Differential Levelling Elevation

Also known as HI method · backsight foresight

E_2 = E_1 + \text{BS} - \text{FS}

Worked example: BM 100.00 m, BS 152 cm, TP at 99.21 m → FS 2.31 m — press Try an example to run it live, then adjust anything.

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Differential Levelling Elevation explained

Differential levelling is the oldest reliable way to move an elevation across a site, and it is nothing but addition and subtraction done in the right order. Sight back to a rod held on the benchmark: that backsight, added to the known elevation, gives the height of instrument — the elevation of the telescope's line of sight, and the number a field book records in its own column. Sight forward to a rod on the new point: that foresight, subtracted from the HI, gives the new elevation. Backsights are plus sights, foresights are minus sights, and the whole discipline of the field book is keeping those two columns straight.

A worked example: benchmark at 100.00 m, backsight 1.52 m, so HI = 101.52 m; foresight to the turning point reads 2.31 m, so the new elevation is 99.21 m. The check is arithmetic and unforgiving: over a closed level loop, the sum of all backsights minus the sum of all foresights must equal the difference between the starting and ending elevations, and it must come back to zero on a loop that returns to the benchmark. Keeping backsight and foresight distances roughly equal at each setup is the other half of good practice — it cancels both collimation error and earth curvature.

Differential Levelling Elevation formula

E_2 = E_1 + \text{BS} - \text{FS}

Where

$E_2$ = Elevation of the new point (m)
$E_1$ = Elevation of the known point (m)
$\text{BS}$ = Backsight rod reading (m)
$\text{FS}$ = Foresight rod reading (m)

Missing one of these? Work it out first, then come back

Elevation of the new point — Elevation from Grade and Distance, Bernoulli's Equation (Two Points)
Elevation of the known point — Elevation from Grade and Distance, Bernoulli's Equation (Two Points)