Levelling Calculator (Rise & Fall and HI)
Reduce a level book by rise and fall or height of instrument, with the arithmetic check.
Staff readings in metres. On a change point, type both the fore sight and the new back sight on the same row.
| Station | BS | IS | FS |
|---|
Free tool by EngineeringNepal.com.np · Results are for guidance; check critical figures with a qualified engineer.
How to reduce a level book
Levelling gives the height of points on the ground compared to a bench mark (BM) of known reduced level (RL). With an auto level or dumpy level you take a back sight (BS) on the BM, intermediate sights (IS) on the points you want, and a fore sight (FS) on a change point before moving the instrument. This calculator turns those staff readings into reduced levels using either of the two standard methods taught in surveying courses at IOE, Pokhara, Purbanchal and other universities.
Rise and fall method
Compare each staff reading with the one before it from the same set-up. If the new reading is smaller, the ground has risen; if it is larger, the ground has fallen.
- Rise or fall = previous reading − current reading
- RL of point = RL of previous point + rise (or − fall)
- Check: ΣBS − ΣFS = ΣRise − ΣFall = Last RL − First RL
Because every rise and fall enters the check, a mistake in any intermediate RL shows up. That is why most teachers and site engineers prefer this method for work that will be checked.
Height of instrument (collimation) method
- HI = RL of the point where the BS was taken + BS
- RL of any point = HI − IS (or FS)
- Check: ΣBS − ΣFS = Last RL − First RL
The HI method is faster when there are many intermediate sights, such as a road profile or a contour grid, but its arithmetic check does not cover the intermediate points.
Worked example
The example loaded in the calculator starts at BM1 (RL 100.000 m) with a BS of 1.585. The instrument height is 101.585, so point A with an IS of 1.950 has an RL of 99.635. At CP1 the FS is 2.375 and a new BS of 1.450 is taken after moving the level. The last point D finishes at RL 99.820 m, and ΣBS − ΣFS = 3.035 − 3.215 = −0.180, which equals 99.820 − 100.000. The check is satisfied.
Misclosure and allowable error
When you finish on a second bench mark or close the loop back on the first, the difference between the calculated and known RL is the misclosure. A common limit for ordinary engineering levelling is ±12√K mm, where K is the length of the route in kilometres. Your project or teacher may set a tighter or looser value, so treat it as a guide.
Frequently asked questions
Where do I write a change point in the level book?
On the same row: the fore sight taken before shifting the instrument and the back sight taken after. The calculator follows this layout, so type both readings on the change point row.
Can I paste my table into Excel?
Yes. Press "Copy table" and paste into Excel or Google Sheets. Columns are separated by tabs.
Does it handle inverted staff readings?
Enter an inverted reading (staff held upside down against a ceiling or bridge soffit) as a negative number. The formulas stay the same.
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