Slope / Gradient
Steepness of terrain as a percentage.
Formula
Variables
Example
A road rising 5 m over 100 m has a gradient of 5%.
How it works
The gradient tells you how steep a slope is by comparing how much height changes to how far you move horizontally. It works because a very steep hill has a large vertical rise for a small horizontal run, while a gentle slope has a small rise over a larger run. Multiplying by 100 turns this ratio into a percentage, making it easier to compare slopes in roads, hills, and terrain maps.
When to use it
Use this formula when you need to describe or compare the steepness of a hill, road, ramp, embankment, or landscape feature. It is also useful in geography, surveying, civil engineering, and outdoor route planning.
Worked example, step by step
A trail climbs 12 m over a horizontal distance of 300 m. Gradient = (rise ÷ run) × 100% Gradient = (12 ÷ 300) × 100% Gradient = 0.04 × 100% Gradient = 4% So, the trail has a gradient of 4%.
Common mistakes to avoid
- using the sloping path length instead of the horizontal distance for the run
- forgetting to multiply by 100 to convert the ratio into a percentage
- mixing up rise and run, which gives the wrong steepness
Did You Know?
Road signs give steepness as a percent grade — a 10% grade rises 10 meters for every 100 traveled.
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