What the columns are doing
Differential levelling moves a known elevation across a site one instrument setup at a time. At each setup you read the rod on a point whose elevation you already have — that is the backsight — and adding it to that elevation gives the height of the line of sight, the height of instrument. Every other reading taken from that setup is subtracted from the HI. Read the rod on the next turning point, subtract, and you have a new known elevation to set up on. Repeat until you get back to where you started.
The backsight is not "behind you" and the foresight is not "in front of you"; the instrument gets spun around constantly. Backsight means the sight onto the known point, foresight means the sight onto the point you are establishing. Crews that think of them as plus sights and minus sights make fewer mistakes with the columns.
The check that proves nothing
Add up all the backsights, add up all the foresights, subtract. That number must equal the last elevation minus the first. If it doesn't, you added something wrong. If it does, you added everything right — and that is the entire extent of what it tells you.
This is worth being blunt about because the arithmetic check gets treated as verification. It isn't. Transpose a rod reading, read 4.27 as 4.72, let a turning point sink an eighth of an inch under someone's boot, forget that the tripod leg is standing on a plank that flexed — every one of those errors flows straight through the columns and balances perfectly at the bottom. The number that tests the field work is the misclosure: run the loop back onto the benchmark you started from and see how far off you land.
Where the error actually comes from
| Source | How it behaves | What reduces it |
|---|---|---|
| Instrument out of adjustment | Grows with the difference between backsight and foresight length | Balance the sight distances at every setup — pace them, don't guess |
| Turning point settling | One-directional, accumulates | Use a solid point: a hub, a pin, a turtle, never soft ground or a stake top that moves |
| Rod not plumb | Always reads high | Wave the rod and take the lowest reading, or use a rod level |
| Reading and booking blunders | Large, random, invisible to the column check | The loop closure; nothing else catches it |
| Refraction and curvature | Grows with sight length, partly cancels on balanced sights | Shorter sights, balanced sights, avoid shooting low over hot pavement |
Balanced sight distances are the one habit that pays for itself immediately. If the backsight and foresight from a setup are the same length, a collimation error in the instrument enters both readings equally and cancels when you subtract. Let one sight be 200 feet and the other 40 and it does not cancel at all.
Adjusting a loop that misses
When the loop closes with a small misclosure, the usual move is to distribute it across the turning points so the last elevation lands on the known value. The version here spreads it evenly by setup, which assumes each leg contributed about the same. Where the legs are wildly different lengths, distributing by distance is the better model, and where the misclosure is large the honest answer is not to adjust it at all — a big miss means something specific went wrong, and smearing it across the loop hides the blunder instead of finding it.
What counts as small is a job question, not a general one, which is why the allowance here is something you type in from your specification. Once the elevations are settled, the grade stake calculator turns them into cut and fill at each station, and the grid cut and fill calculator turns a whole grid of them into earthwork volume.
Questions people ask
What is the height of instrument, exactly?
It is the elevation of the line of sight through the instrument, not the height of the tripod or the eyepiece above the ground. You get it by adding the backsight reading to the elevation of the point the rod was standing on. If the rod is on a benchmark at 100.00 and reads 5.42, the line of sight is at 105.42 whatever the ground under the tripod is doing. Every foresight and every intermediate sight from that setup gets subtracted from 105.42.
Why does my loop close perfectly but the elevations look wrong?
Because the closure check and the column check are different things, and it sounds like you are looking at the column check. Sum of backsights minus sum of foresights always equals the last elevation minus the first, no matter what the readings were — it is an algebraic identity, not a test. A misread rod, a settled turning point or a transposed booking passes it every time. Only running the loop back onto a point of known elevation and comparing tests the readings themselves.
How close does a loop have to close?
That depends entirely on what the elevations are for and what the job specification says, which is why it is an input here rather than a number this page supplies. A rough grading loop and a loop setting anchor bolts are held to nothing like the same figure. Specifications often express the allowance as a coefficient times the square root of the loop distance, so the field can be given something and the coefficient comes from the spec document. If nobody has written one down, that is a question for whoever is accepting the work, not something to invent.
What is the difference between a turning point and an intermediate sight?
A turning point carries the elevation forward: you foresight onto it, move the instrument, backsight onto the same physical point, and everything after depends on it. An intermediate sight is a shot taken from a setup purely to get the elevation of something — a grade shot, an existing invert, the top of a footing — and nothing downstream depends on it. That is why turning points want a hard, stable object and intermediate shots can land wherever you need a number: an error in a turning point propagates through the rest of the loop, an error in an intermediate sight stays where it is.
Can I use an assumed benchmark elevation?
Yes, and on a small job it is common. Set a stable object as 100.00 and every elevation on the site becomes relative to it, which is all you need for cut, fill, floor heights and drainage falls. What you lose is any relationship to a real vertical datum, so it will not tie into a public benchmark, a flood elevation, or anything on a survey drawing. If elevations on the drawings are on a named datum and you set your own, the two sets of numbers will never agree and someone will eventually build to the wrong one.