Calculate height of instrument, point elevation, and target rod reading from benchmark, backsight, foresight, and design elevation for surveying work.

Enter enough related known values, usually three. Leave unknown values blank. All elevations must use the same vertical datum.

Leveling with a benchmark

The calculator above uses a single instrument setup: height of instrument (HI) = benchmark elevation + backsight, and point elevation = HI − foresight. Enter enough related known values and leave unknown values blank. For example, a 100 ft benchmark, 5.25 ft backsight and 3.40 ft foresight give HI = 105.25 ft and point elevation = 101.85 ft, a rise of 1.85 ft. All elevations must reference the same vertical datum.

The slope method below is a separate way to estimate a point elevation from a known grade and horizontal distance; it is not the backsight/foresight method used by this calculator.

Point Elevation (from a Benchmark) Formula

The following formula is used to calculate the elevation at a target point from a known starting elevation, a horizontal distance, and a slope (grade).

BE = SD + (D × S)

Variables:

  • BE is the elevation at the target point, relative to the chosen vertical datum (meters or feet)
  • SD is the known elevation at the starting reference point (often a benchmark), relative to the same vertical datum (meters or feet)
  • D is the horizontal distance (run) between the two points (use consistent units)
  • S is the slope/grade as rise/run (dimensionless; for percent, divide by 100; for degrees, use tan(angle))

To calculate the target elevation, multiply the horizontal distance (D) by the slope (S) to get the elevation change, then add that change to the starting elevation (SD). The result (BE) is the target point’s elevation relative to the same vertical datum.

What is Benchmark Elevation?

A benchmark is a permanent physical mark with a known elevation referenced to a vertical datum (for example, a local mean sea level–based datum or an official national datum). The benchmark elevation is the published elevation value for that mark. Benchmarks provide a starting or reference point for surveyors to determine elevations of other points in the surrounding area.

How to Calculate a Point Elevation From a Benchmark (Slope Method)?

The following steps outline how to calculate a point’s elevation using a known reference elevation and a slope:

  1. Determine the known elevation at the starting reference point (SD) relative to your chosen vertical datum.
  2. Determine the horizontal distance (D) between the starting point and the target point.
  3. Determine the slope/grade (S) between the points as rise/run (or as percent/angle and convert as needed).
  4. Use the formula BE = SD + (D × S) to calculate the target elevation.
  5. Insert the values of SD, D, and S into the formula and calculate the result.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Starting Elevation (SD) = 10 meters

Horizontal Distance (D) = 50 meters

Slope (S) = 2% (0.02 m/m) → Target Elevation (BE) = 11 meters