What it does
Levelling finds heights. A level is set up, a staff is read on a point of known height (the back sight, BS), then on other points (intermediate sights, IS), and finally on a change point (the fore sight, FS) before the level moves on. The field book of readings is then reduced to heights, called reduced levels (RL).
This tool reduces a whole book by both classic methods, height of collimation and rise and fall. It runs every arithmetic check, compares the end with a known benchmark or with the start of a loop, tests the misclosure against a limit you set, shares the error out and draws the profile. Nothing leaves your browser.
How to use it
- Paste or open the book: one row per reading with station, BS, IS, FS, and optionally distance and remarks. Separate the columns with tabs or commas and leave empty cells blank. A change point has its FS and BS on the same row.
- Enter the reduced level of the first point (the starting benchmark).
- Say how the run closes: on a known benchmark, back at the start (a loop), or not at all.
- Enter k for the allowed misclosure, k√K millimetres, where K is the route length in km or the number of setups. Use the value from your job’s specification.
- Choose how to share the error: equally per setup, or in proportion to distance.
The checks
- ΣBS − ΣFS = last RL − first RL: confirms the arithmetic of either method.
- ΣRise − ΣFall = ΣBS − ΣFS: the rise-and-fall check.
- Full collimation check: Σ(RLs after the first) = Σ(each height of instrument × readings taken from it) − ΣIS − ΣFS. Unlike the first check, this one also catches mistakes in intermediate sights.
The arithmetic checks only prove the sums. Only closing on a known level shows how good the field work was.
Worked example
The made-up example levels a road centre line from BM A (RL 85.210) to BM B (known RL 85.821) over 165 m with two change points. ΣBS − ΣFS = 0.615, so BM B comes out at 85.825: a closing error of +4.0 mm. With k = 12 mm per √km the limit is 12 × √0.165 = 4.9 mm, so the work passes. Sharing the error equally over the 3 setups takes about 1.3 mm off the first setup’s readings, 2.7 mm off the second’s and 4 mm off the third’s.
Good to know
- Keep back and fore sight lengths about equal on each setup, so collimation and curvature errors cancel.
- An intermediate sight is never checked by closing on a benchmark: a misread IS gives a wrong level with no warning except the full collimation check.
- For feet, enter readings in feet; the misclosure is then shown as thousandths of a foot labelled mm, so read it as such or convert.
FAQ
Which method should I use? Both give the same levels. Rise and fall has a check on every reading; height of collimation is quicker for many intermediate sights. The tool shows both.
Where does k come from? From the specification for the job or the agency you work to. Typical values range from a few millimetres for precise work to tens of millimetres for rough construction levelling.
Where the numbers come from
- Rise-and-fall and height-of-collimation reduction, their arithmetic checks, k√K misclosure limits and the distribution of the closing error: standard plane surveying, written by fibub from first principles.
- No national or agency levelling standards are bundled: the user enters k from the specification for their job.
- The example level book is made up by fibub for illustration.
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Last updated 2026-11-08.