Calculate slope percentage, angle, and rise-to-run instantly. Switch between percent (%) and permille (‰). Convert angles to degrees, radians, gradians, or multiples of π. Use metric or imperial units without manual conversions.
What this calculator does
- Turns rise and run into slope percentage and angle.
- Converts percent ↔ permille for fine-grained grades.
- Accepts mm, cm, m, km, in, ft, yd, mi, nmi plus split entries like ft/in or m/cm.
- Shares a prefilled link so teammates see the same numbers.
Use it for ramps, roads, roofs, drainage, railways, trails, and site design where grade drives decisions.
How to use the calculator
- Enter Rise. Type the vertical change and choose its unit.
- Enter Run. Type the horizontal distance. Units can match or differ.
- Read the Angle. Pick degrees, radians, gradians, or π radians.
- Read the Slope Percentage. Toggle between percent and permille.
- Optional tools: swap rise/run, clear all values, or copy a shareable link.
The idea behind slope
Slope describes how quickly elevation changes along a horizontal distance. A bigger rise over the same run means a steeper grade.
rise
│\
│ \
│ \ hypotenuse
│ \
└────┘
run
angle θ
Formulas you can trust
Slope percentage
Slope% = 100 × rise / run
Slope permille
Slope‰ = 1000 × rise / run
Angle from rise and run
θ = arctan(rise / run)
Percent from angle
Slope% = 100 × tan(θ)
Degrees ↔ radians
θ(rad) = θ(deg) × π / 180 | θ(deg) = θ(rad) × 180 / π
Background reading: Grade (slope) and Trigonometric functions.
Quick examples
1) Accessible ramp
A ramp rises 0.9 m over a 12 m run.
- Slope% = 100 × 0.9 ÷ 12 = 7.5%
- Angle = arctan(0.9/12) ≈ 4.29°
- Slope‰ = 75‰
The grade feels gentle for most users and works well for many access designs.
2) Road climb
A road gains 320 ft over 0.5 mi.
- Run in feet = 0.5 × 5280 = 2640 ft
- Slope% = 100 × 320 ÷ 2640 ≈ 12.12%
- Angle ≈ 6.93°
3) Roof pitch cross-check
A 6-in-12 roof rises 6 inches for each 12 inches of run.
- Slope% = 100 × 6 ÷ 12 = 50%
- Angle ≈ 26.57°
Conversion tables
Table A — Percent grade to angle
| Slope % | Angle (deg) | Angle (rad) | Notes |
|---|---|---|---|
| 1 | 0.57° | 0.010 | Very gentle grade |
| 5 | 2.86° | 0.050 | Common sidewalk ramp |
| 10 | 5.71° | 0.100 | Noticeable climb |
| 25 | 14.04° | 0.245 | Steep driveway |
| 50 | 26.57° | 0.464 | 6-in-12 roof |
| 100 | 45.00° | 0.785 | Rise equals run |
Table B — Angle to percent and permille
| Angle (deg) | Slope % | Slope ‰ |
|---|---|---|
| 2° | 3.49% | 34.9‰ |
| 5° | 8.75% | 87.5‰ |
| 10° | 17.63% | 176.3‰ |
| 20° | 36.40% | 364.0‰ |
| 30° | 57.74% | 577.4‰ |
Percent vs permille
Use percent (%) for everyday grades in roads, ramps, roofs, and paths. Use permille (‰) for fine control on long runs such as railways, pipelines, and drainage where small changes matter.
Units without headaches
- Enter values in metric or imperial. The calculator normalizes units internally then formats the result in your chosen units.
- Integers and decimals work. The tool ignores commas used as thousands separators.
- European decimal commas get recognized when used alone such as 12,5.
- If run equals zero the angle becomes 90° and slope shows ∞ because the line is vertical.
Featured steps: how to calculate slope percentage
- Measure rise (vertical change).
- Measure run (horizontal distance).
- Divide rise by run to get a ratio.
- Multiply the ratio by 100 for percent or by 1000 for permille.
- Use arctan(rise/run) if you need the angle.
Example: rise 3 m, run 40 m → 3 ÷ 40 = 0.075 → 7.5%.
Common mistakes to avoid
- Mixing units by accident. Choose the unit that matches each measurement.
- Rounding too early. Keep at least two decimals until the final step.
- Confusing pitch with percent. A 4-in-12 roof equals 33.33% not 4%.
- Using the hypotenuse as run. Run is always the horizontal leg of the triangle.
Where slope percentage shows up in the real world
Civil engineering
- Roadway alignment: Designers limit grades for safety and fuel economy. Guidance lives in agency design manuals and DOT resources such as the United States Department of Transportation.
- Drainage: Gravity lines need minimum slopes to keep flow moving. Plans often specify percent or permille for clarity.
- Earthwork: Cuts and fills follow grade constraints that control erosion risk.
Architecture and building
- Ramps and accessibility: A small change in slope changes wheelchair effort a lot.
- Roofs: Pitch influences water shedding, materials, and snow load.
- Decks and walkways: Slight falls prevent puddles while keeping surfaces comfortable.
Outdoor recreation
- Hiking and trail design: Grade affects difficulty and erosion control.
- Ski runs: Slope helps classify terrain for signage and safety planning.
- Cycling routes: Climbs above 10% feel demanding even for fit riders.
Land surveying and GIS
- Survey workflows compute slope from rise and run across map coordinates. See helpful context from the USGS.
Field tips for better measurements
- Use a tape measure or laser for run. A distance wheel helps on long segments.
- Use a level and a rod for short rises. A rotary laser or auto-level improves accuracy over long runs.
- Record units in your notes to prevent mix-ups at the desk.
- Measure twice when grade drives cost or safety decisions.
- Average several readings if the ground undulates.
FAQs
What does a 10% slope mean?
A 10% slope climbs 10 units vertically for every 100 units horizontally. The angle is about 5.71°.
Is a 1 in 12 slope the same as 8.33%?
Yes. Divide 1 by 12 then multiply by 100. The result equals 8.33%.
How steep is 100% slope?
Very steep. Rise equals run which forms a 45° angle.
How do I convert degrees to percent?
Use percent = 100 × tan(degrees × π / 180). For 30° the grade is about 57.74%.
When should I use permille?
Use permille for long utilities and rail lines where small grade changes matter across long distances.
What if the run is zero?
The line is vertical. The angle equals 90° and the slope reads ∞.
Slope% = 100 × rise ÷ run. Angle comes from arctan(rise/run). Switch to permille when you want finer control. Keep units tidy. Then share your result so the whole team stays aligned.
