---
title: "Types and sources of measurement errors"
subject: "Metrology"
chapter: 2
key: "semester_3/metrology:types-sources-of-errors"
source: https://www.bctengineer.com/q/semester_3/metrology/types-sources-of-errors
site: BCT Engineering
---

# Types and sources of measurement errors

Metrology · Chapter 2: Errors in measurement

- Asked in: year not given, 8 marks
- Video: [Errors, Types and Source Errors in measurement.](https://www.youtube.com/watch?v=JymFExJbAQM) — Akhtar's Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/metrology/types-sources-of-errors
- Whole chapter: https://www.bctengineer.com/md/semester_3/metrology/chapter-2

## Question

Explain the different types of errors in measurement and describe the main sources of error in a measuring process.

## Short answer

Errors are gross (human mistakes), systematic (fixed, predictable: instrumental, environmental, observational) and random (unpredictable variations, treated statistically). Main sources: standard/calibration, workpiece, instrument (backlash, wear, zero error), environment (temperature ≠20°C, vibration), operator (parallax, measuring force), and method (cosine error, alignment).

## Answer

**Error** is the difference between the measured value and the true value of the quantity: $e = V_m - V_t$. Absolute error is $e$; relative (percentage) error is $e/V_t \times 100$.

#### Types of error
1. **Gross errors**: caused by human mistakes such as wrong reading, wrong recording, using the instrument wrongly or forgetting to correct zero error. They can be avoided by care and by repeating the measurement.
2. **Systematic (fixed) errors**: they follow a definite law and have the same magnitude and sign for repeated readings under the same conditions, so they can be predicted and corrected.
   - *Instrumental*: worn anvils, wrong calibration, zero error, backlash.
   - *Environmental*: temperature, humidity, pressure, vibration, dust.
   - *Observational*: parallax, wrong estimation of the fraction of a division.
3. **Random (accidental) errors**: small variations in repeated readings that cannot be predicted individually, caused by small changes in temperature, friction, operator judgement and so on. They are treated by statistics: the mean of many readings is taken and the scatter is described by standard deviation.

#### Sources of error
| Source | Examples |
|---|---|
| Standard / calibration | Master or slip gauge worn or not calibrated |
| Workpiece | Surface roughness, form errors, elastic deformation, out-of-roundness |
| Instrument | Friction, backlash, hysteresis, zero error, poor resolution, wear of anvils |
| Environment | Temperature different from the standard $20^\circ$C, vibration, humidity, dust |
| Operator | Parallax, unequal measuring force, bad technique, fatigue |
| Method / contact | Abbe's principle not followed, cosine error, contact pressure, alignment errors |

#### Reducing errors
Measure at standard temperature $20^\circ$C or allow the work and instrument to soak, apply corrections for known systematic errors, calibrate regularly, use correct measuring force (ratchet), follow Abbe's principle, and take the mean of several readings to reduce random error.

## Check yourself

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

1. Error in measurement is defined as:
   A. True value minus the mean of readings
   B. Measured value minus true value
   C. The standard deviation of readings
   D. The least count of the instrument
   Answer: B. Error e = Vm - Vt, the difference between measured and true value; relative error is e/Vt x 100. (Key point: Definition of error)

2. Which describes a systematic error?
   A. It follows a definite law, has the same size and sign for repeated readings, and can be corrected
   B. It varies unpredictably from reading to reading
   C. It is a human mistake such as wrong recording
   D. It is removed by taking the mean of many readings
   Answer: A. Systematic errors are fixed in magnitude and sign under the same conditions, so they can be predicted and corrected; averaging does not remove them. (Key point: Systematic errors)

3. How are random errors handled?
   A. By applying a fixed correction
   B. By calibrating the instrument once
   C. By repeating the measurement only if a gross error is suspected
   D. By taking the mean of many readings and describing scatter by standard deviation
   Answer: D. Random errors cannot be predicted individually, so they are treated statistically with the mean and standard deviation. (Key point: Random errors)

4. Parallax while reading a scale is classed as which kind of error?
   A. Observational systematic error
   B. Instrumental error
   C. Random error due to friction
   D. Gross error
   Answer: A. Parallax and wrong estimation of a division fraction are observational systematic errors. (Key point: Classifying errors)

5. Why is measurement ideally done at 20°C?
   A. It is the temperature at which instruments never wear
   B. It removes all random errors
   C. It is the standard temperature, so temperature differences cause environmental error
   D. It makes parallax zero
   Answer: C. 20°C is the standard reference temperature; deviation from it causes environmental errors, so work is measured at 20°C or allowed to soak. (Key point: Standard temperature)

## Related in Metrology

- [Thread errors and effect of pitch error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Ascrew-thread-errors-and-pitch-effect) — Metrology, chapter 12
- [Fringe measurement of flatness error](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Ainterference-fringes-flatness-numerical) — Metrology, chapter 8
- [End bar and universal measuring machines](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aend-bar-and-universal-measuring-machines) — Metrology, chapter 14

## Related in other subjects

- [Types of measurement errors and minimization](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_i%3Ameasurement-errors-minimization) — Instrumentation I, chapter 1
- [Sources of errors in chaining/taping](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aerrors-in-taping-sources-directions) — Surveying I, chapter 2, asked 4×
- [Short note: sources of error in levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Ashort-note-sources-of-error-leveling) — Surveying I, chapter 5
- [Principles of EDM measuring distances](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aedm-principles) — Surveying I, chapter 2, asked 12×