Slope Calculator turns rise and run into grade percent, angle, ratio, and drop per foot. It also gives the true surface length and checks the slope against the 1:12 ramp limit.
The Formula Behind the Slope Calculator
Every output on this page comes from one division: rise over run.
$$ S = \frac{\text{rise}}{\text{run}} $$
Base slope ratio
That single number is then dressed in five different formats, one per trade.
$$ G\% = S \times 100 \qquad D_{\text{in/ft}} = S \times 12 $$
$$ \theta = \arctan(S) \qquad \text{ratio} = 1 : \frac{1}{S} $$
Percent, inches per foot, degrees, ratio
Surface length is separate, because it follows the hypotenuse rather than the plan view.
$$ L = \sqrt{\text{rise}^2 + \text{run}^2} $$
True surface length
Take the default 6 ft rise over a 12 ft run. \(S = 6/12 = 0.5\), so the grade is 50%, the drop is 6 in/ft, the angle is 26.57°, and the ratio is 1:2. Surface length is \(\sqrt{6^2+12^2} = 13.42\) ft.
Slope Conversion Table
| Percent | Inches per foot | Ratio | Degrees | Typical use |
|---|---|---|---|---|
| 1% | 0.12 in | 1:100 | 0.57° | Sheet drainage, long drains |
| 1.04% | 1/8 in | 1:96 | 0.60° | 4 in and larger sewer pipe |
| 2% | 0.24 in | 1:50 | 1.15° | Yard grading, walkway cross slope |
| 2.08% | 1/4 in | 1:48 | 1.19° | Drain pipe minimum, ADA cross slope |
| 4.17% | 1/2 in | 1:24 | 2.39° | Short, steeper drain runs |
| 5% | 0.60 in | 1:20 | 2.86° | First 10 ft away from a foundation |
| 8.33% | 1 in | 1:12 | 4.76° | Maximum ramp running slope |
| 10% | 1.20 in | 1:10 | 5.71° | Steep walkway, driveway |
| 25% | 3 in | 1:4 | 14.04° | 3:12 roof pitch |
| 50% | 6 in | 1:2 | 26.57° | 6:12 roof pitch, 2:1 fill slope |
| 100% | 12 in | 1:1 | 45° | 1:1 cut slope |
Two rows look interchangeable and are not. A 2% slope is 0.24 in/ft, while 1/4 in/ft is 2.08%. Over a 50 ft run that is 12 in of fall against 12.5 in.
More Slope Ratios
| Ratio or percent | Equivalent | Typical use |
|---|---|---|
| 1:8 | 12.5%, 7.13° | Steep wheelbarrow ramp, temporary access |
| 15% | 1:6.67, 8.53° | Maximum grade on many DOT driveway standards |
| 1.5:1 (excavation) | 66.7%, 33.69° | OSHA Type B soil maximum trench slope |
| 2:1 (excavation) | 50%, 26.57° | Common fill slope, OSHA Type C soil |
Inches Per Foot and Total Drop
Plumbers, roofers, and tile setters work in inches per foot. The conversion runs both ways.
$$ D_{\text{in/ft}} = \frac{G\% \times 12}{100} \qquad G\% = \frac{D_{\text{in/ft}}}{12} \times 100 $$
Percent to inches per foot, and back
Total fall over a run follows from either form.
$$ \text{fall} = D_{\text{in/ft}} \times \text{run}_{\text{ft}} $$
Total drop across a run
A 1/4 in/ft line over 50 ft drops \(0.25 \times 50 = 12.5\) in. A 1% grade over 10 ft drops \(0.12 \times 10 = 1.2\) in. A 2% grade over 20 ft drops 4.8 in.
Reading Slope Ratios
Ratios come from inverting the slope, which is why the number grows as the grade gets gentler.
$$ X = \frac{1}{S} = \frac{\text{run}}{\text{rise}} = \frac{100}{G\%} $$
The X in a 1:X slope ratio
Trades write the two numbers in opposite orders. Ramp and pipe work puts rise first, so 1:12 is one unit up per twelve along. Earthwork puts run first, so 2:1 is two along per one up, which is 50%.
That makes 1:2 and 2:1 completely different slopes. Check the grading notes when a sheet is ambiguous. The tool prints 1:X with the rise first.
Drainage and Sewer Fall
Gravity drainage has a working band. Too flat and solids settle out. Too steep and the water outruns them.
The usual minimum for drain pipe is 1/4 in/ft, which is 2.08% or 1:48. Pipe 4 in and larger is often allowed at 1/8 in/ft, or 1.04%, since the bigger bore carries more flow at the same grade. Plumbing codes differ by state and pipe size, so confirm the figure for your jurisdiction.
Invert levels come straight from the fall equation. A 60 ft run at 1/4 in/ft drops 15 in, so an outlet invert 15 in below the inlet sets the trench depth at the far end.
Site grading is gentler. Sheet flow works at 1% to 2%. Next to a building the IRC calls for 6 in of fall in the first 10 ft, which is 5%.
Ramps and the 1:12 Limit
The ADA caps a ramp’s running slope on an accessible route at 1:12.
$$ \text{run}_{\min} = \text{rise} \times 12 \qquad S \le 0.0833 $$
Minimum ramp run, and the 1:12 slope limit
That is 8.33% or 4.76°. A 30 in rise needs 30 ft of ramp, and a 24 in rise needs 24 ft.
The tool checks slope only. A compliant ramp also needs:
- Cross slope no steeper than 1:48, about 2.08%
- A level landing after every 30 in of rise, so one run tops out at 30 ft
- Landings at least 60 by 60 in, and no steeper than 1:48 in any direction
- At least 36 in of clear width, measured between the handrails
- Handrails on both sides once a run rises more than 6 in
Alterations to existing sites allow steeper ramps for small rises, such as 1:10 up to a 6 in rise and 1:8 up to 3 in. New work is held to 1:12. Residential ramps sit outside ADA scope, though the geometry is what makes them usable.
Roof Pitch as X:12
Roof pitch is rise per 12 in of run, so it is the same number as inches per foot.
$$ \text{pitch} = (S \times 12) : 12 \qquad G\% = \frac{\text{pitch}_{\text{rise}}}{12} \times 100 $$
Slope to roof pitch
A 6:12 roof is 50% and 26.57°. A 4:12 is 33.3% and 18.43°. A 3:12 is 25% and 14.04°. Most shingle makers require doubled underlayment below 4:12 and will not warrant shingles below 2:12, which is 16.7%.
Excavation and Fill Slopes
Earthwork ratios say how far a bank lays back for each foot of depth, and they come from soil type. OSHA’s tables set maximum trench slopes, commonly 1.5:1 in Type B soil and 1:1 in Type A, with flatter slopes for Type C.
$$ \text{setback} = \text{depth} \times X \qquad W_{\text{top}} = W_{\text{bottom}} + 2\,(\text{depth} \times X) $$
Bank setback and top width for an X:1 slope
An 8 ft deep trench at 1.5:1 lays back 12 ft per side, so a 4 ft bottom opens to 28 ft at the top. As slopes, 1.5:1 is 66.7% and 33.69°, while 2:1 is 50% and 26.57°. Trench safety answers to the excavation standard and a competent person on site, not to a conversion.
Surface Length Versus Flat Run
Material follows the slope, not the plan view. The multiplier between them comes from the same right triangle.
$$ k = \frac{L}{\text{run}} = \sqrt{1 + S^2} $$
Surface length multiplier
Gentle slopes barely register. At 8.33%, \(k = 1.003\), so the surface is 0.3% longer. Steep ones matter: at 50%, \(k = 1.118\), so a 100 ft run needs 111.8 ft of material, and at 100% it is 41.4% longer.
This is also the classic measurement error. Measure the true horizontal run, not the distance along the ground. Using the diagonal understates the slope, and past about 10° the error grows fast.
Working From Elevations
Survey and grading work starts from two spot elevations instead of a rise.
$$ S = \frac{|E_{\text{start}} – E_{\text{end}}|}{\text{distance}} $$
Slope from two elevations
An inlet at 100.00 ft and an outlet at 98.75 ft over 60 ft gives \(1.25/60 = 0.0208\), which is 2.08%, or 1/4 in/ft. Use the same mode to check a grade stake against a plan.
Slope Conversion FAQs
What is 2% slope in inches per foot?
0.24 in/ft, from \(2 \times 12 / 100\). Most crews round it to 1/4 in, which is really 2.08%. Across 50 ft, 2% drops 12 in while 1/4 in/ft drops 12.5 in, and over 100 ft the gap doubles to an inch. On a tight invert that half inch decides whether the pipe daylights where you planned.
What is 1/4 inch per foot as a percent?
2.08%, from \(0.25/12 \times 100\). As a ratio it is 1:48, and in degrees 1.19°. That figure is both the common minimum fall for drain pipe under 4 in and the ADA cross slope limit, which is why 1:48 turns up in plumbing and accessibility drawings alike.
How much drop is 1% slope over 10 feet?
1.2 in. One percent is 0.12 in/ft, so ten feet gives \(0.12 \times 10 = 1.2\) in. The same grade over 100 ft drops 12 in, which is where the plain description comes from: a 1% slope falls 1 ft in 100.
What slope is 1:12?
8.33%, 4.76°, or exactly 1 in of rise per foot of run, since \(S = 1/12 = 0.0833\). It is the ADA maximum running slope, so a 24 in rise needs at least 24 ft of ramp. Slope is only the first test: landings every 30 in of rise, 36 in of clear width, a cross slope within 1:48, and handrails past a 6 in rise all apply.
Does 2:1 mean the same as 1:2?
No. Earthwork writes run first, so 2:1 is 2 ft across per foot up, which is 50% and 26.57°. Ramp and pipe work writes rise first, so 1:2 would be a foot of rise per 2 ft of run, a 50% ramp nobody could use. Same digits, opposite meaning, so read the sheet’s convention before staking.
What is the minimum slope for a drain pipe?
Commonly 1/4 in/ft, which is 2.08% or 1:48. Pipe 4 in and larger is often permitted at 1/8 in/ft, or 1.04%, because the larger bore carries more flow at the same grade. Codes vary by state and size, so check the adopted plumbing code. Steeper is not automatically better, since fast water can leave solids behind in the line.
How do I convert slope percent to degrees?
Take \(\theta = \arctan(G\%/100)\). So 2% is 1.15°, 8.33% is 4.76°, and 50% is 26.57°. The relationship is not proportional: doubling the percent does not double the angle, and 100% is 45°, not 90°. Degrees only reach 90° as the run approaches zero.
What roof pitch is a 25% slope?
3:12, since \(0.25 \times 12 = 3\) in of rise per foot of run, or 14.04°. For comparison 4:12 is 33.3% and 6:12 is 50%. Shingle manufacturers generally require doubled underlayment below 4:12 and will not warrant shingles below 2:12, which is 16.7%.