Slope Percentage Calculator
Calculate slope as a percentage grade from rise and run, or convert between degrees and percent grade. Essential for road design, accessibility ramps, and construction.
How to Use
- Rise & Run tab: Enter the vertical rise and horizontal run in the same units (feet, meters, etc.). The calculator computes the grade percentage and angle automatically.
- Degrees → Grade % tab: Enter an angle in degrees to find the equivalent grade percentage. Useful when working from architectural drawings.
- Grade % → Degrees tab: Enter a grade percentage (e.g. 8.33%) to find the equivalent angle in degrees.
- Units do not matter as long as rise and run use the same unit.
What You'll Discover
- Grade % — in the Rise & Run tab, the slope as a percentage: rise ÷ run × 100. A negative rise gives a negative (downhill) grade.
- Angle in degrees — the same slope as an angle from horizontal, found with the arctangent of rise ÷ run.
- Ratio (1 in X) — how many units of run you travel for each unit of rise. 1 in 12 is the same slope as 1:12 or 8.33%.
- Degree and grade conversions — the Degrees → Grade % and Grade % → Degrees tabs convert one value directly, without rise and run.
Results are rounded to two decimal places. A run of zero would be a vertical wall with no defined grade, so the calculator shows no result; the Degrees tab accepts angles between −90° and 90°, not including those limits.
Formula
Grade % from rise and run:
Grade % = (Rise ÷ Run) × 100
Angle from rise and run:
Angle = arctan(Rise ÷ Run) × (180 ÷ π)
Grade % from degrees:
Grade % = tan(Degrees × π ÷ 180) × 100
Degrees from grade %:
Degrees = arctan(Grade ÷ 100) × (180 ÷ π)
Key reference points: A 100% grade = 45°. A 0% grade is perfectly flat. Negative grades indicate a downhill slope.
Slope Percentage to Degrees and Ratio: Conversion Table
Grade and angle are not proportional. A 10% grade is about 5.71°, not 10°, and a 100% grade is 45°. Use this table for common values; all figures are rounded to two decimal places.
| Grade % | Angle | Ratio (1 in X) |
|---|---|---|
| 1% | 0.57° | 1 in 100 |
| 2% | 1.15° | 1 in 50 |
| 2.08% | 1.19° | 1 in 48 |
| 5% | 2.86° | 1 in 20 |
| 8.33% | 4.76° | 1 in 12 |
| 10% | 5.71° | 1 in 10 |
| 12.5% | 7.13° | 1 in 8 |
| 15% | 8.53° | 1 in 6.67 |
| 20% | 11.31° | 1 in 5 |
| 25% | 14.04° | 1 in 4 |
| 33.33% | 18.43° | 1 in 3 |
| 50% | 26.57° | 1 in 2 |
| 100% | 45° | 1 in 1 |
| 173.21% | 60° | 1 in 0.58 |
For small slopes there is a handy shortcut: each degree is roughly 1.75% of grade. It works well below about 10° (10° is actually 17.63%) and breaks down on steep slopes.
ADA Ramp Slope Requirements
In the United States, the 2010 ADA Standards for Accessible Design set these limits for ramps. Section 106.5 defines a ramp as a walking surface with a running slope steeper than 1:20 (5%).
| Requirement | Limit | Section |
|---|---|---|
| Maximum running slope | 1:12 (8.33%, about 4.76°) | 405.2 |
| Maximum cross slope | 1:48 (about 2.08%) | 405.3 |
| Minimum clear width | 36 inches | 405.5 |
| Maximum rise per ramp run | 30 inches | 405.6 |
| Minimum landing length | 60 inches | 405.7.3 |
| Handrails required | When a ramp run rises more than 6 inches, on both sides | 405.8, 505.2 |
For existing sites with space limits, section 405.2 allows a steeper slope only for short rises: up to 1:10 (10%) for a rise of 6 inches or less, and up to 1:8 (12.5%) for a rise of 3 inches or less. A slope steeper than 1:8 is not permitted. Local building codes may add further rules, so check with your local authority before you build.
To size a ramp, multiply the rise by 12 to get the minimum run. A 24-inch rise needs at least 288 inches (24 feet) of run.
Examples
| Rise | Run | Grade % | Angle |
|---|---|---|---|
| 3 ft | 20 ft | 15% | 8.53° |
| 1 m | 12 m | 8.33% | 4.76° |
| 6 ft | 100 ft | 6% | 3.43° |
| 1 ft | 1 ft | 100% | 45° |
| 10 m | 50 m | 20% | 11.31° |
Slope Notations and Common Mistakes
Ratio formats run in different directions
Accessibility rules write slope as rise:run, so 1:12 means 1 unit up for every 12 across. Earthwork and landscape drawings often use horizontal:vertical, so a "3:1" embankment means 3 across for every 1 up, which is 33.33% (about 18.43°). Roof pitch is written as rise per 12 units of run: a 6/12 roof is 50%, or about 26.57°. Always check which convention a drawing uses.
Measuring along the slope instead of horizontally
Run is the horizontal distance, not the length along the surface. If you measure 20 ft along a ramp that rises 2 ft, the true run is √(20² − 2²) ≈ 19.90 ft, and the grade is about 10.05%, not 10%. The difference is small on gentle slopes and grows as slopes get steeper.
Downhill and very steep slopes
A negative rise gives a negative grade, which simply means downhill: a road that drops 50 m over 1,000 m is −5%, or about −2.86°. Grades above 100% are steeper than 45°; a 60° slope is about 173.21%. As the angle approaches 90°, the grade grows without limit.
What Is the Slope Percentage If...
What is the slope percentage if a ramp rises 2 ft over 24 ft?
A 2 ft rise over a 24 ft run is an 8.33% grade, about 4.76°. 2 ÷ 24 × 100 ≈ 8.33%. That is a 1:12 slope, the maximum running slope for a new ADA ramp.
What is the slope percentage if the rise is 1 m over a 5 m run?
1 m of rise over 5 m of run is a 20% grade, about 11.31°. The ratio is 1 in 5.
What is the slope percentage of a 10 degree angle?
A 10° slope is about a 17.63% grade. tan(10°) ≈ 0.1763, and × 100 gives 17.63%. Going the other way, a 10% grade is only about 5.71°.
What is the slope percentage of a 30 degree angle?
A 30° slope is about a 57.74% grade. tan(30°) ≈ 0.5774. Every 100 units across, the surface climbs about 57.74 units.
What is the slope percentage if a driveway climbs 3 ft over 40 ft?
3 ft over 40 ft is a 7.5% grade, about 4.29°. 3 ÷ 40 × 100 = 7.5%, a ratio of about 1 in 13.33.
What is the slope percentage if a road drops 50 m over 1 km?
A 50 m drop over 1,000 m is a −5% grade, about −2.86°. Enter the rise as −50 and the run as 1,000. The minus sign marks a downhill grade.
What is the slope percentage of a 3:1 embankment?
A 3:1 (horizontal:vertical) slope is about 33.33%, or 18.43°. Enter a rise of 1 and a run of 3. If your drawing means 3 up for every 1 across, the grade is 300% instead.
What is the slope percentage of a 6/12 roof pitch?
A 6/12 roof pitch is a 50% slope, about 26.57°. Enter a rise of 6 and a run of 12. A 12/12 pitch is 100%, or 45°.
How long must a ramp be for a 24-inch rise?
At the 1:12 ADA maximum, a 24-inch rise needs at least 288 inches (24 ft) of horizontal run. 24 × 12 = 288. The rise is under the 30-inch limit per ramp run, so a single run can work. Because the rise is over 6 inches, handrails are needed on both sides.
What is the slope percentage if I measured 20 ft along the slope with a 2 ft rise?
The grade is about 10.05%, not 10%, because 20 ft is the sloped length, not the run. The horizontal run is √(400 − 4) ≈ 19.90 ft, and 2 ÷ 19.90 × 100 ≈ 10.05%.
People Also Search For
How to convert slope percentage to degrees
Take the arctangent of the grade divided by 100. For 15%: arctan(0.15) ≈ 8.53°. On a scientific calculator, make sure it is in degree mode, or multiply a radian answer by 180 ÷ π.
How to convert degrees to slope percentage
Take the tangent of the angle and multiply by 100. For 5°: tan(5°) ≈ 0.0875, so the grade is about 8.75%.
How to calculate slope from rise and run
Divide the rise by the run. The result is the slope as a decimal (m in y = mx + b). Multiply by 100 for percent grade: a rise of 4 over a run of 20 is 0.2, or 20%.
What is a 1:12 slope in percent?
A 1:12 slope is about 8.33%, or 4.76°. 1 ÷ 12 × 100 ≈ 8.33%. It is the maximum running slope for new ramps under the 2010 ADA Standards.
How to calculate run from rise and slope percentage
Divide the rise by the grade as a decimal. A 1 m rise at 5% needs 1 ÷ 0.05 = 20 m of run. At 8.33% (1:12), a 30-inch rise needs 360 inches, or 30 ft.
Is slope percentage the same as angle?
No. Percentage compares rise with run, while the angle is measured from horizontal. They are close only for very gentle slopes. 45° is 100%, and 90° has no finite percentage.
Frequently Asked Questions
What does a 10% road grade mean?
A 10% road grade means that for every 100 units of horizontal distance (run), the road rises or falls 10 units vertically. In practical terms, driving 1,000 feet horizontally on a 10% grade means you climb (or descend) 100 feet. This equals approximately 5.71 degrees of angle.
What is the maximum grade for an ADA-compliant wheelchair ramp?
Under the 2010 ADA Standards (section 405.2), a new ramp run can be no steeper than 1:12, which equals 8.33% grade or about 4.76 degrees. For every 1 inch of vertical rise, the ramp must extend at least 12 inches horizontally. A ramp run that rises more than 6 inches needs handrails on both sides (sections 405.8 and 505.2), and each run can rise at most 30 inches (section 405.6).
Why does a 100% grade equal 45 degrees and not 90 degrees?
Grade percentage is the ratio of rise to run multiplied by 100, not the ratio of rise to the hypotenuse. A 100% grade means rise equals run, which forms a 45-degree angle (an isosceles right triangle). A 90-degree angle would require an infinite grade percentage because the run would be zero — a perfectly vertical wall.
How do hiking trails describe slope difficulty?
Trails are often described by average grade: total elevation gain divided by horizontal distance. A trail that climbs 300 m over 3 km of horizontal distance averages 10%. There is no single standard for what counts as easy or hard, and short sections can be much steeper than the average, so check the steepest pitch as well.
Can I use different units for rise and run?
No — rise and run must be in the same units for the formula to work correctly. If rise is in feet, run must also be in feet. If rise is in meters, run must be in meters. The grade percentage is dimensionless (a ratio), so the unit cancels out. Converting rise to meters and leaving run in feet would give an incorrect result.
Can slope percentage be negative?
Yes. A negative grade means the surface goes downhill in the direction you are measuring. Enter a negative rise to get it: −5 over 100 is −5%, or about −2.86°.
Can slope percentage be over 100%?
Yes. Any slope steeper than 45° has a grade above 100%. A 60° slope is about 173.21%, and a 75° slope is about 373.21%.
What does the "1 in X" ratio mean?
It shows how many units of run you cover for each unit of rise. A 3 ft rise over 20 ft is 1 in 6.67. A larger X means a gentler slope: 1 in 20 is 5%, while 1 in 8 is 12.5%.
Why is a 10% grade not 10 degrees?
Grade is based on the tangent of the angle, which is not a straight-line relationship. A 10% grade is about 5.71°, and a 10° angle is about 17.63%. Use the Degrees → Grade % or Grade % → Degrees tab to convert exactly.
Is my data stored or sent anywhere?
No. All calculations run in your browser. Nothing you type is sent to a server or saved, and no account is needed.
Last reviewed: November 2026 — formulas and worked examples verified.