# What is the RSD of my data?

Computes the relative standard deviation (RSD, %RSD) of a list of numbers: 100 times the sample or population standard deviation divided by the size of the mean.

- Page: https://www.acalculator.org/statistics/relative-standard-deviation-calculator
- JSON spec: https://www.acalculator.org/statistics/relative-standard-deviation-calculator.json
- Version: 7a2d124dc255

## Default answer

Example with the default inputs (Data values [98.2, 101.5, 99.7, 100.4, 100.9, 99.3], Data are a Sample (n − 1)): The relative standard deviation of the 6 values is 1.18659%.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| x | Data values | The numbers, separated by commas, spaces, semicolons, or new lines. |
| type | Data are a | Sample: the standard deviation divides by n − 1. Population: every member is listed, so it divides by N. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| percent | Coefficient of variation (CV) | The standard deviation as a percent of the mean: 100 × s ÷ x̄ (negative when the mean is). |
| rsd | Relative standard deviation (RSD) | The standard deviation as a percent of the size of the mean: 100 × s ÷ \|x̄\|. |
| cv | CV as a ratio | s ÷ x̄, not multiplied by 100. |
| mean | Mean (x̄) | The sum of the values divided by their count. |
| sd | Standard deviation (s) | The sample (n − 1) or population (N) standard deviation, as chosen. |
| n | Count (n) | How many values there are. |

## Method

RSD = 100 × s ÷ |x̄| percent; s is the sample (n − 1) or population (N) standard deviation.

## Assumptions

- The RSD suits data on a ratio scale (a true zero), such as repeat measurements of a concentration.
- The RSD is not defined when the mean is 0.
- The RSD equals the coefficient of variation as a percent, except that it uses the size of the mean, so it is never negative.

## Worked examples

1. x = 98.2 or 101.5, type = sample gives rsd = 1.186592%, mean = 100, sd = 1.186592, n = 6. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02); NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (s² = Σ(Y − Ȳ)² ÷ (N − 1)), https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm (retrieved 2026-10-02).
2. x = 10 or 12, type = population gives rsd = 27.216553%, mean = 18, sd = 4.898979. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02).
3. x = -4 or -6, type = sample gives rsd = 33.333333%, percent = -33.333333%. Source: NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s / x̄; relative standard deviation = 100 s / |x̄|), https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02).

## FAQ

### What is the relative standard deviation?

The standard deviation as a percent of the mean: RSD = 100 × s ÷ |x̄|. NIST defines it this way. It is also written %RSD, and it is the coefficient of variation expressed as a percent.

### How do I calculate %RSD?

Find the mean and the standard deviation, divide the standard deviation by the mean, and multiply by 100. For 98.2, 101.5, 99.7, 100.4, 100.9 and 99.3: the mean is 100, s = 1.18659, so the RSD is 1.18659%.

### What is the difference between RSD and the coefficient of variation?

The coefficient of variation is s ÷ x̄, a ratio. The RSD is the same ratio as a percent, with the size of the mean, so the RSD is never negative. For a positive mean, an RSD of 1.5% is a CV of 0.015.

### What is an acceptable RSD?

It depends on the method and the field, and each lab or standard sets its own limit. Repeat injections in chromatography are often held to a few percent or less, while field data can vary far more. A lower RSD means more repeatable results.

### Should I use the sample or population standard deviation for RSD?

Use the sample standard deviation (dividing by n − 1) for repeat measurements, which are a sample of what the method could give. Use the population one (dividing by N) only when the list is the whole group.

### Why is there no RSD when the mean is 0?

Dividing by 0 is not defined. Near 0, a small change in the mean makes the RSD very large, so the RSD suits data with a true zero and positive values, such as concentrations or weights.

## Sources

- NIST Dataplot Reference Manual, COEFFICIENT OF VARIATION (cv = s ÷ x̄; the relative standard deviation is the absolute value of the coefficient of variation in percent, 100 s ÷ |x̄|). https://itl.nist.gov/div898/software/dataplot/refman2/auxillar/coefvari.htm (retrieved 2026-10-02)
- NIST/SEMATECH e-Handbook of Statistical Methods, §1.3.5.6 Measures of Scale (sample variance and standard deviation with N − 1). https://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm (retrieved 2026-10-02)