Vertical Distance
Elevation change from a slope distance and angle.
Formula
Variables
Example
L=50 m, θ=10°: V = 50×0.174 = 8.7 m
How it works
This formula gives the vertical change in height when you know the length of a sloping line and its angle to the horizontal. It works because the vertical part of the sloped distance is just the opposite side of a right triangle, so trigonometry lets us find it using the sine ratio. In surveying, this is how a measured slope distance is turned into an elevation difference.
When to use it
Use this when you have a slope distance and a slope angle and need the rise or fall between two points. It is common in land surveying, leveling, construction layout, and any situation where distances are measured along an incline rather than flat ground.
Worked example, step by step
A surveyor measures a slope distance of L = 120 m at an angle of θ = 6°. V = L sinθ V = 120 × sin(6°) V = 120 × 0.1045 V = 12.54 m So the vertical distance is about 12.5 m.
Common mistakes to avoid
- Using the angle in degrees as if it were the sine value
- Mixing up slope distance with horizontal distance
- Forgetting that a negative angle would mean a downward change in elevation
Did You Know?
Horizontal and vertical components together let surveyors reconstruct 3D terrain from a tape and angle.
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