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Level Loop Misclosure Calculator

Work out level loop misclosure instantly with clear inputs, formula shown and shareable results.

About Level Loop Misclosure Calculator

In a closed level loop the sum of backsights minus the sum of foresights should equal the change in level, which is zero for a loop returning to its start. Any residual is the misclosure. Allowable misclosure grows with the square root of loop length because random errors accumulate in that way, with the constant set by the order of levelling.

Formulas

Misclosure

Misclosure = sum of backsights - sum of foresights

Allowable

Allowable mm = constant x sqrt(loop length in km), typically 12 mm for ordinary work

Worked example

With the default values below, Level Loop Misclosure Calculator returns Loop misclosure of -56.00. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sum of backsightsminimum 0 m
12.345 m
Sum of foresightsminimum 0 m
12.401 m
Loop lengthminimum 0.01 km
2.5 km
Allowable misclosure constantminimum 1 mm per root km
12 mm per root km

Results

Loop misclosure
-56.00 mm
Allowable misclosure
18.97 mm
Assessment
Exceeds the allowable misclosure — re-level the loop
Misclosure per kilometre
-22.400 mm/km

Step by step

  1. 1Values used
  2. 2Misclosure
  3. 3Allowable
  4. 4Loop misclosure= -56.00 mm
  5. 5Allowable misclosure= 18.97 mm
  6. 6Assessment= Exceeds the allowable misclosure — re-level the loop
  7. 7Misclosure per kilometre= -22.400 mm/km

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is the Level Loop Misclosure figure worked out?

Misclosure = sum of backsights - sum of foresights. In a closed level loop the sum of backsights minus the sum of foresights should equal the change in level, which is zero for a loop returning to its start.

How is the correction distributed?

In proportion to the distance or the number of setups between benchmarks, applied with opposite sign to the misclosure so the loop closes exactly.

What values do I need to enter?

This calculator takes 4 inputs: Sum of backsights, Sum of foresights, Loop length, Allowable misclosure constant. The pre-filled defaults are a realistic worked example — replace them with your own site or project figures.

Related Calculators

Level Loop Misclosure Calculator – Calculate Loop misclosure