Welcome to the Hill Grade Calculator! This tool helps you measure the steepness of a hill or slope as a percentage. Whether you’re a hiker, cyclist, civil engineer, or driver planning a safe route, understanding hill grade is an essential way to evaluate how challenging or demanding a slope might be.
The calculator is simple to use. Just enter the rise (change in elevation) and the run (horizontal distance). If you don’t have the horizontal run but know the slope distance, the calculator can work that out too. You can start calculating right now, or keep reading to explore the formula, a step-by-step example, and explanations of the parameters.
Understanding the Formula
The main formula for calculating hill grade is:
Hill Grade (%) = (Rise / Run) × 100
Where:
Rise = End Elevation − Start Elevation
Run = Horizontal Distance
If you only know the distance traveled along the slope, you can calculate the run using:
Run = √(Slope Distance² − Rise²)
Related Calculation:
Hill Angle (degrees) = arctan(Rise / Run)
In simple terms, the hill grade formula compares how much elevation is gained (rise) to the horizontal distance covered (run). The result, expressed as a percentage, shows how steep the slope is. A higher percentage means a steeper climb.
Parameters Explained
Rise
This is the vertical elevation difference between the start and end points. For instance, if you start at 100 m and end at 140 m, the rise is 40 m.
Run
This is the horizontal distance across the ground, not the slope distance. It’s the “base” of the slope and is necessary for accurate grade calculations.
Slope Distance
If you only know the distance traveled along the slope, you can use it to calculate the run. This ensures you still get an accurate grade.
Hill Grade (%)
This is the final output. It represents the slope steepness as a percentage. For example, a 10% grade means the hill rises 10 meters for every 100 meters of horizontal distance.
Hill Angle
The grade can also be expressed as an angle in degrees. This trigonometric relation is often useful in construction, physics, or hiking assessments.
How to Use the Hill Grade Calculator — Step-by-Step Example
Let’s walk through an example.
-
Input values:
- Start elevation = 200 m
- End elevation = 260 m
- Slope distance = 120 m
-
Find the rise:
Rise = 260 − 200 = 60 m -
Calculate the run:
Run = √(120² − 60²)
= √(14400 − 3600)
= √10800 ≈ 103.92 m -
Find the hill grade:
Hill Grade (%) = (60 ÷ 103.92) × 100
≈ 57.7% -
Related angle (optional):
Hill Angle = arctan(60 ÷ 103.92)
≈ arctan(0.577)
≈ 30°
Result: The hill has a grade of about 57.7%, which corresponds to a steep slope with a 30° angle.
Additional Information
Here is a quick reference table of common hill grades:
| Hill Grade (%) | Hill Angle (°) | Description |
|---|---|---|
| 0–5% | 0–3° | Gentle incline |
| 6–15% | 3–9° | Moderate slope |
| 16–30% | 9–17° | Steep slope |
| 31–60% | 17–31° | Very steep slope |
| 61%+ | 31°+ | Extremely steep slope |
FAQs
Hill grade is expressed as a percentage, while hill angle gives the slope steepness in degrees. Both describe the same concept in different formats.
Yes. Hill grade is especially important in road and railway design because it affects vehicle safety, fuel efficiency, and construction planning.
No. Slope distance is the actual path length along the incline, while the run is the horizontal ground distance. The calculator adjusts for this difference.