Calculate vertical distance between two elevations, or find the vertical rise from total and horizontal distance, slope distance and angle, or a grade.

Enter both elevations from the same datum, such as sea level.

Horizontal geometry
Leave blank if unknown. Enter 0 only for a known vertical line.

Vertical Distance Formula

The following formula is used to calculate the Vertical Distance.

Dv = √(TD2-HD2)
  • Where Dv is the Vertical Distance
  • TD is the total distance 
  • HD is the total horizontal distance 

To calculate vertical distance, square the total distance, subtract the square of the horizontal distance from that result, then take the square root of this number.

How to Calculate Vertical Distance?

The following example problems outline how to calculate Vertical Distance.

Example Problem #1:

  1. First, determine the total distance.
    • The total distance is given as 100.
  2. Next, determine the total horizontal distance.
    • The total horizontal distance is provided as 30.
  3. Finally, calculate the Vertical Distance using the equation above: 

Dv = √(TD2-HD2)

The values given above are inserted into the equation below and the solution is calculated:

Dv = √(1002-302) = 95.39

Example Problem #2: 

For this problem, the variables needed are provided below:

total distance = 50

total horizontal distance = 20

This example problem is a test of your knowledge on the subject. Use the calculator above to check your answer. 

Dv = √(TD2-HD2) = ?