Slope Calculator
Convert slope to percent, degrees, and ratio for drainage, ramps, roofs, and grades. Two points, rise and run, or missing values, with a live diagram.
Four solve modes, live diagram, per-field units, and instant conversion between ratio, percent grade, degrees, and per mille. Built for site work, not just homework.
Slope calculation finds how steep a line or surface is by comparing vertical rise to horizontal run. The result can be expressed as a ratio (1:X), a percentage grade, an angle in degrees, or per mille. Our free slope calculator converts between all four formats instantly from two points, rise and run, or any two known values.
Quick reference: common slopes
Use | Ratio | Percent | Degrees |
|---|---|---|---|
| Minimum drainage | 1:100 | 1% | 0.57° |
| Subtle landscape grade | 1:50 | 2% | 1.15° |
| 1/4 in fall per ft | 1:48 | 2.08% | 1.19° |
| Comfortable walkway | 1:20 | 5% | 2.86° |
| Max ramp (verify locally) | 1:12 | 8.33% | 4.76° |
| Steep driveway feel | 1:10 | 10% | 5.71° |
See the slope conversion reference tables and slope to angle chart farther down this page for longer lists, unit conversions, and positive versus negative grade examples.
Whether you are setting fall on a storm drain, checking a wheelchair ramp, or plotting a line in algebra class, this rise over run calculator keeps the math honest on your phone at the jobsite. Contractors occassionally mix metric fall with imperial run; per-field units handle that without a spreadsheet. Once you've nailed down your slope, Invoice Mama makes it simple to turn those site measurements into a professional construction or landscaping invoice.
How to calculate slope
Same workflow as the tool above: mode, values, four formats
- 1
Pick how you want to solve
Use two points for graph work, rise and run for grades, missing value when you know two of three, or project run/fall for real-world drainage and paving layouts.
- 2
Enter measurements in your units
Mix millimeters for small fall, meters or feet for run, and coordinate pairs in any unit. Direction toggle marks uphill versus downhill without redoing math.
- 3
Read and share every format
Ratio, percent, degrees, and per mille show together. Edit one field to update the rest, copy a value, or bookmark the share link for your crew.
Slope formula: rise over run
Gradient calculator math used on this page
Step | Formula |
|---|---|
| Slope (m) | (y₂ − y₁) / (x₂ − x₁) or rise ÷ run |
| Angle (°) | atan(rise / run) × (180 / π) |
| Percentage (%) | (rise / run) × 100 |
| Per mille (‰) | (rise / run) × 1000 |
| Ratio (1:X) | 1 : (run / rise) |
| Slope length | √(rise² + run²) |
| Rise from run + slope | run × tan(angle) |
| Run from rise + slope | rise / tan(angle) |
| Degrees to % | tan(d) × 100 |
| % to degrees | atan(s / 100) × (180 / π) |
Slope intercept form y = mx + b uses the same m value you get from rise ÷ run. Percent grade and per mille are just scaled versions of that ratio, which is why a 1:100 slope always equals 1% whether you are grading a lawn or checking a pipe lay.
Slope percentage vs. degrees vs. ratio
One steepness, four languages
Civil plans love percent grade. Roofers speak in x:12 ratios. Surveyors still write per mille on rail grades. Students see degrees in trigonometry. None of them disagree; they are unit conversions on the same tangent. This slope percentage calculator shows all four side by side so you do not transpose digits on a busy site.
Slope conversion reference tables
Common grades at a glance
Ratio (1:X) | Percent (%) | Degrees (°) | Per mille (‰) |
|---|---|---|---|
| 1:200 | 0.5% | 0.29° | 5‰ |
| 1:100 | 1% | 0.57° | 10‰ |
| 1:50 | 2% | 1.15° | 20‰ |
| 1:20 | 5% | 2.86° | 50‰ |
| 1:12 | 8.33% | 4.76° | 83.3‰ |
| 1:10 | 10% | 5.71° | 100‰ |
| 1:8 | 12.5% | 7.13° | 125‰ |
| 1:4 | 25% | 14.04° | 250‰ |
| 1:2 | 50% | 26.57° | 500‰ |
| 1:1 | 100% | 45° | 1000‰ |
Percent | Angle | Notes |
|---|---|---|
| 0.5% | 0.29° | Nearly flat swale |
| 1% | 0.57° | Minimum sheet drainage |
| 2% | 1.15° | Subtle landscape grade |
| 5% | 2.86° | Comfortable walkway |
| 10% | 5.71° | Steep driveway feel |
| 15% | 8.53° | Strong ramp territory |
| 25% | 14.04° | Hiking-trail steep |
| 45% | 24.23° | Roof-like slope on ground |
| 100% | 45° | 1:1 rise to run |
Unit | To meters | Example |
|---|---|---|
| Millimeters | ÷ 1,000 | 1,000 mm = 1 m |
| Centimeters | ÷ 100 | 250 cm = 2.5 m |
| Meters | × 1 | 10 m = 10 m |
| Inches | ÷ 39.3701 | 39.37 in ≈ 1 m |
| Feet | ÷ 3.28084 | 10 ft ≈ 3.05 m |
| Yards | ÷ 1.09361 | 1 yd ≈ 0.91 m |
Sign | Meaning | Real-world example |
|---|---|---|
| Positive (+) | Rise increases as you move right (uphill ahead) | Driveway climbing a hill, ramp rising to a porch, roof ridge rising toward peak |
| Negative (−) | Rise decreases as you move right (downhill ahead) | Storm drain falling toward a catch basin, sidewalk sloping to the curb, ski run dropping |
| Zero (0) | Perfectly flat horizontal | Level patio slab, flat warehouse floor (within construction tolerance) |
| Undefined | Vertical line (run = 0) | Wall face on a plan, cliff drop with no horizontal offset |
Slope for driveways, ramps, and drainage
Recommended slope by project type (verify locally)
Project | Typical percent | Typical ratio | Notes |
|---|---|---|---|
| Driveway / road grade | 2% – 5% | 1:50 – 1:20 | Enough fall for rain without uncomfortable climb |
| Roof pitch (shingles) | 18% – 50% | 4:12 – 12:12 | Match manufacturer minimum pitch tables |
| Stormwater pipe / swale | 0.5% – 2% | 1:200 – 1:50 | Confirm authority having jurisdiction |
| Wheelchair ramp (typical max) | 8.33% | 1:12 | Local ADA or building code may be stricter |
| Walkway / sidewalk | 1% – 4% | 1:100 – 1:25 | Add cross-slope for drainage where required |
Driveway and road grades
Worked example with real numbers
A driveway rises 450 mm over a 12 m run. Rise = 0.45 m, run = 12 m, slope = 0.45 ÷ 12 = 0.0375 = 3.75% = about 2.15° = ratio 1:26.7. That is inside the usual 2–5% band for residential driveways and sheds water without feeling like a ski jump. Enter 450 mm rise and 12 m run in the calculator to match.
Roof pitch and drainage
Connecting slope to roof pitch calculator workflows
A 6:12 roof pitch (common shingle roof) is 6 in rise per 12 in run = 50% grade = 26.57°. Gutters still need fall toward downspouts, often 1:200 (0.5%) minimum. Pair this tool with our roof pitch calculator when you are converting between x:12 labels and percent for fascia layout.
Accessible ramp design
Percent grade limits matter for compliance
A 1:12 ramp climbing 24 in (610 mm) needs 12 ft (3.66 m) of run if you use the full allowed slope. At exactly 8.33% the math is rise × 12 = run in feet when rise is in inches. Project run/fall mode answers "how long must my landing layout be?" before you order lumber.
Stormwater and pipe drainage
Fall per metre or foot of run
100 m of storm sewer at 1% grade drops 1 m total (1,000 mm fall). At 2% the same run drops 2 m. Plumbers often think in mm per m: 1% = 10 mm/m. Enter run = 100 m and slope = 1% in project mode to read fall = 1 m without a spreadsheet.
Landscaping and retaining walls
Grade for berms, swales, and backfill
A retaining wall backfill zone might need 2% fall toward a drain tile. Over 8 m of length that is 160 mm (about 6.3 in) of drop. Landscapers pairing berms and swales can sketch rise and run in feet, then convert to percent for the crew laser. Our gravel calculator helps with volume once grade is set.
Math and engineering: two-point slope
Graphing and coordinate geometry
Points (2, 5) and (8, 17): slope m = (17 − 5) / (8 − 2) = 12/6 = 2. That is 200% grade (steep!) and about 63.43°. Distance between points = √(6² + 12²) ≈ 13.42 units. Two-point mode returns m, angle, and distance together, which is handy when you are checking homework or CAD exports. Keep rise and run seperate in your head: slope uses both, but they measure different directions.
Frequently Asked Questions
Slope calculator, percent grade, and rise over run answers
What is a 2 percent slope in degrees?
A 2% slope is about 1.15°, the same as a ratio of 1:50. That is also close to 1/4 inch of fall per foot (2.08%, about 1.19°). Enter 2 in the percent field here to see degrees update live.
What is 1/4 inch per foot slope in percent?
One quarter inch of rise per foot of run is about 2.08% grade, roughly 1.19°, and a ratio near 1:48 (0.25 ÷ 12 = 0.0208). Use rise and run mode with 0.25 in rise and 12 in run to match.
How do I calculate slope between two points?
Subtract the y-values and divide by the difference in x-values: m = (y₂ − y₁) / (x₂ − x₁). That rise-over-run ratio is your slope. Enter both points in our two-point mode and you get slope, angle, distance, and all four format outputs without rearranging the formula yourself.
How do I convert slope percentage to degrees?
Treat percent as rise per hundred units of run: slope m = percent ÷ 100. Then degrees = atan(m) × (180/π). Example: 10% → m = 0.1 → about 5.71°. Type 10 in the percent field here and the degree box updates automatically, or use the slope to angle chart below.
What does a 1:100 slope mean?
A 1:100 slope rises 1 unit vertically for every 100 units horizontally. That equals 1% grade, 10‰, or roughly 0.57°. It is a common minimum for surface drainage and gentle ramps. Enter 100 in the ratio field (as X in 1:X) to see the matching percent and degrees.
What is the maximum slope for a wheelchair ramp?
In many US accessibility guides the steepest allowed running slope is 1:12 (8.33%). Some jurisdictions allow 1:10 for short rises only. Always check your local building code and landings at the top and bottom. Use ramp project hints here, then confirm with the authority having jurisdiction.
What slope is required for stormwater drainage?
Open swales often target 0.5% to 2% (1:200 to 1:50). Buried storm pipes frequently need at least 1% (1:100) so solids do not settle. Steeper is not always better if erosion becomes a problem. Our drainage project hint shows typical ranges; your engineer or municipality sets the final number.
How do I calculate the rise from a known run and slope?
Multiply run by the slope ratio: rise = run × (rise/run). If you know percent, rise = run × (percent ÷ 100). If you know degrees, rise = run × tan(angle). Project run/fall mode does this for you: enter horizontal run and target slope to get vertical fall instantly.
What is the difference between slope ratio and slope percentage?
Ratio is written 1:X where X is how much horizontal run matches one unit of rise (or the inverse depending on convention). Percent is rise divided by run, times 100. A 1:50 ratio equals 2% because 1/50 = 0.02. Both describe the same steepness; contractors often use ratio for drains and percent for roads.
How steep is a 10% slope?
Ten percent means 10 units of rise per 100 units of run, a ratio of 1:10 and about 5.71°. Walking feels noticeably uphill; vehicles handle it on driveways but you may need traction in ice. It is steeper than typical ADA ramps (8.33% max) but common on residential streets in hilly areas.
What is the slope of a horizontal line?
A perfectly flat horizontal line has zero slope because rise is zero while run can be any nonzero value. The angle is 0° and percent grade is 0%. Vertical lines are different: run is zero so slope is undefined, not zero. Our calculator explains which case you hit with plain-English messages.
How do I calculate slope for a roof?
Roof pitch is still rise over run, usually quoted as inches of rise per 12 inches of run (such as 6:12). Measure vertical rise and horizontal run along the roof plane, enter them in rise and run mode, and read percent or degrees. For preset x:12 conversions, try our roof pitch calculator too.
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You verified the slope on site. Invoice Mama helps contractors and landscapers turn those measurements into professional estimates and invoices in seconds.