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Math • Slope Percentage Calculator

Slope Percentage Calculator

Convert rise and run into slope percentage (grade) and the equivalent angle in degrees.

Slope / Grade (%)
15.00%
Angle of Incline (Degrees)
8.53°
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Calculation Guide & Reference

Slope Percentage (Grade) & Angle Mathematics

Slope percentage calculator converts rise and run into slope percentage (grade) and the equivalent angle in degrees.

Standardized Mathematical Formula
Slope % = (Rise / Run) × 100 | Angle = arctan(Rise / Run)

Slope percentage (also called "grade") expresses steepness as rise over run, converted to a percentage; the equivalent angle in degrees comes from the arctangent of that same ratio.

Variables:
Rise:Vertical change in elevation
Run:Horizontal distance covered
How It Works (Step-by-Step)
  • 1Enter the rise (vertical change) and run (horizontal distance), in the same units.
  • 2View the slope as both a percentage grade and an angle in degrees.
Real-World Numerical Example
A Ramp Rising 15 ft Over a 100 ft Run

A ramp climbs 15 feet in elevation over a horizontal distance of 100 feet.

•Slope %: (15 / 100) × 100 = 15%.
•Angle: arctan(15/100) = 8.53°.
Result: This ramp has a 15% grade, equivalent to about 8.53°.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

Take the arctangent of (rise ÷ run) — for example, a 15% grade (rise 15, run 100) is arctan(0.15) ≈ 8.53°.

In the US, road grades above about 7-8% are generally considered steep for highways, while mountain roads can reach 15-20%+ — a 100% grade (45°) would be far too steep for any vehicle road.

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