Enter a known starting elevation (often a benchmark elevation), the horizontal distance, and the slope/grade into the calculator to determine the elevation at a target point. This calculator can also solve for any one variable when the other three are known.

Benchmark Elevation Calculator

Use a known benchmark elevation to calculate height of instrument, point elevation, or the target rod reading needed to hit design grade.

Benchmark to Point Elevation
Target Rod Reading

Benchmark to Point Elevation

Enter benchmark elevation, backsight, and foresight to calculate height of instrument and point elevation.

Formula: Height of Instrument = Benchmark Elevation + Backsight. Point Elevation = Height of Instrument – Foresight.

Target Rod Reading

Enter benchmark elevation, backsight, and target design elevation to find the rod reading needed to set grade. You can also enter an actual rod reading to check whether you need cut or fill.

Formula: Target Rod Reading = Height of Instrument – Target Design Elevation.

Results

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