Enter the grade rise and the grade run into the Grade Slope Calculator. The calculator will evaluate and display the Grade Slope.
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Grade Slope Formula
Grade slope describes how much vertical change occurs over a horizontal distance. It is usually expressed as a percentage, which makes it easy to compare the steepness of roads, driveways, drainage lines, landscaping features, roof surfaces, and site elevations.
GS = \frac{GY}{GX} \times 100| Variable | Meaning | What to Enter |
|---|---|---|
| GS | Grade slope | The slope expressed as a percent |
| GY | Grade rise | The vertical change in elevation |
| GX | Grade run | The horizontal distance |
To use the calculator correctly, the rise and run must be in the same units. For example, feet should be divided by feet, inches by inches, or meters by meters. The run is the horizontal distance, not the length measured along the sloped surface.
How to Calculate Grade Slope
- Measure the total vertical rise between two points.
- Measure the horizontal run between those same points.
- Divide the rise by the run.
- Multiply the result by 100 to convert it to a percent grade.
If the slope goes downward, the signed result may be negative. If you only care about steepness, use the magnitude of the value.
Example 1
A path rises 50 feet over a horizontal distance of 1000 feet.
GS = \frac{50}{1000} \times 100 = 5\%This means the path rises 5 units for every 100 horizontal units traveled.
Example 2
A surface rises 60 units over a run of 700 units.
GS = \frac{60}{700} \times 100 \approx 8.57\%An 8.57% grade is noticeably steeper than a 5% grade, because the vertical change is larger relative to the horizontal distance.
Grade Slope Conversion Reference
Percent grade, decimal slope, angle, and ratio are all different ways to describe the same incline.
S_d = \frac{GY}{GX}GS = S_d \times 100
\theta = \arctan\left(\frac{GY}{GX}\right)GS = \tan(\theta) \times 100
N = \frac{100}{GS}In the ratio form 1:N, the value N tells you how many horizontal units are needed for 1 unit of vertical rise. For example, a 5% grade is about 1:20.
| Percent Grade | Rise per 100 Horizontal Units | Approximate Ratio |
|---|---|---|
| 1% | 1 unit | 1:100 |
| 2% | 2 units | 1:50 |
| 5% | 5 units | 1:20 |
| 10% | 10 units | 1:10 |
| 25% | 25 units | 1:4 |
| 50% | 50 units | 1:2 |
| 100% | 100 units | 1:1 |
How to Interpret Grade Slope
- Small percentages indicate gentle inclines and gradual elevation changes.
- Larger percentages indicate steeper slopes and faster elevation gain over a short run.
- 0% means the surface is level.
- 100% means the rise equals the run.
- More than 100% means the rise is greater than the horizontal run.
Percent grade is especially useful because it gives an immediate sense of steepness without needing trigonometry. If a surface has a 12% grade, it rises 12 units for every 100 horizontal units.
Common Uses for Grade Slope
- Checking driveway and road steepness
- Estimating site grading and earthwork changes
- Designing drainage paths and runoff direction
- Comparing trail, hill, or embankment steepness
- Planning trenches, channels, or sloped surfaces
- Converting field measurements into a simple percent value
Common Mistakes
- Mixing units: convert both measurements to the same unit before dividing.
- Using slope length instead of run: grade uses horizontal run, not the diagonal distance along the surface.
- Reversing the formula: rise should be divided by run, not the other way around.
- Forgetting the percent conversion: multiplying by 100 is what turns the decimal into percent grade.
- Using a zero run: division by zero is undefined, so the run must be greater than zero.
Frequently Asked Questions
What does a 5% grade mean?
A 5% grade means the elevation increases by 5 units for every 100 horizontal units. That could be 5 feet per 100 feet, 5 meters per 100 meters, or any other matching unit pair.
Is grade slope the same as slope angle?
No. Grade slope is expressed as a percentage, while slope angle is expressed in degrees. They describe the same incline in different formats.
Can grade slope be negative?
Yes. A negative value indicates the surface falls as you move forward along the run. In many practical situations, people report the absolute value when they only want the steepness.
Can grade slope be greater than 100%?
Yes. That happens when the rise is larger than the horizontal run. It represents a very steep incline.
Why is horizontal run important?
Horizontal run gives a consistent basis for comparison. Using the sloped surface length instead would understate the actual grade.
