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Slope as Percentage

Slope percentage = (Rise / Run) × 100. A 6% grade means 6 units of vertical rise per 100 units horizontal. Used for road grades, wheelchair ramps (ADA 1:12 ≈ 8.33%), roof pitch (4:12), hiking trails, and drainage.

Concept Fundamentals
Rise 6, Run 100
6% grade
1:12 ≈ 8.33%
ADA ramp
33.33%
4:12 roof
atan(rise/run)
Angle

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6% road grade = 6 ft rise per 100 ft horizontal—common max for highways. ADA: 1:12 max slope = 8.33%. 1:20 is gentler (5%) for longer ramps. Roof pitch 4:12 = 4/12 × 100 = 33.33% slope.

Key quantities
Rise 6, Run 100
6% grade
Key relation
1:12 ≈ 8.33%
ADA ramp
Key relation
33.33%
4:12 roof
Key relation
atan(rise/run)
Angle
Key relation

Ready to run the numbers?

Why: Highway grades are posted as percentages. ADA requires wheelchair ramps ≤ 1:12 (8.33%). Roof pitch uses rise:run (e.g., 4:12). Hiking trails use % grade. Drainage needs minimum slope.

How: Slope % = (Rise / Run) × 100. Ensure same units (rise and run in feet, or both in meters). Angle in degrees = atan(Rise/Run). ADA 1:12 = 1/12 × 100 ≈ 8.33%.

6% road grade = 6 ft rise per 100 ft horizontal—common max for highways.ADA: 1:12 max slope = 8.33%. 1:20 is gentler (5%) for longer ramps.
Sources:Grade (slope)ADA Ramp

Run the calculator when you are ready.

Rise Over RunSlope % = 100 × (vertical / horizontal). Steeper = higher %.

Quick Examples — Click to Load

Input Values

slope_calc
CALCULATED
$ slope --rise=6 --run=100
Slope %
6.00%
Angle
3.43°(0.0599 rad)
Ratio
3:50
ADA Compliant
✓ Yes (≤ 8.33%)
Visual Slope
6.0%
Share:

Common Slopes Comparison

Rise vs Run Proportion

Step-by-Step Breakdown

CALCULATION
Formula
Slope % = (Rise / Run) × 100
Divide rise by run
6 ÷ 100 = 0.060000
ext{Rise} div ext{Run}
Multiply by 100
0.060000 × 100
ext{Convert} ext{to} ext{percentage}
RESULT
Slope Percentage
6.00%
Slope Angle
3.43° (0.059928 rad)
ext{arctan}( ext{Rise}/ ext{Run})
Slope Ratio
3:50
ext{Rise} : ext{Run} ( ext{simplified})
ACCESSIBILITY
ADA Compliant
Yes (≤ 8.33% or 1:12)

For educational and informational purposes only. Verify with a qualified professional.

🧮 Fascinating Math Facts

🛣️

Slope % = 100 × (rise/run). A 45° grade = 100% (rise equals run).

— Formula

♿

ADA wheelchair ramp: maximum 1:12 slope = 8.33%. 1:20 preferred for longer ramps.

— ADA

Key Takeaways

  • • Slope percentage = (Rise ÷ Run) × 100 — a 6% grade means 6 units up per 100 units forward
  • • ADA requires wheelchair ramps to be ≤ 8.33% (1:12 ratio) for safe, independent use
  • • Roof pitch is often expressed as rise:run (e.g., 4:12 = 33.3% slope)
  • • Highway grades rarely exceed 6–8%; steeper roads need special design and signage
  • • A 100% slope equals a 45° angle — rise equals run

Did You Know?

♿The ADA 1:12 ramp rule (8.33%) was chosen so most wheelchair users can ascend without assistance — steeper ramps require help or powered devicesSource: ADA Standards
🛣️The steepest paved road in the world is Baldwin Street in New Zealand at 35% — cars park with wheels chockedSource: Engineering
🏔️Ski slopes use a different system: green (easiest), blue, red, black. A black diamond can be 40%+ slopeSource: Recreation
🚂Railways avoid grades over 2–3% because steel wheels on steel rails have very low friction — trains would slip on steeper slopesSource: Transportation
💧Drainage slopes need only 1–2% (0.25 in 12) to move water — too flat causes pooling, too steep causes erosionSource: Civil Engineering
📐A 45° angle equals 100% slope because tan(45°) = 1 — rise and run are equalSource: Trigonometry

How to Calculate

Slope measures steepness as the ratio of vertical change (rise) to horizontal change (run). Enter rise and run in the same units (feet, meters, inches). The calculator outputs slope as a percentage, angle in degrees, and simplified ratio.

Formulas

Slope % = (Rise ÷ Run) × 100

Angle (°) = arctan(Rise ÷ Run) × 180/π

Ratio = Rise : Run (simplified using GCD)

Expert Tips

Construction

Use a level and tape measure: measure rise over a known run (e.g., 12 inches). Rise of 1 inch over 12 inches = 8.33% — right at ADA max.

Accessibility

ADA allows 1:12 (8.33%) max for ramps. Add landings every 30 inches of rise. Consider 1:16 or 1:20 for easier use when space allows.

Roof Pitch

Roof pitch 4:12 means 4 inches rise per 12 inches run = 33.3%. Low slope: 2:12–4:12. Steep: 6:12+.

Hiking

Trail grades: <5% easy, 5–10% moderate, 10–15% strenuous, >15% very difficult. Use GPS or altimeter for rise.

ADA Compliance Table

ApplicationMax SlopeRatioNotes
Wheelchair ramp8.33%1:12Maximum for ADA compliance
Curb ramp8.33%1:12Same as ramp max
Cross slope (walkway)2%1:50Perpendicular to direction of travel
Parking access aisle2%1:50For drainage only
Door threshold1.5%~1:67Beveled edge preferred

Frequently Asked Questions

What is slope percentage?

Slope percentage = (Rise ÷ Run) × 100. A 6% slope means 6 units of vertical rise per 100 units of horizontal run. It is the most common way to express grade in civil engineering and construction.

What slope is ADA compliant for wheelchair ramps?

ADA requires a maximum slope of 1:12 (8.33%). That means 1 inch of rise per 12 inches of run. Ramps steeper than this may require assistance for wheelchair users.

How do I convert roof pitch (e.g., 4:12) to percentage?

Divide rise by run and multiply by 100. 4:12 = 4÷12 × 100 = 33.33%. So a 4:12 roof has a 33.33% slope.

What is a 100% slope?

A 100% slope means rise equals run — a 45° angle. For every 1 unit forward, you go 1 unit up. tan(45°) = 1.

How steep is too steep for a road?

Interstate highways typically max at 6% (7% in mountains). Residential streets often 4–8%. Grades over 10% need advisory signs and may be unsafe in ice or snow.

What units should I use for rise and run?

Use the same units for both (feet, meters, inches). The slope percentage and ratio are unitless — only the ratio matters. A 6 ft rise over 100 ft run = 6% = 6 in rise over 100 in run.

Quick Reference

1:12
ADA Max (8.33%)
6%
Typical Road Max
4:12
Common Roof Pitch
45°
100% Slope

Disclaimer: This calculator provides mathematical results for educational and planning purposes. For construction, accessibility, or engineering projects, always consult local building codes, ADA guidelines, and qualified professionals. Slope requirements vary by jurisdiction and application.

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