Quick answer
Slope = rise ÷ run, grade = slope × 100% and angle = arctan(slope). A rise of 3 over a run of 12 is a slope of 0.25, a 25% grade and an angle of 14.04°.
Enter the rise and the run. The calculator returns slope, grade and angle.
Related tools: Area Calculator: Area of common two-dimensional shapes. Right Triangle Calculator: Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter. Pythagorean Theorem Calculator: Find the hypotenuse or a missing leg of a right triangle.
How to use the Rise Over Run Calculator
- Enter rise.
- Enter run.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Rise | A number | — |
| Run | A number | — |
Formula and method
Formula
slope = rise ÷ run; grade = slope × 100%; angle = arctan(slope)
IEEE-754 double precision; shown to the decimals indicated.
Rise and run must use the same unit. Informational estimate, not medical advice. Talk to a qualified health professional about your own situation.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Rise = 3; Run = 12.
| Result | Value |
|---|---|
| Slope (rise ÷ run) | 0.25 |
| Grade | 25% |
| Angle | 14.0362° |
Example 2
Inputs: Rise = -2; Run = 5.
| Result | Value |
|---|---|
| Slope (rise ÷ run) | -0.4 |
| Grade | -40% |
| Angle | -21.8014° |
Example 3
Inputs: Rise = 7; Run = 7.
| Result | Value |
|---|---|
| Slope (rise ÷ run) | 1 |
| Grade | 100% |
| Angle | 45° |
The first line is the headline result (slope (rise ÷ run)). Below it the rise Over Run Calculator lists grade and angle, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Everyday slopes
A wheelchair ramp is limited to 1:12 (8.33%, 4.76°). A steep road sign of 10% is a rise of 10 per 100. A 25% grade is too steep for most roads, but typical for a staircase section.
Units
Rise and run must be in the same unit. Run cannot be zero. Roof pitch is expressed per 12, so a rise of 3 over 12 is a 3:12 pitch.
How the result changes with rise
Holding every other input at the first worked example, this table changes only rise. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Rise | Slope (rise ÷ run) | Grade | Angle |
|---|---|---|---|
| 1.5 | 0.125 | 12.5% | 7.125° |
| 3 | 0.25 | 25% | 14.0362° |
| 6 | 0.5 | 50% | 26.5651° |
| 12 | 1 | 100% | 45° |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Run: entering "0" shows "Run cannot be zero." beside that field and no result.
- Rise: left empty shows "Enter rise." beside that field and no result.
Choosing between the Rise Over Run Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Right Triangle Calculator](/math/right-triangle-calculator/) | leg a and leg b | Hypotenuse c |
| [Pythagorean Theorem Calculator](/math/pythagorean-theorem-calculator/) | find, leg a and other side | Hypotenuse c |
| [Triangle Calculator](/math/triangle-calculator/) | side a, side b and side c | Area |
| [Circle Calculator](/math/circle-calculator/) | i know the and value | Area |
Background: fitness estimates
Fitness formulas are estimates whose accuracy depends on the input. One-rep-max formulas such as Epley and Brzycki give different answers, and predictions from hard sets of a few repetitions are better than from sets of ten or more. Age-based maximum heart rate formulas can be off by 10 to 30 beats a minute for an individual; Tanaka's 208 − 0.7 × age is generally preferred to 220 − age but is still an estimate.
Pace models built from a race result assume a maximal effort and work best for distances from about 5 km to the marathon. Use the output as a guide, not a prescription.
Assumptions and limitations
- Run cannot be zero
- Not a diagnosis
Estimates from formulas describe averages. They are not a training or medical prescription; check with a qualified professional before changing your exercise or diet.
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for run and rise to confirm this.
Frequently asked questions
How do I convert grade to angle?
Angle = arctan(grade ÷ 100).
What is a 45° slope?
A 45° slope has a rise equal to the run, which is a 100% grade.
What is the ADA ramp slope?
ADA ramps are limited to 1:12 (8.33%, about 4.76°), meaning 1 inch of rise per 12 inches of run.
What does the Rise Over Run Calculator calculate?
Slope, grade and angle from rise and run. It returns Slope (rise ÷ run), Grade and Angle.
What formula does the Rise Over Run Calculator use?
slope = rise ÷ run; grade = slope × 100%; angle = arctan(slope). Rise and run must use the same unit.
What do I need to enter in the rise Over Run Calculator?
You enter Rise and Run.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Run cannot be zero.
What are the limits of this calculator?
Run cannot be zero. Not a diagnosis.
What is an example of a rise Over Run result?
With rise 3 and run 12, the slope (rise ÷ run) is 0.25.
Can I rely on this calculator for a decision?
Estimates from formulas describe averages. They are not a training or medical prescription; check with a qualified professional before changing your exercise or diet. For this calculator in particular: Run cannot be zero.
Related calculators
- Area Calculator — Area of common two-dimensional shapes.
- Right Triangle Calculator — Solve a right triangle from its two legs: hypotenuse, angles, area and perimeter.
- Pythagorean Theorem Calculator — Find the hypotenuse or a missing leg of a right triangle.
- Triangle Calculator — Area, perimeter, angles and type of a triangle from its three sides.
- Circle Calculator — Radius, diameter, circumference and area of a circle from any one of them.
- Circumference Calculator — Circumference of a circle.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.