Last updated: July 5, 2026
Slope conversion in one line: percent grade is (rise ÷ run) × 100, degrees is arctan(rise ÷ run), and the ratio is 1 : (run ÷ rise). A 6 in rise over 10 ft is a 5 % grade, about 2.9°, or 1 : 20. Percent and degrees only match at gentle slopes. At 100 % grade the angle is 45°, not 100°.
Water Doesn’t Read Your Site Plan: It Follows the Grade
After a heavy rain the homeowner notices a puddle growing against the foundation wall. The yard looked flat, and nobody checked the percent grade before the landscaper finished. Turns out the grade runs at 0.8 % toward the house instead of away from it. Fixing it now means regrading 30 ft of lawn, replacing the sod, and rerouting a downspout. A five-minute slope check would have prevented all of it.
This calculator converts rise and run into percent grade, degrees, and ratio, and compares the result against common drainage and driveway targets. Enter two elevations and the distance between them, or plug in a target slope to find the rise or run you need. It handles the trigonometry. You still bring the tape measure, the laser level, and your local code book.
Percent, Degrees, Ratio: Three Labels for the Same Slope
Percent grade is rise divided by run, multiplied by 100. A 6 ft rise over 80 ft of run is 7.5 %. Degrees come from the arctangent of the same fraction: arctan(6 ÷ 80) ≈ 4.3°. Ratio expresses the relationship as 1 : N. Here that’s 1 : 13.3, one foot of rise for every 13.3 ft of run.
Grade (%) = (Rise ÷ Run) × 100
Angle (°) = arctan(Rise ÷ Run)
Ratio = 1 : (Run ÷ Rise)
For gentle slopes the percent number and the degree number are close (5 % ≈ 2.9°). They diverge as slopes get steeper: 100 % grade is 45°, not 100°. Mixing the two up on a grading plan is one of the fastest ways to order the wrong amount of fill or build a driveway that’s too steep to use in winter.
Grade vs Slope: Is There a Difference?
Not in practice. Grade and slope both describe how steeply the ground rises over a horizontal distance, and site work uses the two words interchangeably. What changes is the unit people reach for. “Grade” is usually written as a percent, like a 5 % grade. “Slope” often shows up as a ratio (1 : 20) or an angle (2.9°). Those are the same pitch in three notations, so a plan calling for a 5 % grade and a spec calling for a 1 : 20 slope are asking for exactly the same thing.
How to Convert Percent Grade to Degrees
Take the arctangent of the grade written as a decimal: degrees = arctan(percent ÷ 100). A 20 % grade is arctan(0.20) = 11.3°. A 10 % grade is arctan(0.10) = 5.7°. The step people skip is dividing by 100 first, because a 20 % grade is a slope of 0.20, not 20. Going the other way, percent = tan(angle) × 100, so 11.3° comes back to about 20 %.
What 1:12, 2:1, and 1 in 80 Mean in Percent and Degrees
Ratios trip people up because the notation runs both directions. A wheelchair ramp at 1 : 12 means one unit of rise for every twelve of run, which is 8.33 % and 4.8°. An earthwork slope written 2 : 1 means the other order, two of run for every one of rise, which is 50 % and 26.6°. “One in eighty” (1 : 80) is a drainage-pipe grade, one of rise per eighty of run, 1.25 % and 0.7°. When a ratio could be read either way, the ramp convention puts rise first and the cut-slope convention puts run first.
Common Grades in Degrees and Ratio
Reach-for-it values, each rounded to one decimal. Angle is arctan(grade); ratio is 1 : (100 ÷ grade).
| Grade | Angle | Ratio (rise:run) |
|---|---|---|
| 1 % | 0.6° | 1 : 100 |
| 2 % | 1.1° | 1 : 50 |
| 5 % | 2.9° | 1 : 20 |
| 8.33 % | 4.8° | 1 : 12 |
| 10 % | 5.7° | 1 : 10 |
| 15 % | 8.5° | 1 : 6.7 |
| 19 % | 10.8° | 1 : 5.3 |
| 20 % | 11.3° | 1 : 5 |
| 25 % | 14.0° | 1 : 4 |
| 33.3 % | 18.4° | 1 : 3 |
| 40 % | 21.8° | 1 : 2.5 |
| 50 % | 26.6° | 1 : 2 |
| 100 % | 45.0° | 1 : 1 |
Drainage and Driveway Targets: How Much Slope Is Enough?
Different surfaces need different grades. Too flat and water ponds; too steep and you get erosion or a driveway that ices over. The table below covers the drainage ranges most codes and field guides agree on.
| Surface | Target grade | Why |
|---|---|---|
| Lawn / yard away from foundation | 2 to 5 % | Keeps water moving without visible erosion |
| Patio or flatwork | 1 to 2 % | Drains without making furniture rock |
| Swale or ditch | 1 to 4 % | Moves runoff to an outlet; over 4 % needs lining |
| Residential driveway | 2 to 12 % | Under 2 % ponds at the garage apron; for the upper limit, check the safe-slope guideline |
| Parking lot cross-slope | 1 to 2 % | Drains toward inlets without tilting cars noticeably |
These are starting-point guidelines for drainage, not code citations. Your jurisdiction may specify tighter ranges, especially for stormwater swales. Always verify with local ordinances.
Backyard Drainage Check: 80 Feet, 6-Inch Rise, One Soggy Foundation
Site: Backyard runs 80 ft from the foundation wall to the property line. A laser level shows the ground is 6 inches (0.5 ft) higher at the property line than at the foundation.
- Current grade: 0.5 ÷ 80 × 100 = 0.625 % (toward the house, the negative direction)
- Drainage target: minimum 2 % away from the foundation for the first 10 ft, then ≥ 1 % to the property line
- Required rise in first 10 ft: 0.02 × 10 = 0.2 ft (2.4 in) drop away from the wall
- Angle equivalent: arctan(0.02) ≈ 1.15°
Right now the yard slopes the wrong way at 0.625 %. To fix it, the first 10 ft must be regraded to fall at least 2.4 in away from the house. The remaining 70 ft can stay gentler (1 % is fine), but the overall direction has to reverse. That means adding fill against the foundation side and smoothing it out, or installing a French drain if regrading isn’t practical.
Slopes That Look Fine Until They Aren’t
- Driveway cross-slope vs longitudinal slope. A driveway at 8 % longitudinal grade may drain well downhill, but if the cross-slope is flat, water sheets across the full width instead of flowing to the edges. Cross-slope should be 1 to 2 % toward one side or crowned in the middle. Miss this and the surface freezes into a skating rink.
- Ponding from too-flat grading. Anything below about 1 % on turf looks flat and acts flat: water sits instead of draining. On clay-heavy soil the problem is worse because infiltration is almost zero. If your laser shows 0.5 % and the soil is clay, assume that section will pond.
- Slope direction that reverses at a midpoint. Checking grade only at the two endpoints misses a low spot in the middle. The grade from A to B reads 2 %, but a belly at 40 ft traps runoff and creates a permanent wet spot. Measure at least one midpoint to catch hidden dips.
What the Calculator Leaves Out
The tool divides rise by run and applies arctan. It doesn’t model soil permeability, runoff volume, pipe sizing, or multi-directional slopes. It assumes a straight line between your two measurement points. Real terrain has dips, crowns, and transitions that only a topographic survey captures. Conversions use standard factors (1 ft = 12 in; 1 m ≈ 3.281 ft). Grading that reroutes drainage or triggers a permit isn't a phone-reading job. Put a licensed civil engineer or surveyor on the design.
Need to know whether a grade is safe or meets driveway and ADA code? Check it with the safe-slope checker. Estimating cut-and-fill volumes for a grading project? Try the mass-balance calculator. Planning a retaining wall where the grade is too steep to hold? Use the retaining wall estimator.
How the numbers are derived. Degrees are the arctangent of rise over run, the inverse-trig identity defined in the NIST Digital Library of Mathematical Functions. The 1:12 (8.33 %) wheelchair-ramp maximum is the US Access Board’s ADA ramp figure, not a rule of thumb. Driveway grade caps are local, so confirm yours against the code your city publishes (many sit on Municode).