---
title: "Accuracy, precision, sensitivity, resolution"
subject: "Instrumentation and Measurement"
chapter: 3
key: "semester_4/instrumentation_and_measurement:accuracy-precision-sensitivity-resolution"
source: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/accuracy-precision-sensitivity-resolution
site: BCT Engineering
---

# Accuracy, precision, sensitivity, resolution

Instrumentation and Measurement · Chapter 3: Static Characteristics of Measurement System

- Asked in: year not given, 3+3 marks
- Video: [Sensitivity Accuracy Precision and Resolution Value in Instrumentation Measurement -](https://www.youtube.com/watch?v=RAiK9tflnZA) — ASHOK ETUTOR
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/instrumentation_and_measurement/accuracy-precision-sensitivity-resolution
- Whole chapter: https://www.bctengineer.com/md/semester_4/instrumentation_and_measurement/chapter-3

## Question

(a) Differentiate between accuracy and precision with a suitable example.

(b) Define sensitivity, threshold, resolution and tolerance of a measuring instrument.

## Short answer

Accuracy is closeness to true value; precision is repeatability. Example: clustered shots far from bullseye are precise but inaccurate. Sensitivity = Δoutput/Δinput; threshold is smallest input from zero that yields output; resolution is smallest detectable change from any value; tolerance is maximum permitted error from a specified value.

## Answer

#### (a) Accuracy and precision
**Accuracy** is the closeness of a measured value to the true value. **Precision** is the closeness of repeated readings of the same quantity to each other (repeatability).

| Point | Accuracy | Precision |
|---|---|---|
| Meaning | Nearness to true value | Nearness of readings to one another |
| Error type | Affected by systematic error | Affected by random error |
| Expressed as | % of full scale or % of reading | Standard deviation, repeatability |
| Improved by | Calibration | Better design, averaging |
| Possible alone? | Average of scattered readings can be accurate | Readings can be precise yet wrong |

**Example:** a target shot. Shots all clustered far from the bullseye are precise but not accurate. Shots scattered evenly around the bullseye are accurate on average but not precise. A voltmeter reading 4.98, 4.99, 4.98 V for a true 5.50 V is precise but inaccurate.

#### (b) Definitions
- **Sensitivity:** ratio of the change in output to the change in input, $S = \Delta q_o/\Delta q_i$ (slope of the calibration curve). Example: 5 mV/bar.
- **Threshold:** the smallest input change from zero that produces a detectable output.
- **Resolution:** the smallest change in input (from a non-zero value) that the instrument can detect. For a digital meter it is one least-count digit.
- **Tolerance:** the maximum permitted departure from a specified value, usually given as $\pm$ value or $\pm\%$; it is the permissible error, not the instrument's inherent accuracy.

## Check yourself

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

1. A voltmeter reads 4.98, 4.99, 4.98 V for a true 5.50 V. It is
   A. Accurate and precise
   B. Accurate but not precise
   C. Neither accurate nor precise
   D. Precise but not accurate
   Answer: D. Readings agree closely (precise) but are far from the true value (inaccurate), indicating systematic error. (Key point: Accuracy vs precision)

2. Which error type mainly affects accuracy and which affects precision?
   A. Random affects accuracy; systematic affects precision
   B. Systematic affects accuracy; random affects precision
   C. Both affect only accuracy
   D. Both affect only precision
   Answer: B. Systematic error shifts readings from the true value; random error scatters repeated readings. (Key point: Error type link)

3. Sensitivity of an instrument is
   A. The smallest detectable input change
   B. The permitted departure from a specified value
   C. Output change divided by input change (slope of calibration curve)
   D. The closeness of readings to each other
   Answer: C. S = Δqo/Δqi, e.g. 5 mV/bar. (Key point: Sensitivity)

4. How do threshold and resolution differ?
   A. Threshold is from zero input; resolution is from a non-zero input value
   B. They are identical
   C. Threshold applies to digital meters only
   D. Resolution is the permissible error
   Answer: A. Threshold is the smallest input change from zero that gives a detectable output; resolution is the smallest detectable change from a non-zero value. (Key point: Threshold vs resolution)

## Related in Instrumentation and Measurement

- [Spring-mass-damper instrument parameters](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aspring-mass-damper-instrument-numerical) — Instrumentation and Measurement, chapter 4

## Related in other subjects

- [Accuracy and precision defined](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aaccuracy-and-precision) — Surveying I, chapter 2, asked 2×
- [Angular vs linear precision in traversing](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-angular-linear-precision-relation) — Surveying II, chapter 1, asked 2×
- [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
- [Unilateral and bilateral tolerance conversion](https://www.bctengineer.com/question.md?key=semester_3%2Fmetrology%3Aunilateral-bilateral-tolerance) — Metrology, chapter 9