Accuracy vs Precision in Measurements
Accuracy is how close a measurement is to the true or accepted value, and precision is how close repeated measurements are to each other. In brief: a scale that always reads 0.50 g too high gives precise but inaccurate results, while a scale that gives scattered readings centered on the true value is accurate on average but not precise.
The two ideas are often mixed up, yet they describe different qualities of data. Good chemistry needs both: results that are close to the truth and that can be repeated. This article defines each term, explains random and systematic errors, shows the four combinations with a data table and calculations, describes how to improve each quality and explains why the terms matter in practice.
What do accuracy and precision mean?
Accuracy compares the result with the true value. We usually do not know the true value exactly, so we use an accepted value from reliable references. A measurement of 100.2 °C for the boiling point of water at standard pressure is accurate, since the accepted value is 100 °C.
Precision describes the agreement between repeated measurements, and it does not depend on the true value. Readings of 98.1, 98.0 and 98.2 °C are precise, because they lie close together, but they are not accurate for boiling water at standard pressure. Precision is often measured by the range or the standard deviation of the data.
What causes poor accuracy and poor precision?
- Systematic errors push all results in the same direction by about the same amount. Examples are a balance that is not zeroed, a thermometer that is incorrectly calibrated or reading a meniscus from the wrong angle every time. They reduce accuracy and are not revealed by repeating the measurement.
- Random errors make results scatter in both directions. Examples are small differences in judging a color change in a titration, electrical noise or drafts affecting a balance. They reduce precision and can be reduced by averaging repeated measurements.
The four combinations
| Case | Accurate? | Precise? | Likely problem |
|---|---|---|---|
| Best result | Yes | Yes | None |
| Precise but not accurate | No | Yes | Systematic error |
| Accurate on average but not precise | Yes (mean) | No | Random error |
| Neither | No | No | Both kinds of error |
Worked example: four students measure a density
The accepted density of a liquid is 2.00 g/mL. Four students each measure it three times.
| Student | Trial 1 | Trial 2 | Trial 3 | Mean | Standard deviation |
|---|---|---|---|---|---|
| A | 1.98 | 2.01 | 1.99 | 1.99 | 0.015 |
| B | 1.50 | 1.51 | 1.49 | 1.50 | 0.010 |
| C | 1.6 | 2.4 | 2.0 | 2.0 | 0.4 |
| D | 2.9 | 3.4 | 1.2 | 2.5 | 1.2 |
- Student A. The mean is 1.9933, rounded to 1.99, which differs from 2.00 by less than 0.01. The percent error is about 0.3%. The standard deviation is only 0.015. A is both accurate and precise.
- Student B. The mean is 1.50, and the percent error is |1.50 − 2.00| ÷ 2.00 × 100% = 25%, but the standard deviation is 0.010. B is precise but not accurate, which suggests a systematic error such as a miscalibrated balance or a volume read incorrectly each time.
- Student C. The mean is exactly 2.0, so on average C is accurate, but the readings are spread from 1.6 to 2.4, with a standard deviation of 0.4. C is accurate on average, but not precise. More trials would improve the mean.
- Student D. The mean of 2.5 has an error of 25%, and the standard deviation is 1.2. D is neither accurate nor precise.
Notice that B and D have the same percent error (25%), but the reasons are different. B needs a correction for a systematic error, and D needs better technique and more careful measurements.
How can you improve accuracy and precision?
- Calibrate instruments against known standards to remove systematic errors.
- Use the right tool: a graduated cylinder gives a better volume than a beaker.
- Repeat measurements and average, to reduce the effect of random errors.
- Standardize technique: read at eye level, use the same procedure every time, and zero instruments.
- Control conditions such as temperature, drafts and vibrations.
- Compare with a reference sample of known value when possible.
What is the role of the instrument?
An instrument with finer divisions has higher resolution, which allows more precise readings, but resolution does not guarantee accuracy. A digital balance that reads to 0.0001 g can still be inaccurate if it has not been calibrated. A reliable result needs a good instrument, correct calibration, good technique and enough repetition.
How did these ideas develop?
Astronomers and surveyors in the 18th and early 19th centuries noticed that repeated measurements of the same quantity do not agree exactly, and they sought the best value. Carl Friedrich Gauss and Adrien-Marie Legendre developed the method of least squares around 1800, and Gauss described how random errors follow a bell-shaped distribution. These ideas, which are now part of statistics, are the basis for the modern treatment of precision and uncertainty.
Which mistakes are common?
Mistake 1: Using the words as synonyms
They describe different things. Accuracy relates to the true value and precision to agreement among data.
Mistake 2: Assuming that precise data must be correct
A consistent systematic error produces precise but wrong data.
Mistake 3: Thinking that averaging removes all errors
Averaging reduces random errors only. It does not remove systematic ones.
Mistake 4: Judging precision from one measurement
Precision needs repeated measurements.