How to use the differential leveling field book calculator
- Enter the known elevation of the first point, such as a benchmark.
- Fill in the field book rows in order. The first row has a backsight only, a turning point has a foresight and a backsight, an intermediate point has one intermediate reading, and the last row has a foresight only.
- If the line ends on a benchmark, enter its known elevation to get the misclosure and adjusted elevations. In Advanced options add the allowed misclosure constant and the length of the line.
- Read the elevations, the arithmetic check and whether the closing error is within the allowance.
Formula
Height of instrument HI = elevation of a known point + backsight
Elevation of another point = HI - its foresight or intermediate reading
Check: sum of backsights - sum of foresights = last elevation - first elevation
Misclosure = computed last elevation - known elevation; adjustment = -misclosure x setup number / number of setups
All readings are the staff readings in meters or feet. Each time the instrument is moved, a new setup begins, which is why the correction grows along the line.
A four point line from a benchmark of 100.000
A first backsight of 1.524, a turning point with foresight 1.352 and backsight 1.210, an intermediate sight of 0.880, a second turning point with foresight 2.105 and backsight 0.995, and a final foresight of 1.442 give elevations of 100.172, 100.502, 99.277 and 98.830. The sum of backsights is 3.729 and of foresights 4.899, a difference of -1.170, which equals 98.830 - 100.000, so the check passes.
If the closing benchmark is known to be 98.842, the misclosure is -0.0120. A constant of 12 mm per root kilometer over 0.4 km allows 0.0076, so the line is over the allowance. Spread over 3 setups, the adjusted elevations are 100.176, 100.510, 99.285 and 98.842.
Keeping a field book
Write each reading as you take it, in the order it happens, and run the arithmetic check at the end of the day before you move on. A failed check means an arithmetic or copying mistake, while a large misclosure with a passing check points to a reading or setup error in the field. Keep the backsight and foresight distances about equal to cancel many instrument errors.
For grades and angles see the slope calculator and the ramp slope calculator. Road curves are covered by the horizontal curve calculator, and earth volumes by the average end area calculator.
Height of instrument and rise and fall
Two methods reduce level notes. The height of instrument method, used here, finds the line of sight for each setup and subtracts readings from it, which is quick when there are many intermediate points. The rise and fall method compares each reading with the one before it. Both give the same elevations, which is how the page checks itself.
Assumptions and limits
- Readings are positive staff readings in one unit, and elevations come out in the same unit.
- The first row has a backsight only, and the last row has a foresight only with no backsight.
- The misclosure is spread evenly over the setups; other adjustment methods exist.
- The allowance constant comes from your own specification. The page does not supply one.
Frequently asked questions
How do I do differential leveling?
Take a backsight on a known point to get the height of instrument, then take a foresight on the next point to subtract from it. Repeat from each turning point until the end.
What is the arithmetic check in leveling?
The sum of the backsights minus the sum of the foresights must equal the last elevation minus the first. If it does not, there is a computing mistake.
What is misclosure?
It is the difference between the elevation you computed for the last point and its known elevation. It shows the combined error of the line.
What is an intermediate sight?
It is a reading on a point that is not a turning point, taken from the same setup, so it does not carry the line forward.