Differential leveling calculator: height differences, elevations and misclosure
Enter the backsight and foresight readings of each setup: the calculator works out the height differences, the elevations and the misclosure, compares it with the allowable misclosure (mm·√km) and returns the adjusted elevations.
| Point (foresight) | Backsight (m) | Foresight (m) | Setup distance (m) |
|---|
Each row is one instrument setup: backsight on the previous point and foresight on the new one. The setup distance (backsight + foresight sight lengths) is optional, but without it the allowable misclosure per km cannot be computed. Readings and distances are in meters; readings above 10 are treated as millimeters (1532 = 1.532 m).
Result
Enter the backsight and foresight readings.
How the leveling is reduced
Height difference of each setup = backsight − foresight. Positive means the ground rises (a rise); negative, it falls (a fall). Elevation of a point = elevation of the previous point + height difference. The arithmetic check: ΣBS − ΣFS = last elevation − first elevation.
Misclosure: in a closed loop the height differences should add up to zero; between two benchmarks they should add up to the difference between their known elevations. The allowable misclosure is t = k·√K, with K = length leveled in kilometers and k in millimeters (e.g. 3 to 5 mm for high-precision work and about 12 mm for ordinary engineering leveling — use the value of the specification that applies to your job).
Adjustment: the misclosure is distributed in proportion to the cumulative distance (or in equal parts per setup when there are no distances). The last elevation then closes exactly on the benchmark.
FAQ
What is the allowable misclosure for differential leveling?
It is given in millimeters times the square root of the distance in kilometers (k·√K). Typical values: about 3 to 4 mm·√km for geodetic (first-order) leveling, 8 to 12 mm·√km for engineering and construction leveling, and 20 mm·√km or more for rough work. Each country or agency publishes its own classes (e.g. the US FGCS standards range from about 3–4 mm·√km for first order to 12 mm·√km for third order); always check the tolerance required for your job.
Why level forward and back?
Running back over the same line (or closing the loop) is what lets you measure the error. An open level run, with no check, will not reveal a wrong reading.
What is the difference between an assumed elevation and a true elevation?
An assumed elevation is a height relative to an arbitrary reference (e.g. a benchmark given 100.000 m). A true elevation refers to the national vertical datum (mean sea level), starting from an official benchmark published by your geodetic agency. The math is the same; only the starting value changes.
Can I use intermediate sights (side shots)?
This version reduces the main line (backsight and foresight at every setup). Intermediate sights taken from the same setup are reduced by the height-of-instrument method: HI = elevation of the backsight point + backsight; elevation of the point = HI − reading on the point.
Where can I find benchmarks near my job?
Your national geodetic or mapping agency publishes benchmark descriptions and elevations (e.g. NGS datasheets in the US). In Brazil, our tool Geodetic marks near you lists the IBGE benchmarks with their elevation, condition and official report.