Slope Percentage Calculator — % to Degrees, Ratio & Drop

Quick Answer

Slope percentage equals rise divided by run times 100 — a 6-inch rise over a 10-foot run is 5%, and degrees = atan(percent ÷ 100), so 5% sits at 2.86°. A 2% drainage slope falls about 1/4 inch per foot (6 inches over 25 feet), and a 100% slope is a 45° angle, not a vertical face.

Slope percentage diagram: rise over run right triangle showing percent grade, angle in degrees and 1-in-N ratio — Percent slope is rise ÷ run × 100 — the same incline written as a percent, an angle, a 1-in-N ratio or an inches-per-foot drop.

Slope Percentage Formula

slope % = rise ÷ run × 100 and degrees = atan(percent ÷ 100).
The rise is the vertical change; the run is the horizontal distance measured flat, not along the sloped surface (USGS method). Because percent slope is the tangent of the angle × 100, a 100% slope is exactly 45°.

The same incline can be written four ways, and every trade uses a different one. This calculator returns all four at once, from whichever one you have:

Notation	Example	Who uses it	Convert from percent
Percent grade	5%	Roads (MUTCD hill signs), site grading	—
Angle in degrees	2.86°	Surveying, CAD, roof geometry	atan(% ÷ 100)
Ratio (1 in N)	1 in 20	Ramps and accessibility codes	N = 100 ÷ %
Inches per foot	0.6 in/ft	Plumbing and drainage	% × 0.12

Slope Percent to Degrees Conversion Chart

The bolded rows are the values building codes are actually written around: 1/8 and 1/4 inch per foot pipe slopes (IPC) and the 1:12 ADA ramp limit — which drops exactly 1 inch per foot.

Slope %	Angle	Ratio	Drop per foot	Drop over 10 ft
0.5%	0.29°	1 in 200	0.06 in	0.6 in
1%	0.57°	1 in 100	0.12 in	1.2 in
1.04% (1/8 in/ft)	0.60°	1 in 96	0.125 in	1.25 in
2%	1.15°	1 in 50	0.24 in	2.4 in
2.08% (1/4 in/ft)	1.19°	1 in 48	0.25 in	2.5 in
3%	1.72°	1 in 33.3	0.36 in	3.6 in
4%	2.29°	1 in 25	0.48 in	4.8 in
5%	2.86°	1 in 20	0.6 in	6 in
6%	3.43°	1 in 16.7	0.72 in	7.2 in
8%	4.57°	1 in 12.5	0.96 in	9.6 in
8.33% (ADA 1:12)	4.76°	1 in 12	1.00 in	10 in
10%	5.71°	1 in 10	1.2 in	12 in
12.5%	7.13°	1 in 8	1.5 in	15 in
15%	8.53°	1 in 6.7	1.8 in	18 in
20%	11.31°	1 in 5	2.4 in	24 in
25%	14.04°	1 in 4	3 in	30 in
33.33%	18.43°	1 in 3	4 in	40 in
50%	26.57°	1 in 2	6 in	60 in
100%	45°	1 in 1	12 in	120 in

How to Use the Slope Percentage Calculator

Pick what you already have.
Choose Rise & run if you measured two distances, Percent slope if you have a grade like 2%, or Angle (degrees) if you have an incline angle.
Enter the value with its unit.
Mixed units are fine — rise in inches, run in feet. The pickers convert everything through the exact foot (0.3048 m).
Set the run length.
In Rise & run mode this is the run itself. In the other modes it is the distance the total-drop read-out is computed over — set it to your patio or pipe length to plan a fall.
Read all four notations at once.
The panel shows percent, degrees, the 1-in-N ratio, the drop per foot and the total drop over your run — no separate conversions needed.

Slope Percentage Examples

Every row is computed exactly the way the calculator does it: slope = rise ÷ run, degrees = atan(slope), drop = slope × run. Laying out steps instead of a ramp? Rise and run are the same idea per tread — the stair stringer calculator handles that layout.

Scenario	Inputs	Slope %	Angle	Drop / rise
Deck sloped for rain run-off	6 in rise over a 10 ft run	5%	2.86°	6 in (given)
Patio at the IRC impervious-surface minimum	2% over a 25 ft slab	2%	1.15°	0.5 ft = 6 in
ADA ramp at the legal limit	30 in rise over a 30 ft run	8.33%	4.76°	30 in — the ADA’s maximum rise for a single run
4-in sewer lateral at the IPC minimum	1/8 in/ft over 40 ft	1.04%	0.60°	5 in
Posted 10% hill, one mile long	10% over 5,280 ft	10%	5.71°	528 ft

The 2% Rule: Drainage and Pipe Slopes in Percent

Most “what slope do I need” searches are drainage questions, and the codes answer them in three different notations at once. The IRC requires the ground to fall 6 inches within the first 10 feet away from a foundation — that is a 5% grade — and impervious surfaces like patios and walks within 10 feet of the building to slope at least 2% away (IRC R401.3). Drain pipes are specified in inches per foot instead (IPC Table 704.1):

Pipe size (IPC Table 704.1)	Minimum slope	As percent	As ratio
2½ in and smaller	1/4 in per ft	2.08%	1 in 48
3 in to 6 in	1/8 in per ft	1.04%	1 in 96
8 in and larger	1/16 in per ft	0.52%	1 in 192

“2%” and “1/4 inch per foot” are not quite the same number. A true 2% slope drops 0.24 in per foot; 1/4 in per foot is 2.083%. The plumbing code itself rounds — the IPC’s grease-interceptor clause calls 1/4 in per ft a “2-percent slope” — so either passes in practice, but if you set a laser level, know which one you dialed in.

Percent Slope vs Degrees: the 45° = 100% Trap

Percent slope is the tangent of the angle × 100, and tangent is not linear. Doubling the percent does not double the angle, and the scale blows up as slopes get steep: 45° is 100%, 60° is 173.2%, 80° is 567%, and at 90° the run is zero, so percent slope is undefined — there is no such thing as a “200% vertical wall”. Going the other way, shallow slopes are nearly linear: below about 10% you can estimate degrees ≈ percent × 0.573.

Measure the run horizontally. Dividing the rise by the length of the sloped surface (the tape stretched along a ramp or roof) gives the sine, not the tangent — it understates every grade, and badly so past 20%. Percent needs the flat, plan-view distance.

Converting angles in the other direction — including degrees as a share of a full circle for pie charts, not just slopes — is covered by the degree to percentage calculator.

Frequently Asked Questions

Divide the rise by the run and multiply by 100, with both lengths in the same unit: a 6-inch rise over a 10-foot (120-inch) run is 6 ÷ 120 × 100 = 5%. The run is the horizontal distance, measured flat — not along the sloped surface.

A true 2% slope falls 0.24 inches per foot. The plumbing trade’s “2%” usually means 1/4 inch per foot, which is exactly 2.083% (1 in 48) — the IPC itself rounds 1/4 in per ft to “2-percent slope”.

2.4 inches — drop = 0.02 × 10 ft = 0.2 ft. At the 1/4-inch-per-foot version of “2%” it is 2.5 inches. Over a 25-foot patio, a 2% slope falls 6 inches.

1 in 20 means 1 unit of rise per 20 units of run: 1 ÷ 20 × 100 = 5%, which is a 2.86° angle. In general, percent = 100 ÷ N for any 1-in-N ratio, so 1 in 12 = 8.33% and 1 in 48 = 2.08%.

Take the arctangent of the percent divided by 100: 10% → atan(0.10) = 5.71°. For slopes under about 10% you can approximate degrees ≈ percent × 0.573 — the error only becomes visible on steep grades.

For a road, yes — 10% (5.71°, 1 in 10) is the kind of grade US agencies flag with a MUTCD hill warning sign, and it climbs 528 feet in a mile. For a wheelchair ramp it is far past the ADA’s 8.33% legal limit, but for a landscape swale it is routine.