ToolwickSlope Percent to Degrees & Inches-per-Foot Calculator
Need to turn a percent slope to degrees, inches per foot or a 1:N ratio? This percent slope to degrees inches per foot calculator converts between all four, shows tape-measure fractions to 1/16", and works out the total rise over any run you enter.
How to Use This Slope Converter
Choose the unit you already know (percent, degrees, inches per foot, or a 1:N ratio), type the value, and press Calculate. You get the slope in every other unit, tape-measure fractions, and a check against common code limits. Add a horizontal run to see the exact rise over that distance, or drag the slider for a quick comparison between grades.
Why This Matters
Slope shows up in almost every build, and each trade speaks a different language. Civil drawings and grading plans use percent. Carpenters and plumbers think in inches per foot because that is what a tape measure and a 4-foot level give them. Digital levels and phone apps often read degrees. A mix-up between them is how a patio ends up draining toward the house or a ramp ends up too steep to pass inspection.
Some real numbers: a 20-foot patio that falls ¼" per foot drops 5" end to end. A 40-foot drain line at ¼" per foot drops 10". A digital level reading 1.2° looks small, but it is 2.09%, which is already above the 2.08% (¼" per foot) many drainage rules of thumb call for. Percent slope is also not "out of 90": 100% is a 45° angle, and a 12:12 roof is 100%. Converting before you cut, dig or pour keeps the numbers consistent across the plan, the level and the tape.
How It's Calculated
Every slope is a ratio of vertical rise to horizontal run. Call that ratio s (rise ÷ run). Everything else follows from it:
- Percent = s × 100
- Degrees = arctan(s) × 180 ÷ π (and from degrees, s = tan(angle))
- Inches per foot = s × 12 (this is also the "x" in an x:12 roof pitch)
- Ratio 1 : N, where N = 1 ÷ s (N units of run per 1 unit of rise)
- Total rise = run × s, and surface length = run × √(1 + s²)
Tape-measure fractions are rounded to the nearest 1/16". Because rounding direction matters, the tool also shows the value rounded down and rounded up. Round up when you must meet a minimum slope (drainage) and round down when you must stay under a maximum (accessible ramps).
| Inches per foot | Percent | Degrees | Ratio |
|---|---|---|---|
| ⅛" | 1.04% | 0.60° | 1 : 96 |
| ¼" | 2.08% | 1.19° | 1 : 48 |
| ½" | 4.17% | 2.39° | 1 : 24 |
| 1" | 8.33% | 4.76° | 1 : 12 |
| 2" | 16.67% | 9.46° | 1 : 6 |
| 3" | 25.00% | 14.04° | 1 : 4 |
| 6" | 50.00% | 26.57° | 1 : 2 |
| 12" | 100.00% | 45.00° | 1 : 1 |
The reference check follows the 2010 ADA Standards (§405.2, §403.3, §405.3), the 2021 IPC §704.1 for drain pipe, and the 2021 IRC §R401.3 (lot grading) and §R905.2.2 (asphalt shingle slope). Local codes vary and may be stricter. This tool is a calculation aid, not engineering, permit or inspection approval.
Worked Example
Say you are setting a 10-foot patio edge and want a 2% fall away from the house (these are the tool's default values).
- Slope ratio: s = 2 ÷ 100 = 0.02.
- Angle: arctan(0.02) = 1.146°.
- Inches per foot: 0.02 × 12 = 0.24". In sixteenths that is 3.84, so the nearest mark is 4/16 = ¼", rounded down is 3/16", and rounded up is ¼".
- Ratio: 1 ÷ 0.02 = 50, so the slope is 1 : 50.
- Total rise over 10 ft (120"): 120 × 0.02 = 2.4" (60.96 mm). Nearest 1/16" is 2⅜"; rounded up is 2 7/16".
- Surface length: 120 × √(1.0004) = 120.02", about 10.002 ft, so the slope barely changes the length.
The reference check shows 2% is within the ADA 1:12 and 1:48 maximums, but slightly below a ¼" per foot minimum (2.083%). If your spec says ¼" per foot, round up and use 2 7/16" over 10 ft, or better, enter 0.25 inches per foot directly.
Tips & Common Mistakes
- Percent is not degrees. A 100% slope is 45°, not 90°. Small slopes are nearly equal in both (1% ≈ 0.57°), but they diverge quickly above 10%.
- Measure the run horizontally, not along the sloped surface. Using the surface length as the run understates the slope slightly.
- Round in the safe direction. Up for minimum drainage slopes, down for maximum ramp slopes. Rounding to the "nearest" can land on the wrong side of a code limit.
- Roof pitch is inches per foot. A 6:12 pitch is 6 in/ft, which is 50% or 26.57°. It is not 6 degrees.
- Check your level. Many digital levels let you switch between degrees, percent and in/ft, but verify calibration by flipping the level end for end on a flat surface before trusting it for a ¼" per foot fall.
Frequently Asked Questions
How do I convert percent slope to degrees?
Divide the percent by 100, then take the inverse tangent (arctan) and read the result in degrees. For example, 8% becomes arctan(0.08) = 4.57°. This calculator does it automatically.
What is ¼ inch per foot in percent and degrees?
¼ inch per foot is 0.25 ÷ 12 = 2.083%, which is about 1.19° or a 1:48 ratio. It is a common minimum for drain pipe up to 2½" and for patio drainage.
What is a 1:12 slope in degrees?
A 1:12 slope is 8.33% and 4.76°, or exactly 1 inch of rise per foot of run. It is the maximum running slope for an accessible ramp under the 2010 ADA Standards.
Is a 100% slope vertical?
No. A 100% slope means the rise equals the run, which is a 45° angle. A truly vertical surface has an infinite percent slope, which is why this tool limits degrees to below 90.
How do I convert inches per foot to degrees?
Divide the inches per foot by 12 to get the rise-over-run ratio, then take arctan of that value. For 3 in/ft, arctan(0.25) = 14.04°.
What slope do I need for drainage?
Common minimums are ¼" per foot (2.08%) for small drain pipes, ⅛" per foot (1.04%) for 3"–6" pipes, and 6 inches of fall in the first 10 feet (5%) for ground away from a foundation. Your local code or the product manufacturer may require more.