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Slope Percentage Calculator — Grade & Incline Calculator

Calculate slope as a percentage from rise/run or angle

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Calculation Method

📐Slope Percentage Formulas

From Rise and Run
Slope % = (Rise / Run) × 100
Where rise is vertical change, run is horizontal distance
From Angle
Slope % = tan(angle) × 100
Where angle is in degrees from horizontal
To Angle
Angle = arctan(Rise / Run)
Convert slope to degrees
Ratio Notation
1:10 slope = 10% grade
Rise of 1 per 10 units of run

💼Common Use Cases

Construction
• Roof pitch
• Ramp design
• Stairs and steps
• Drainage systems
Transportation
• Road grades
• Railway inclines
• Bike paths
• Runway slopes
Outdoor Activities
• Hiking trails
• Ski slopes
• Mountain biking
• Rock climbing routes

💡Common Slope Percentages

• 1% = Minimum for drainage
• 2% = Gentle slope, walkways
• 5% = Moderate slope, driveways
• 8.33% = 1:12 ADA ramp maximum
• 15% = Steep road grade
• 100% = 45° angle (1:1 ratio)

Slope Percentage Calculator: Calculate Grade, Pitch, and Incline

Table of Contents - Slope Percentage

How to Use This Calculator - Slope Percentage

Select your input type:

  • Rise and run (vertical and horizontal distances)
  • Angle in degrees
  • Two points (coordinates)

Enter the relevant measurements in the input fields.

Click "Calculate" to see results. The output displays:

  • Slope as a percentage (grade)
  • Slope as a ratio
  • Angle in degrees
  • Visual representation of the slope
  • Classification (gentle, moderate, steep, etc.)

Understanding Slope Percentage

Slope percentage, also called grade or gradient, measures the steepness of an incline. It's the ratio of vertical rise to horizontal run, expressed as a percentage. This is fundamental in construction, road design, accessibility planning, hiking, and cycling.

The fundamental formula: Slope % = (Rise / Run) × 100

Key conversions:

  • Slope % = tan(angle) × 100
  • Angle = arctan(rise / run)
  • Rise = Run × (Slope % / 100)
  • Run = Rise / (Slope % / 100)

Common terminology:

  • Rise: Vertical change (height difference)
  • Run: Horizontal distance
  • Grade: Slope percentage (US roads)
  • Gradient: Slope percentage (UK railways)
  • Pitch: Slope ratio (roofing, expressed as rise:run)

Interpreting values:

  • 0% = Flat, level surface
  • 1-5% = Gentle slope, easily walkable
  • 5-10% = Moderate slope, noticeable incline
  • 10-15% = Steep slope, challenging for walking
  • 15-25% = Very steep, difficult without assistance
  • Greater than 25% = Extremely steep, may require steps or equipment

Direction convention: Positive slope = uphill (rising) Negative slope = downhill (descending) Both use same formula with appropriate sign.

How to Calculate Slope Percentage Manually

From rise and run: Slope % = (Rise / Run) × 100

Example 1: Wheelchair ramp Rise: 2 feet Run: 24 feet Slope = (2 / 24) × 100 = 8.33%

Example 2: Road grade Elevation gain: 100 meters Horizontal distance: 1,000 meters Slope = (100 / 1,000) × 100 = 10%

Example 3: Roof pitch Rise: 6 inches Run: 12 inches Slope = (6 / 12) × 100 = 50% Also expressed as 6:12 pitch

From angle to slope percentage: Slope % = tan(angle°) × 100

Example 4: Converting angle Angle: 15 degrees Slope = tan(15°) × 100 = 0.2679 × 100 ≈ 26.79%

Example 5: Gentle slope Angle: 5 degrees Slope = tan(5°) × 100 = 0.0875 × 100 ≈ 8.75%

From slope percentage to angle: Angle = arctan(Slope % / 100)

Example 6: Finding angle Slope: 20% Angle = arctan(0.20) = 11.31 degrees

From two points (coordinates): Rise = y₂ - y₁ Run = x₂ - x₁ Slope % = (Rise / Run) × 100

Example 7: Hiking trail Point A: elevation 500m at distance 0m Point B: elevation 650m at distance 2,000m Rise = 650 - 500 = 150m Run = 2,000 - 0 = 2,000m Slope = (150 / 2,000) × 100 = 7.5%

Special cases:

  • Vertical (90°) = undefined (infinite slope %)
  • Horizontal (0°) = 0%
  • 45° = 100%

Real-World Applications

ADA wheelchair ramps. Maximum slope: 8.33% (1:12 ratio). For 30-inch rise, need 30 × 12 = 360 inches (30 feet) of run. Ensures accessibility.

Road design standards. Highway maximum grade typically 6-8%. Mountain roads may reach 10-12%. Affects vehicle performance, braking distance, fuel economy.

Railway gradients. Mainline railways typically less than 3%. Steep grades 4-5% require special locomotives. Cable railways can handle greater than 50% grades.

Roofing pitch. 4:12 pitch = 33.3% slope. Minimum for asphalt shingles: 17% (2:12). Steeper roofs shed water better but are harder to work on.

Hiking trail difficulty. Less than 5% = easy. 5-10% = moderate. 10-15% = strenuous. Greater than 15% = very difficult. Used in trail rating systems.

Cycling route planning. 3-5% = rolling hills. 6-8% = challenging climb. 9-12% = very steep. Greater than 12% = extreme. Professional races feature 15-20% sections.

Drainage systems. Minimum slope for sewer pipes: 1-2%. Ensures gravity flow. Parking lots: 1-5% for water runoff without creating hazards.

Skiing slopes. Beginner: 6-25%. Intermediate: 25-40%. Advanced: 40-60%. Expert: greater than 60%. Affects difficulty and speed.

Slope Grades and Safety Standards

Accessibility regulations (ADA).

  • Ramps: Maximum 8.33% (1:12), preferred 7.14% (1:14)
  • Curb ramps: Maximum 8.33%
  • Cross slope: Maximum 2%
  • Landings required every 30 feet of rise

Pedestrian pathways.

  • Sidewalks: Preferred less than 5%, maximum 8%
  • Crosswalks: Maximum 2% cross slope
  • Steep sections require handrails greater than 5%

Roadway standards.

  • Urban streets: Typically less than 10%
  • Rural highways: less than 8%
  • Interstate highways: less than 6%
  • Residential driveways: less than 15% preferred, less than 20% maximum
  • Parking lot aisles: 1-5%

Stairway equivalents.

  • 35% slope ≈ comfortable stairs
  • 50-70% = typical indoor stairs
  • greater than 100% = ladder territory

Construction site safety.

  • Less than 10%: Wheeled equipment safe
  • 10-20%: Caution for vehicles
  • Greater than 20%: May require tracked equipment
  • Greater than 33%: Fall protection may be required

Railway grades.

  • Adhesion railways: less than 4% typical, less than 6% maximum
  • Rack railways: Can handle 25-48%
  • Funiculars and cable cars: 50-110%

Erosion control.

  • Greater than 30%: High erosion risk, requires stabilization
  • Steep slopes need retaining walls, terracing, or vegetation

Related Topics

Trigonometry. Slope calculations use tangent: tan(θ) = rise/run. Understanding trig functions helps convert between slope and angle.

Pythagorean theorem. Actual distance along slope (hypotenuse) = √(rise² + run²). Important for calculating actual walking/driving distance.

Contour maps. Topographic maps use contour lines to show elevation. Closer lines = steeper slope. Can calculate slope from contour spacing.

Civil engineering. Grading plans, cut-and-fill calculations, retaining wall design all depend on accurate slope calculations.

Horizontal and vertical curves. Road design combines grade changes with horizontal turns, requiring careful calculation for safety and comfort.

Explore more at Percentage Calculator and Percent Error Calculator.

How This Calculator Works

From rise and run:

slopePercentage = (rise / run) × 100
angleInDegrees = arctan(rise / run) × (180 / π)
slopeRatio = rise : run (simplified to lowest terms)

From angle:

slopePercentage = tan(angle × π / 180) × 100
rise = run × tan(angle × π / 180)

From two points:

rise = y2 - y1
run = x2 - x1
slopePercentage = (rise / run) × 100

Actual slope distance:

slopeDistance = √(rise² + run²)

Validation: The calculator:

  • Handles both positive and negative slopes
  • Converts between percentage, ratio, and degrees
  • Checks for zero run (vertical slope)
  • Provides appropriate units and interpretations
  • Classifies slope severity

All calculations happen locally in your browser.

FAQs

How do I calculate slope percentage?

Divide vertical rise by horizontal run, multiply by 100: (Rise / Run) × 100. Example: 5-foot rise over 50-foot run = (5 / 50) × 100 = 10% slope.

What's the difference between slope and grade?

Same concept, different terms. "Grade" is commonly used for roads (US), "gradient" for railways (UK), "slope" is the general mathematical term. All calculated the same way.

How do I convert slope percentage to degrees?

Use arctan: Angle = arctan(slope% / 100). Example: 20% slope = arctan(0.20) = 11.31°.

How do I convert degrees to slope percentage?

Use tangent: Slope% = tan(angle°) × 100. Example: 15° = tan(15°) × 100 ≈ 26.8% slope.

What does a 10% slope mean?

For every 100 units of horizontal distance, you rise 10 units vertically. 10 feet of rise over 100 feet of run, or 10 meters over 100 meters.

Is a 20% slope steep?

Yes, quite steep. Difficult for walking, challenging for cycling, steep for a road. Many regulations classify greater than 15% as steep. For reference, 20% ≈ 11.3° angle.

What's the maximum slope for a wheelchair ramp?

ADA standard: 8.33% maximum (1:12 ratio). This means 1 foot of rise requires 12 feet of run. Gentler slopes (7.14% or 1:14) are preferred where possible.

How do I calculate the actual distance up a slope?

Use Pythagorean theorem: Distance = √(rise² + run²). For 3m rise and 4m run: √(9 + 16) = √25 = 5m actual distance.

What's a 4:12 roof pitch as a percentage?

4:12 means 4 units of rise per 12 units of run. (4 / 12) × 100 = 33.33% slope.

Can slope percentage exceed 100%?

Yes. 100% slope = 45° (rise equals run). 200% slope = 63.4° (rise is twice the run). Vertical is theoretically infinite slope.

What's the slope percentage of a 45-degree angle?

100%. At 45°, rise equals run, so (rise / run) × 100 = (1 / 1) × 100 = 100%.

How steep is too steep for a road?

Context-dependent. Highways rarely exceed 6-8%. Urban streets up to 10-12%. San Francisco's steepest streets reach 31%. Driver skill, vehicle type, weather all factor in.

What slope is needed for drainage?

Minimum 1-2% for proper water flow. Parking lots: 1-5%. Roof: depends on material, typically 17%+ for shingles. Sewer pipes: 1-2% minimum.

How do I calculate rise if I know run and slope percentage?

Rise = Run × (Slope% / 100). Example: 200-foot run at 6% slope = 200 × 0.06 = 12 feet rise.

How do I calculate run if I know rise and slope percentage?

Run = Rise / (Slope% / 100). Example: 8-foot rise at 8% slope = 8 / 0.08 = 100 feet run.

What's cross slope?

Slope perpendicular to the direction of travel. Roads have crown (center higher than edges) for drainage. Typically 1-2% cross slope. Excessive cross slope creates hazards.

Is negative slope the same as going downhill?

Yes. Negative slope indicates descending. The magnitude (absolute value) is still calculated the same way. -10% slope means 10% grade going downward.

How does slope affect vehicle performance?

Steeper slopes require more power, reduce speed, increase braking distance. 10% grade can reduce truck speed by 50%+. Affects fuel economy significantly.

What's the difference between slope and pitch?

Pitch is typically used for roofs, expressed as ratio (4:12). Slope is more general, often expressed as percentage. Same mathematical concept, different conventions.

How do trail maps show slope?

Topographic maps use contour lines (lines of equal elevation). Closer spacing = steeper slope. Calculate by dividing elevation change by distance between contours.