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RL Difference Calculator

Derives reduced levels from backsight and foresight readings using the height-of-collimation method.

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How to use this calculator

Inputs

One setup: HI from the known RL and backsight, the new RL from the foresight.

More options

An inverted staff (held against a soffit) reads upward from the line of sight, so its reading counts as negative.

Enter the values and press Calculate.

Or load an example to see a worked result.

Your setup
Schematic
Your setupSchematic level between a known point and a new point.HI = RL + BSBSFSknown RLnew RLknown pointnew point
Calculate to label the setup with your readings, HI and RLs.

Booking table (several setups)

One row per staff position, in order. Row 1 is the backsight on the starting point; a turning point takes its foresight and the next backsight on the same row; intermediate sights stand alone.

How the method works

Height of collimation
Illustrative method
Height of collimationA level set up between a staff on a known point and a staff on a new point, with the line of collimation and both staff readings.HI = 101.250BS 1.250FS 0.880RL 100.000RL 100.370known pointnew point
Reduce both readings from the same instrument height: HI = known RL 100.000 + BS 1.250 = 101.250 m; new RL = HI − FS 0.880 = 100.370 m. The change, BS − FS = +0.370 m, is positive because the new point is higher. Heights schematic.

Fixed example values for illustration — not your result.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. One setup: enter the known RL, the backsight on it and the foresight on the new point.
  2. Several setups: use the booking table — one row per point with a BS, IS or FS (a turning point carries both FS and BS) — and an optional known closing RL.
  3. Read each HI and RL, the Σ BS − Σ FS arithmetic check and the closure.
  4. For an inverted staff held against a soffit, choose the signed convention under More options and enter that reading as negative. The setup diagram follows the result; the booking table below handles several setups.

How it works

Height-of-collimation method: HI = known RL + BS, and each RL = HI − its staff reading. The difference between two points is BS − FS.

At a turning point the foresight closes one setup and the new backsight sets the next HI. Intermediate sights are reduced from the current HI and never enter the Σ BS − Σ FS check.

Arithmetic check: Σ BS − Σ FS = last RL − first RL. Closure against a known benchmark = computed end RL − known end RL.

Worked example

RL 100.000, BS 1.250, FS 0.880. HI 101.250, new RL 100.370 m, a rise of +0.370 m. Swapping the readings gives −0.370 m.

Common mistakes

  • Leaving a reading blank and expecting it to count as zero — the table refuses it.
  • Adding intermediate sights into the Σ BS − Σ FS check.
  • Taking a new backsight before closing the setup with a foresight on the same turning point.

Frequently asked questions

Backsight or foresight first?

Backsight is read on the known point; foresight on the new point. New RL = known + BS − FS.

Is this rise and fall?

No — it is the height-of-collimation method. Rise and fall reaches the same RLs by a different booking and check.

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Cite this tool

Zerdly. (2026). RL Difference Calculator. Retrieved from https://www.zerdly.com/tools/rl-difference-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.