Horizontal Distance
Level distance from a slope distance and its inclination angle.
Formula
Variables
Example
L=50 m, θ=10°: H = 50×0.985 = 49.2 m
How it works
When a measured line is sloping up or down, only part of that length lies horizontally on the map or plan. The cosine of the slope angle gives the fraction of the slope distance that acts in the horizontal direction, so multiplying the slope distance by cosb8 projects it onto a level line. This comes directly from right-triangle trigonometry, where the horizontal distance is the side adjacent to the angle.
When to use it
Use this in surveying, land measurement, and construction whenever you know the length of an inclined line and need its level equivalent. It is common when reducing tape measurements on sloping ground to horizontal map distance.
Worked example, step by step
A surveyor measures a slope distance of L = 80 m along a hillside with an inclination of b8 = 15 b0. H = L cosb8 H = 80 cos(15 b0) H = 80 d7 0.966 H = 77.3 m So the horizontal distance is 77.3 m.
Common mistakes to avoid
- Using sin(b8) instead of cos(b8) for the horizontal component
- Forgetting that the angle must match the formula 5c's definition and should be the slope angle from the horizontal
- Rounding too early, which can noticeably change the final horizontal distance
Did You Know?
Maps always show horizontal distance, which is why a hiked trail feels longer than the map says.
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