Rise Over Run Calculator
Enter a rise and a run to get the simplified rise:run ratio, the decimal slope, the percent grade, and the angle in degrees - with a labeled triangle diagram and every calculation step shown.
Calculator
Enter rise & run
Your rise over run expressed as a percentage: grade = 100 × rise ÷ run
Diagram
Rise-run triangle
Show your work
Step-by-step
Reference
Common rise:run slopes
| Use case | Ratio | Slope | Grade | Angle |
|---|
Worked examples
Calculated step by step
Example 1: a gentle ramp: rise 6 ft, run 12 ft
Ratio 1:2 (already simplest) → slope 0.5 → percent grade 50% → angle 26.57°; slope length 13.42 ft.
Example 2: a typical stair: rise 7 in, run 11 in
Ratio 7:11 (already simplest) → slope 0.6364 → percent grade 63.64% → angle 32.47°; slope length 13.04 in.
Example 3: an ADA-max ramp: rise 1 ft, run 12 ft
Ratio 1:12 (already simplest) → slope 0.0833 → percent grade 8.33% → angle 4.76°; slope length 12.04 ft.
Not the tool you need?
- This calculator goes one way: rise + run → ratio, slope, percent grade, and angle, with a diagram and worked steps.
- For two-way conversion (type a percent grade or an angle and solve back for rise/run), use our rise-run-degrees-calculator.
- For the equation of a line through two coordinate points (x₁,y₁) and (x₂,y₂) - slope-intercept, standard, and point-slope forms - use line-equation-from-two-points. That tool takes points; this one takes rise and run directly.
- For converting between percent and part-to-part ratios, see percent-to-ratio-calculator; for model-railroad grades, see railroad-grade-lab.
Methodology
Formulas used
Percent grade compares vertical change to horizontal distance, not to the slope length: a 100% grade means rise equals run, which is a 45° angle - not a vertical wall. A truly vertical rise has an infinite percent grade.
FAQ
Rise over run questions
What is rise over run?
Rise over run is the ratio of vertical change (rise) to horizontal distance (run). It is the same idea as slope in algebra: slope m = rise ÷ run. A rise of 3 over a run of 4, for example, is the ratio 3:4 and a slope of 0.75.
How do you calculate rise over run?
Divide the rise by the run. Example: a rise of 6 ft over a run of 12 ft gives 6 ÷ 12 = 0.5. The simplified ratio is 1:2, because the greatest common divisor of 6 and 12 is 6.
How do I convert rise over run to a percent grade?
Multiply by 100: percent grade = 100 × rise ÷ run. Example: a 1:12 wheelchair ramp is 100 × 1 ÷ 12 = 8.33%. Percent grade is the headline number this calculator shows first.
How do I convert rise over run to degrees?
Take the arctangent of the slope: angle = atan(rise ÷ run), expressed in degrees. Example: a 1:12 ramp is atan(1 ÷ 12) = 4.76°.
Is a 100% grade the same as 45 degrees?
Yes. When rise equals run - for example 5 over 5 - the slope is 1, the percent grade is 100 × 1 = 100%, and atan(1) = 45°. A common mistake is thinking 100% means a vertical wall; a truly vertical rise has an infinite percent grade, not 100%.
What percent grade is a staircase or an ADA ramp?
A typical stair with a 7-inch rise and an 11-inch run is 100 × 7 ÷ 11 = 63.64% (32.47°). The ADA maximum slope for a wheelchair ramp is 1:12, which is 8.33% (4.76°).
How do you simplify a rise:run ratio?
Divide both numbers by their greatest common divisor (GCD). Example: 6:12 - the GCD of 6 and 12 is 6, so 6:12 simplifies to 1:2. A ratio like 7:11 is already in lowest terms because 7 and 11 share no common divisor.
Is roof pitch the same as rise over run?
Yes. A 4/12 roof pitch means a rise of 4 over a run of 12: a slope of 0.3333, a percent grade of 33.33%, and an angle of 18.43°.
What does a negative rise over run mean?
A downhill slope. Example: a rise of -5 over a run of 12 gives a slope of -0.4167, a percent grade of -41.67%, and an angle of -22.62°.
How is this different from the rise-run-degrees converter?
This calculator goes one direction: rise + run → simplified ratio, slope, percent grade, and angle, with a triangle diagram and step-by-step working. If you want to convert the other way - type a percent grade or an angle and solve back for rise and run - use our rise-run-degrees-calculator instead.
Free tool by NRTechStudio