How this calculation works
Carry a turning-point level from one instrument setup to the next. Keep backsights positive and subtract the foresight from that setup’s height of instrument. Check arithmetic separately from any comparison with an independently known closing level; no closure adjustment is applied.
HI = prior RL + BS; next RL = HI − FS; final RL = start RL + ΣBS − ΣFSA worked example
From RL 100 m, BS 1.5 and FS 0.8 give HI 101.5 m and next RL 100.7 m. The next BS 1.2 and FS 2 give final RL 99.9 m. If a known closing RL is 99.85 m, calculated minus known is +0.05 m.
Good to know
Upright-staff paired setups only; no intermediate/inverted sights, angular observation reduction, curvature/refraction or instrument-error corrections. No closure distribution or acceptance tolerance. A zero arithmetic residual follows from the calculation and cannot verify the measurements or benchmark.
Reference: FAO: direct levelling, backsights, foresights and turning points (opens in a new tab) ↗
Check the land-unit definitions and sources
The standard factors use the international foot and an acre of 43,560 sq ft. Cent means 1/100 acre; gunta means 1/40 acre; the selected Chennai ground means 2,400 sq ft.
The Assam report defines bigha as 14,400 sq ft, katha as 2,880 sq ft and lecha as 144 sq ft. The cited West Bengal court order mentions a 720-sq-ft katha convention. These are explicit presets, not an automatic definition for every record or every place using the same name. Match your record to the stated convention, or use its verified custom factor.
- NIST: exact international-foot and acre factors (opens in a new tab) ↗
- API Setu MDDS: acre/cent and acre/gunta relationships (opens in a new tab) ↗
- Greater Chennai Corporation: one ground is 2,400 sq ft (opens in a new tab) ↗
- Government of Assam AIRBMP framework: section 7.2, page 28 (bigha, katha and lecha) (opens in a new tab) ↗
- Supreme Court order, 7 May 2025: paragraph 2, page 2 (West Bengal katha) (opens in a new tab) ↗
The acre relationships are converted using exact base factors. Rounded or unrelated regional values in a reference table are not substituted for these definitions.
Carry the turning-point level between instrument setups
A backsight is taken to a point whose reduced level is already available. Adding its upright-staff reading to that level gives the height of instrument in the chosen vertical datum. A foresight is then subtracted to calculate the next point’s reduced level. Height of instrument here is an elevation, not the tripod’s physical height above the ground.
Starting from RL 100 m, a backsight of 1.5 m gives HI 101.5 m. A foresight of 0.8 m gives the turning point RL 100.7 m. After moving the instrument, a backsight of 1.2 m gives the new HI 101.9 m, and a foresight of 2 m gives final RL 99.9 m.
Enter one BS/FS pair for each setup. The point foresighted in one row is the point backsighted in the next. Intermediate sights and inverted-staff readings require a different observation structure and are deliberately not interpreted as these paired setup rows.
A land elevation profile also needs horizontal station distances to find gradients. A backsight/foresight level book alone does not supply those distances.
Arithmetic agreement is different from independent closure
In the example, backsights total 2.7 m and foresights total 2.8 m. Their difference is −0.1 m, which equals final RL minus starting RL. The displayed arithmetic residual is zero because the calculator constructs both quantities from the same supplied observations.
A known closing benchmark provides a separate comparison. If its RL is 99.85 m, calculated minus known is +0.05 m. That sign means the calculated closing level is higher. This page reports the difference without inventing an acceptable tolerance or distributing a correction.
Adding 500 m to the starting datum adds 500 m to every calculated RL and HI, while all BS−FS differences remain unchanged. To explore gradients afterward, the land elevation profile tool also needs horizontal station distances. No equally spaced profile is drawn from these staff-reading rows because those distances were not supplied.
A few questions, answered
Can the start level be an arbitrary local datum?
Yes, provided all benchmarks and closing comparisons use that same datum. The result does not become mean-sea-level altitude merely because it is labelled an elevation.
Why is the arithmetic residual zero even for bad observations?
It checks the calculation identity using the same entered readings. A mistyped reading can affect both sides consistently. Independent observations and a known closing level provide different evidence.
Will it balance my level loop?
No. It reports raw reduced levels and an optional closing difference. It applies no distance-weighted, setup-weighted or other adjustment.