Slope of a Road
Calculator and formulas for converting road slope between degrees and percent
Road Slope Calculator
Slope Converter
Select the input type that you know and enter its value. The calculator converts between angle (degrees) and slope (%).
Road Slope - Overview
What is Road Slope?
The slope indicates how much a road rises over a given distance.
Example: 8% Slope
An 8% slope means: The road rises 8m over a length of 100m.
Slope in Percent
The slope in percent is the ratio of height difference to horizontal distance, multiplied by 100.
- 0%: Flat road (horizontal)
- 5-8%: Moderate slope
- 10-15%: Steep slope
- >20%: Very steep road
Slope Angle in Degrees
The slope angle is the inclination angle of the road to the horizontal.
- 0°: Horizontal (0% slope)
- 5°: approx. 8.75% slope
- 10°: approx. 17.6% slope
- 45°: 100% slope (45° angle)
- 90°: Vertical wall (theoretical)
Important Notes
- Slope ≠ Angle! 100% slope = 45°, not 100°
- For small angles: Slope (%) ≈ Angle (degrees) × 1.75
- Traffic signs usually show slope in %
- In mountainous regions, 10-15% are common slopes
Practical Examples
- Garage ramp: 10-15% slope
- Alpine serpentines: 8-12% slope
- Steepest street (New Zealand): 35% (19°)
- Bike path: max. 6% recommended
- Wheelchair ramp: max. 6% by law
Formulas for Slope or Grade
From Angle to Slope
Degree → Slope (%)
\(\displaystyle slope(\%) = 100 \cdot \tan(degree)\)
Example: Convert 5° to percent
\(\displaystyle slope = 100 \cdot \tan(5°) = 100 \cdot 0.0875 = 8.75\%\)
Explanation
The slope is derived from the tangent of the angle. The tangent of an angle is the ratio of opposite side (height) to adjacent side (horizontal distance). Multiplied by 100 gives percent.
From Slope to Angle
Slope (%) → Degree
\(\displaystyle degree = \arctan\left(\frac{slope(\%)}{100}\right)\)
Example: Convert 8.75% to degrees
\(\displaystyle degree = \arctan\left(\frac{8.75}{100}\right) = \arctan(0.0875) = 5°\)
Important
The inverse function of tangent is arctangent (arctan or atan). This calculates the angle from the ratio height/length. Note: The result is in degrees (for degree measure) or radians (for radian measure).
Geometric Representation
Relationships:
- α = Slope angle (in degrees)
- h = Height difference
- l = Horizontal length
- tan(α) = h / l
- Slope (%) = (h / l) × 100
- α = arctan(h / l)
Conversion Table Degree ↔ Slope
| Angle (Degree) | Slope (%) | Description | Application |
|---|---|---|---|
| 0° | 0% | Horizontal | Flat road |
| 1° | 1.75% | Very slight slope | Highway |
| 3° | 5.24% | Slight slope | Normal road |
| 5° | 8.75% | Moderate slope | Mountain road, ramp |
| 10° | 17.6% | Steep slope | Steep mountain road |
| 15° | 26.8% | Very steep slope | Extremely steep road |
| 20° | 36.4% | Extremely steep | Cable car, special vehicles |
| 30° | 57.7% | Very steep | Via ferrata |
| 45° | 100% | 45-degree angle | Theoretical |
Practical Tips
For Drivers:
- Traffic signs show slope in %
- 8% slope: Shift down a gear
- 12% slope: Very steep mountain road
- In wet/snow conditions: Even more careful!
For Cyclists:
- 4-6% slope: Challenging for beginners
- 8-10% slope: Demanding
- >12% slope: Very difficult
- Professionals manage even >20% slope
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