What the instrument measures
A level's line of sight is perpendicular to gravity — once it's set up, every reading on a vertical rod tells you a height relative to the eyepiece. Two rod readings, one looking back at a known benchmark and one looking ahead at the next point, are enough to carry the elevation forward.
- BS — backsight. Rod reading on the known elevation. Added to the elevation to get the instrument height.
- FS — foresight. Rod reading on the next point. Subtracted from instrument height to get that point's elevation.
- HI — height of instrument. The elevation of the line of sight itself. Always equals elev + BS.
- TP — turning point. A temporary station you reuse for both an FS (from the old setup) and a BS (from the new setup). Choose a stable, repeatable spot — a stake top, a chiseled mark on rock.
Two formulas, used over and over
Every station boils down to the same two lines. Master these and the rest is bookkeeping.
Why you close back to where you started
One leg of leveling tells you a difference. A loop — back to the same benchmark or forward to another known one — tells you whether you can trust it. The closing check is one line of arithmetic:
Plug numbers into the table below. Edit any BS or FS — the closing arithmetic check at the bottom updates live. Try blanking out a single turning point's FS to see why one bad reading cascades through every elevation downstream.
| Station | BS | HI | FS | Elev |
|---|---|---|---|---|
| BM-A | 104.320 | 100.000 | ||
| TP-1 | 103.080 | 97.900 | ||
| TP-2 | 101.300 | 98.230 | ||
| TP-3 | 99.080 | 96.140 | ||
| BM-B | — | 95.870 | ||
| ΣBS / ΣFS | 15.510 | 19.640 |
Try this: change BM-A's starting elevation to 250.00 — every elev shifts but the differences (and ΣBS, ΣFS) stay constant. That's leveling's superpower: it measures differences, never absolutes. Now blank out one of the BS or FS values — see how the rest of the column goes "—"? Real field books have the same dependency chain. Lose a turning point and you lose every elevation downstream of it.
How small the misclosure has to be
Federal Geodetic Control Subcommittee (FGCS) standards bound the allowable misclosure as a function of the loop's total length. The bigger the loop, the more error you're allowed — but it grows as the square root of distance, not linearly.
| Order | Max misclosure | Typical use |
|---|---|---|
| 1st | 4 mm × √K | Geodetic primary control, monument readjustment |
| 2nd Class I | 6 mm × √K | Major boundary, dam / bridge construction |
| 2nd Class II | 8 mm × √K | Photo-control vertical, control densification |
| 3rd | 12 mm × √K | Topographic, most boundary, engineering layout |
In practice, hold yourself to 3rd-order or better for boundary, construction, and most engineering work. 2nd-order shows up in NAVD88 readjustment work or any project tied to a published vertical control monument.
Spreading the error over the loop
Once the misclosure is inside tolerance, you distribute it back through the loop in proportion to the distance leveled. Each station's corrected elevation is the raw elevation minus the share of the closing error attributable to that station's share of the total distance.
Mistakes the field eats first
- Unbalanced setups. Keep BS and FS sight lengths roughly equal at each setup. Equal distances cancel collimation error, earth curvature, and refraction — the three things you can't see in the bubble.
- Plumb the rod. A rod leaning one inch at six feet introduces a measurable error. A circular bubble on the rod or a second rodman calling plumb solves it.
- Re-read on every setup. Always re-shoot the same BS twice when you move the instrument. The two readings agreeing is cheap insurance.
- Close it the same day. If you can, finish at a known elevation before the sun has moved enough to change atmospheric refraction. A 6-hour gap between BS and FS readings on long sights is where mystery errors hide.
How well did it stick?
A quick 5-question check on Differential Leveling. See where you stand and what to review.