---
title: "Closing error in a level circuit"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:closing-error-level-circuit"
source: https://www.bctengineer.com/q/semester_3/surveying_i/closing-error-level-circuit
site: BCT Engineering
---

# Closing error in a level circuit

Surveying I · Chapter 5: Leveling

- Asked in: 2075 Chaitra, 4 marks
- Video: [Level circuit adjustment](https://www.youtube.com/watch?v=JIZ4AvUZdAc) — Todd Horton
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/closing-error-level-circuit
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

What is closing error in a level circuit? How can the closing error be adjusted in a level circuit? Explain.

## Short answer

Closing error is the computed minus known RL of a closing BM. If within permissible limit (e.g., ±24√K mm), distribute the error proportionally to distance or number of setups: correction = -e × (distance from start / total length). The correction is applied to change points and benchmarks.

## Answer

**Closing error** (misclosure) in a level circuit is the difference between the computed RL of the closing benchmark (or of the starting BM, if the levelling returns to it) and its known RL. It results from the accumulation of instrumental, natural and personal errors.

$$
\text{Closing error} = \text{computed RL of last point} - \text{known RL of last point}
$$

**Permissible closing error:** this depends on the class of work and the project specification, for example about $\pm 24\sqrt{K}$ mm for ordinary levelling and $\pm 12\sqrt{K}$ mm for more accurate levelling (K = length of the circuit in km). If it is exceeded, the levelling must be repeated.

#### Adjustment

When the error is within the limit, it is distributed among the levels of the intermediate points. The correction is proportional to the distance (or to the number of instrument setups) from the starting point:

$$
\text{Correction at a point} = -\,e \times \frac{\text{distance of the point from the start}}{\text{total length of the circuit}}
$$

In terms of setups: the correction at the $n$-th setup $= -\,e \times n/N$, where N is the total number of setups. The correction is applied to the CPs and BMs; each intermediate point takes the same correction as the change point just before it.

**Example:** computed RL of the end BM $= 100.036$ m, known RL $= 100.000$ m, 4 setups. Error $= +0.036$ m. The corrections at the CPs after the 1st, 2nd, 3rd and 4th setups are $-0.009$, $-0.018$, $-0.027$ and $-0.036$ m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. The closing error in a level circuit is:
   A. Computed RL of the closing point minus its known RL
   B. Sum of BS minus sum of FS
   C. Sum of rises
   D. Known RL minus the starting RL
   Answer: A. It is the misclosure between computed and known RL at the end. (Key point: Closing error definition)

2. How is a permissible closing error distributed?
   A. Entirely to the first point
   B. Proportional to distance (or number of setups) from the start
   C. Equally to all points
   D. Entirely to the last point
   Answer: B. Correction = -e x (distance from start / total length) because error accumulates along the line. (Key point: Distribution)

3. The computed RL of the end BM is 100.036 m and the known RL is 100.000 m. The correction applied is:
   A. Zero at the end
   B. Doubled
   C. Negative (subtract)
   D. Positive (add)
   Answer: C. Error is +0.036, so corrections are negative, totalling -0.036 at the end. (Key point: Sign of correction)

4. With 4 setups and e = +0.036 m, the correction at the 2nd setup CP is:
   A. -0.009 m
   B. -0.027 m
   C. -0.036 m
   D. -0.018 m
   Answer: D. Correction = -0.036 x 2/4 = -0.018 m. (Key point: Example correction)

## Related in Surveying I

- [Two peg: closing error and precision of level](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-cd-50m-e-mid-f-5m) — Surveying I, chapter 5
- [Closing error and graphical adjustment](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-graphical-adjustment) — Surveying I, chapter 4, asked 13×
- [Factors of closing error; graphical adjustment](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-factors-graphical) — Surveying I, chapter 4
- [Closing error; plotting methods in compass traverse](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aclosing-error-plotting-methods) — Surveying I, chapter 4
- [Collimation error with level mid-way and near B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-peg-60m-staff-1-855-1-625) — Surveying I, chapter 5

## Related in other subjects

- [Closing resistance Rs to limit overvoltage to 1.8 pu](https://www.bctengineer.com/question.md?key=semester_8%2Fhigh_voltage_engineering%3Ars-closing-resistor-0-12-ohm) — High Voltage Engineering, chapter 3