Leveling Rise & Fall Calculator

Differential leveling runs a level line from a known benchmark to a destination point, taking a backsight (BS) and foresight (FS) reading at each instrument setup along the way. The Rise and Fall method reduces those readings without ever computing an instrument height: since the backsight and foresight of one setup are both taken from the same horizontal line of sight, their difference alone gives the elevation change for that section — rise = BS − FS, a rise when positive, a fall when negative.

How it works

1. Starting RL is the reduced level (elevation) of the benchmark — the known point the level run starts from.
2. Readings are entered one setup per line as BS, FS (an optional leading label names the setup, e.g. BM to CP1, 1.505, 0.845).
3. For each setup, rise = BS − FS. A positive value is a rise (ground went up); a negative value is a fall (ground went down).
4. Each point's reduced level is the previous point's RL plus that setup's rise, or minus its fall.
5. Arithmetic check: ΣBS − ΣFS should equal ΣRise − ΣFall, which should equal the final RL minus the starting RL — the same three-way check a hand-reduced level book is checked against.
6. Closing error (optional): if you already know the true RL of the final point (surveyed from another benchmark, say), enter it and the tool reports the misclosure — how far the computed run drifted from the known value.

Reading the result

The table lists every setup's BS, FS, rise, fall and running reduced level. The summary line packs the starting/final RL, the totals, the arithmetic check, and (when provided) the closing error into one copyable block for a field note or a report.

What if my rise/fall figures don't balance the arithmetic check?

They always will here — the check is computed from the same numbers as the table, so it's a sanity confirmation rather than an independent audit. Its real purpose is standard: it's what you'd hand-verify against if you were reducing the same run in a paper level book, and it's what a reviewer expects to see attached to a leveling result.

What does a nonzero closing error mean?

It's the difference between the run's computed final RL and a final RL you already trust. A small nonzero value is normal instrument/reading error accumulated over the run; a large one usually means a misread staff, a bumped tripod, or a transcription mistake somewhere in the readings.

Does this support intermediate sights (IS)?

Not directly — each line is one full setup's backsight-to-foresight section. If your run has intermediate sights between setups, reduce those separately or split the run at each IS as its own single-reading "setup" against the previous point.