# Accuracy vs Precision: Differences and Examples

People often use precise and accuracy as if they mean the same thing, but they measure two separate properties of a measurement system. Accuracy tells you how close a result is to the true or accepted value. Precision tells you how close repeated measurements are to each other. A device can be accurate without being precise, precise without being accurate, both, or neither [1][2].

## Quick Answer

- **Accuracy** is the closeness of a measured value to a standard or known value [3].
- **Precision** is the closeness of two or more measurements to each other [3].
- The two properties are independent. You can be very precise but inaccurate, and you can be accurate on average while your individual readings are spread far apart [3].
- In statistics, the same ideas are usually called **bias** (the amount of inaccuracy) and **variability** (the amount of imprecision) [1].
- Increasing the sample size or the number of measurements generally improves precision but does not fix accuracy, because a systematic error stays in the data [1][2].

## Key Differences

| Aspect | Accuracy | Precision |
|---|---|---|
| What it measures | Closeness to the true or accepted value [2] | Closeness of repeated measurements to each other [2] |
| Statistical name | Bias, the difference between the average of measurements and the true value [4] | Variability, the spread of measurements [1] |
| Typical metric | Mean error, absolute error, percent error | Standard deviation, variance, range |
| Effect of more measurements | Does not improve accuracy if a systematic error is present [1] | Generally improves precision [1][2] |
| Effect of a better instrument | Can improve accuracy if the bias is removed | A more precise tool can measure smaller increments [5] |
| Main cause of failure | Systematic error, such as a miscalibrated device [1] | Random error, such as noise or inconsistent technique |

The meaning of accuracy is about correctness against a reference. The meaning of precision is about repeatability. A caliper that reads to the nearest 0.01 millimeter has finer resolution than a ruler that reads to the nearest millimeter, so it can resolve smaller differences in length [5], although finer resolution alone does not guarantee better precision.

## Accuracy Explained

Accuracy is a qualitative term for whether a measurement agrees with the true, target or reference value [4]. When you want a number, you quantify it as bias: the difference between the average of your measurements and the true value [4].

For a single measurement, the error is:

$$e = x - x_{\text{true}}$$

For a set of measurements, you compare the mean to the true value:

$$\text{mean error} = \bar{x} - x_{\text{true}}$$

A positive mean error means your system reads high on average. A negative one means it reads low. Percent error rescales that difference to the size of the true value:

$$\text{percent error} = \frac{|\bar{x} - x_{\text{true}}|}{x_{\text{true}}} \times 100$$

Accuracy is affected by systematic error. If an experiment contains a systematic error, taking more readings gives you a consistent but inaccurate string of results, and removing the systematic error improves accuracy without changing precision [1]. This is why a lab that always reads 1 g high on a 100 g standard stays wrong no matter how many times it repeats the weighing.

## Precision Explained

Precision is about reproducibility and repeatability. Repeating measurements under the same conditions and getting the same or similar results is high precision [2]. The standard way to quantify it is the spread of the values, most often the standard deviation.

For a sample of $n$ measurements, the sample variance is:

$$s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}$$

The standard deviation is its square root:

$$s = \sqrt{s^2}$$

A small standard deviation means the readings cluster tightly. A large one means they scatter. Precision says nothing about whether the cluster sits on the true value. A GPS that returns five positions bunched together but far from the restaurant has high precision and low accuracy [5]. A GPS that returns five positions spread widely but centered on the restaurant has low precision and high accuracy [5].

If you want to go deeper into spread, see [measures of variability](/blog/data-analysis/measures-of-variability), which covers range, variance and standard deviation in more detail.

## Worked Example

The dataset is five repeated measurements of a 100 g reference weight on the same balance.

| measurement_id | mass_g |
|---|---|
| 1 | 101.2 |
| 2 | 100.9 |
| 3 | 101.5 |
| 4 | 100.8 |
| 5 | 101.1 |

**Step 1. List the measurements.**

Measurements (g): [101.2, 100.9, 101.5, 100.8, 101.1]

**Step 2. Compute the mean.**

$$\bar{x} = \frac{101.2 + 100.9 + 101.5 + 100.8 + 101.1}{5} = 101.1000 \text{ g}$$

**Step 3. Compute the mean error, which is the accuracy measure.**

$$101.1000 - 100.0 = +1.1000 \text{ g}$$

**Step 4. Take the absolute error.**

$$|+1.1000| = 1.1000 \text{ g}$$

**Step 5. Convert to percent error.**

$$\frac{1.1000}{100.0} \times 100 = 1.1000\%$$

**Step 6. Compute the sample variance.**

$$\frac{\sum (x_i - 101.1000)^2}{5 - 1} = 0.0750 \text{ g}^2$$

**Step 7. Compute the standard deviation, which is the precision measure.**

$$\sqrt{0.0750} = 0.2739 \text{ g}$$

The balance is biased high by 1.1000 g, so accuracy is poor at about 1.1 percent error. The readings sit within a standard deviation of 0.2739 g of each other, so precision is good. This is the classic precise but inaccurate pattern.

Here is the same calculation in Python:

```python
import statistics
measurements = [101.2, 100.9, 101.5, 100.8, 101.1]
true_value = 100.0
mean_meas = statistics.mean(measurements)
mean_error = mean_meas - true_value      # accuracy (bias)
sd = statistics.stdev(measurements)      # precision (spread)
print(f"{mean_error:+.4f} {sd:.4f}")  # +1.1000 0.2739
```

Output:

```text
mean_error = +1.1000 g (accuracy/bias)
std_dev    = 0.2739 g (precision/spread)
Excel: =AVERAGE(A1:A5) -> 101.1000; =STDEV.S(A1:A5) -> 0.2739
```

In a spreadsheet, `=AVERAGE(A1:A5)` returns 101.1000 and `=STDEV.S(A1:A5)` returns 0.2739. The average feeds the accuracy check, and the standard deviation feeds the precision check.

## Which One Should You Use?

Use accuracy when the question is whether your result is correct. Calibration checks, method validation and any comparison against a certified reference value are accuracy questions. You need a known true value to measure it, which is why accuracy is harder to assess than precision.

Use precision when the question is whether your process is repeatable. If you have no reference value, precision is often the only thing you can measure directly, and it is the basis of repeatability and reproducibility studies.

In practice you report both. A measurement system can be accurate but not precise, precise but not accurate, neither, or both [1]. The goal is a device that is both accurate and precise, but that combination is not always available, and knowing which property a device has helps you interpret results and make decisions [2]. For a full walkthrough of checking both against a standard method, see [verification of precision and accuracy for a standard method](/knowledge/diagnostics/emerging-tech/verification-of-precision-and-accuracy-for-a-standard-method-minimal-performance-checks-and-acceptan).

If your precision is poor, the problem is usually random error or technique. If your accuracy is poor, look for a systematic error such as a calibration offset. [Troubleshooting poor precision in analytical method validation](/knowledge/diagnostics/emerging-tech/troubleshooting-poor-precision-in-analytical-method-validation-root-causes-and-corrective-actions) covers the first case, and [experimental errors: types, sources, and how to minimize them](/blog/guides/experimental-errors-types-sources-and-how-to-minimize-them) covers both.

## Common Mistakes

- **Treating the words as synonyms.** They describe independent properties. Fix: report a bias metric and a spread metric separately, such as mean error and standard deviation.
- **Assuming more measurements fix accuracy.** Increasing the sample size generally increases precision but does not improve accuracy when a systematic error is present [1]. Fix: identify and remove the systematic error first, then repeat.
- **Judging precision from two readings.** Two close values can happen by chance. Fix: use at least five repeats and report the standard deviation.
- **Using the wrong standard deviation.** Population and sample formulas differ by the denominator. Fix: use the sample formula with $n - 1$ for repeated measurements, which is what `STDEV.S` computes.
- **Confusing precision with resolution.** A display with more decimal places is not automatically more precise. Fix: check the spread of repeated readings, not the number of digits shown.
- **Ignoring the reference value's own uncertainty.** A bias of 1.1 g means little if the reference itself is uncertain by 2 g. Fix: compare your error against the stated uncertainty of the standard.

## Limitations

Accuracy requires a true or accepted value, and that value is rarely known perfectly. Reference standards carry their own uncertainty, so a measured bias is always a difference between two uncertain quantities [4]. When the reference uncertainty is large relative to your bias, you cannot conclude that your system is inaccurate.

Precision metrics describe spread under the conditions you measured. They do not tell you how the system behaves on a different day, at a different temperature, or with a different operator. A single standard deviation from five readings is a narrow snapshot, and it says nothing about accuracy at all. High precision can also be misleading when it comes from rounding or from a device that repeats the same wrong value.

## Frequently Asked Questions

### What is the difference between accuracy and precision in simple terms?

Accuracy is how close you are to the target. Precision is how close your shots are to each other. A basketball player who always hits the same spot on the backboard but never the basket is precise and inaccurate, while a player whose shots land all around the rim but average out to the center is accurate and imprecise [3].

### Can something be precise but not accurate?

Yes. Five readings of 3.2 kg on a substance whose true weight is 10 kg are very precise and not accurate at all [3]. The readings agree with each other but not with the known value. This pattern usually points to a systematic error such as a miscalibrated instrument [1].

### Does increasing sample size improve accuracy or precision?

It generally improves precision. With a systematic error present, more measurements give you a tighter cluster around the wrong value, so accuracy stays the same [1]. Removing the systematic error improves accuracy but does not change precision [1].

### How do I calculate accuracy and precision in Excel?

Put your repeated measurements in a column, say A1:A5. Accuracy comes from comparing the mean to the true value, so use `=AVERAGE(A1:A5)` and subtract the true value. Precision comes from the spread, so use `=STDEV.S(A1:A5)`. In the worked example those return 101.1000 and 0.2739.

### Is accuracy the same as bias in statistics?

They are closely related but not identical. Accuracy is a qualitative term for agreement with the true value, while bias is the quantitative difference between the average of your measurements and the true value [4]. Statistics prefers bias and variability over accuracy and precision for exactly this reason [1]. If your work involves classification models, the word accuracy takes on a different meaning, which is covered in [accuracy, precision and recall: differences and when to use each](/blog/data-analysis/accuracy-precision-recall-differences).

## References

1. [Accuracy and precision - Wikipedia](https://en.wikipedia.org/wiki/Accuracy_and_precision)
2. [Accuracy and Precision | The Risk Project](https://blogs.extension.msstate.edu/theriskproject/accuracy-and-precision/)
3. [Accuracy and Precision](https://labwrite.ncsu.edu//Experimental%20Design/accuracyprecision.htm)
4. [2.1.1.3. Bias and Accuracy](https://www.itl.nist.gov/div898/handbook/mpc/section1/mpc113.htm)
5. [1.3: Accuracy, Precision, and Significant Figures - Physics LibreTexts](https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/01%3A_The_Nature_of_Science_and_Physics/1.03%3A_Accuracy_Precision_and_Significant_Figures)

## Further Reading

- [Wilson G, Bryan J, Cranston K et al. (2017). Good enough practices in scientific computing. PLOS Computational Biology](https://doi.org/10.1371/journal.pcbi.1005510)

## Related Articles

- [Accuracy, Precision and Recall: Differences and When to Use Each](/blog/data-analysis/accuracy-precision-recall-differences)
- [Measures of Variability: Range, Variance and Standard Deviation](/blog/data-analysis/measures-of-variability)
- [Mean vs Median: Differences and When to Use Each](/blog/data-analysis/mean-vs-median-differences)
- [Correlation vs Covariance: Differences and When to Use Each](/blog/data-analysis/correlation-vs-covariance)
- [Nominal vs Ordinal Variables: Differences and Examples](/blog/data-analysis/nominal-vs-ordinal-variables)
- [Verification of Precision and Accuracy for a Standard Method](/knowledge/diagnostics/emerging-tech/verification-of-precision-and-accuracy-for-a-standard-method-minimal-performance-checks-and-acceptan)
- [Precision and Recall in Variant Calling: How to Calculate and Interpret Performance Metrics](/knowledge/bioinformatics/precision-and-recall-in-variant-calling-how-to-calculate-and-interpret-performance-metrics)
- [Laboratory Measurements: Units, Accuracy, and Significant Figures in Experimental Data](/knowledge/diagnostics/molecular/laboratory-measurements)