---
title: "Corrections in linear measurement"
subject: "Surveying I"
chapter: 2
key: "semester_3/surveying_i:corrections-linear-measurement"
source: https://www.bctengineer.com/q/semester_3/surveying_i/corrections-linear-measurement
site: BCT Engineering
---

# Corrections in linear measurement

Surveying I · Chapter 2: Distance Measurements

- Asked in: 2065 Shrawan, 7 marks; 2066 Bhadra, 8 marks; 2069 Chaitra, 4 marks; 2063 Baisakh, 5 marks (asked 4 times)
- Video: [Surveying | Corrections in Tape Part 1 of 2](https://www.youtube.com/watch?v=MdHdzGSSz7Q) — the Engineer's Insight
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/corrections-linear-measurement
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-2

## Question

What are the corrections applied in linear measurement? Explain briefly.

## Short answer

Corrections for standardisation (tape length), temperature, pull, sag (negative), slope (negative), alignment and reduction to mean sea level. The true length is the measured length plus the sum of all corrections.

## Answer

When a tape or chain is used in the field, the measured length differs from the true horizontal length because of the tape's condition and the field conditions. The following corrections are applied. Let $L$ be the measured length.

**1. Correction for incorrect length of tape (standardisation)**
$$
C_a = \frac{L\,(l' - l)}{l}
$$
where $l'$ is the actual tape length and $l$ the nominal length. It is positive if the tape is too long, negative if too short.

**2. Correction for temperature**
$$
C_t = \alpha\,(T_m - T_0)\,L
$$
where $\alpha$ is the coefficient of linear expansion, $T_m$ the mean field temperature and $T_0$ the standard temperature. Positive if $T_m > T_0$.

**3. Correction for pull (tension)**
$$
C_p = \frac{(P - P_0)\,L}{A\,E}
$$
$P$ = applied pull, $P_0$ = standard pull, $A$ = cross-sectional area, $E$ = Young's modulus. Positive if $P > P_0$.

**4. Correction for sag**
$$
C_s = -\frac{L\,w^{2}\,l_s^{2}}{24\,P^{2}} = -\frac{n\,W^{2}\,l_s}{24\,P^{2}}
$$
where $w$ = weight per metre, $l_s$ = length of each span between supports, $W = w\,l_s$. It is always **negative** when the tape is standardised on the flat and used suspended.

**5. Correction for slope**
$$
C_h = -\frac{h^{2}}{2L} \quad\text{(approx.)} \qquad\text{or}\qquad C_h = -L(1-\cos\theta)
$$
where $h$ is the height difference. Always negative.

**6. Correction for alignment** (tape not in line): always negative.

**7. Reduction to mean sea level**
$$
C_{msl} = -\frac{L\,h}{R}
$$
where $h$ is the elevation above MSL and $R$ is the radius of the earth (6370 km). Negative.

True length $= L + C_a + C_t + C_p + C_s + C_h + C_{msl}$.

## Check yourself

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

1. What is the sign of the tape-length correction C_a = L(l' - l)/l when the tape is too long?
   A. Negative
   B. Positive
   C. Zero
   D. Depends on slope
   Answer: B. A too-long tape reads too small a number, so the measured length must be increased (positive). (Key point: Tape length correction)

2. When is the temperature correction positive?
   A. When mean field temperature is below standard
   B. When the field temperature is above the standard temperature
   C. Always
   D. Never
   Answer: B. C_t = alpha (Tm - T0) L is positive when Tm > T0 since the tape has expanded. (Key point: Temperature correction)

3. A tape standardised on the flat is used suspended. The sag correction is
   A. Positive
   B. Always zero
   C. Negative
   D. Equal to slope correction
   Answer: C. The hanging tape follows a curve longer than the chord, so the correction is subtracted. (Key point: Sag correction)

4. Which is the approximate slope correction for height difference h on measured length L?
   A. +h^2 / 2L
   B. -h^2 / 2L
   C. -L h / R
   D. +L (1 - cos theta)
   Answer: B. C_h = -h^2/(2L); it is always negative because the slope length exceeds the horizontal. (Key point: Slope correction)

## Related in Surveying I

- [Principle applied in two-way linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atwo-way-linear-measurement-principle) — Surveying I, chapter 1
- [Field sketch and mapping by linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Achain-field-sketch-mapping) — Surveying I, chapter 3
- [Linear measurement methods; sag correction](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amethods-of-linear-measurement-sag) — Surveying I, chapter 2
- [Eight methods of linear measurement](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alist-eight-linear-methods) — Surveying I, chapter 2

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