same unit before dividing.

How do you calculate slope from rise over run?

Slope equals rise divided by run. A board that rises 3 ft over a 12 ft horizontal run has a slope of 0.25, which converts to a 25 percent grade, 14.04 degrees, or a 3 in 12 pitch. Use the same units for both rise and run before dividing — feet over feet, inches over inches. Keep the rise negative when calculating downhill slope, especially for drainage calculations where direction matters. Worked example: a French drain pipe with 1 in fall per 10 ft horizontal run has a slope of 1/120 = 0.0083, which is the 1 percent minimum drainage grade. Common mistake: using horizontal distance versus actual board length interchangeably — they differ. Run is the horizontal projection (the shadow on the ground), not the diagonal length of the board itself. For a 12 ft long ramp board at 25 percent slope, the actual run is 11.65 ft, not 12 ft.

How do you calculate rise over run for a roof?

Roof pitch uses vertical rise per 12 in of horizontal run. A roof that rises 6 in over 12 in of horizontal run is a 6 in 12 pitch — same as a 50 percent grade, 0.5 slope, or 26.57 degrees. Common residential roofs run from 4 in 12 (low) to 12 in 12 (very steep). Anything below 2 in 12 needs a sealed membrane instead of shingles because water sits too long. Worked example: a gable roof spanning 24 ft total (12 ft per side) at 6 in 12 pitch has a vertical rise of 6 ft at the ridge — rise = 12 × (6/12) = 6 ft. The rafter length is √(12² + 6²) = 13.42 ft per side. Common mistake: confusing roof pitch with roof slope angle — pitch is rise/12, slope is rise/run as a decimal, and angle is in degrees. They describe the same thing but are not interchangeable numbers.

How do you calculate rise over run for stairs?

Stair calculations use total stair rise divided by total horizontal run. A staircase with 49 in of total rise over 70 in of total run has a slope of 49/70 = 0.7, or 35 degrees, which is at the upper end of comfortable residential stairs. But the bigger constraint is per-step compliance: IRC R311.7 caps the riser at 7.75 in maximum and requires a tread depth of 10 in minimum. Worked example: a 49 in total rise needs at least 49 / 7.75 = 7 risers (rounded up), so each step has 49/7 = 7 in rise. The total horizontal run is 7 treads × 10 in = 70 in (or 6 treads if the top landing counts as the seventh). Common mistake: dividing total rise by an arbitrary number of risers without checking per-step compliance — riser heights over 7.75 in are a code violation and a tripping hazard, especially for older homeowners.

How do you calculate rise over run on a graph?

Pick two clear points, subtract y values to get rise, and subtract x values to get run. For points (3, 2) and (7, 5), rise = 5 − 2 = 3 and run = 7 − 3 = 4, so the slope is 3/4 = 0.75. Always subtract the same point's coordinates in the same order: if you start with the first point's y, also start with the first point's x. Worked example: for points (1, 8) and (5, 2), rise = 2 − 8 = -6 (negative because the line descends) and run = 5 − 1 = 4, slope = -6/4 = -1.5. Negative slope means the line goes downhill from left to right. Common mistake: subtracting in inconsistent order — using y₂ − y₁ for rise but x₁ − x₂ for run inverts the sign and gives the wrong slope direction. Always go in the same order on top and bottom.

What does rise over run calculate?

Rise over run calculates slope — the steepness of any inclined surface or line. It compares vertical change (rise) to horizontal change (run). The same incline can be expressed four ways: as a decimal (0.25), as a percent grade (25 percent), as an angle in degrees (14.04°), or as a roof pitch (3 in 12). All four are mathematically equivalent. Worked example: an 8 in rise over a 32 in run = 0.25 slope = 25 percent grade = 14.04 degrees = 3 in 12 pitch. The decimal form drives most engineering and code calculations (ADA caps wheelchair ramps at 1:12 = 0.083, IRC caps stair slope at about 0.83). Common mistake: assuming a 100 percent grade is vertical — it's actually 45 degrees, because a 100 percent grade means rise equals run (1:1). A vertical wall is infinite percent grade or 90 degrees, not 100 percent.

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