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Relative Standard Deviation Calculator

Enter your data values to find the relative standard deviation.

How it is calculated

Paste your measurements separated by spaces, commas or semicolons. The tool computes the mean, the standard deviation and then expresses the spread as a percentage of the mean:

RSD = |s ÷ x̄| × 100

with x̄ = Σx ÷ n and s = √(Σ(x − x̄)² ÷ d). The divisor d is n − 1 for a sample (the default) and n for a population. At least two numbers are required. Entries that are not numbers are skipped silently, and when the mean is zero, or so close to zero that only rounding noise is left (0.1 0.2 −0.3 adds up to nothing), no result is shown because the ratio is undefined. The sign of the mean is dropped, so RSD is always positive. RSD is shown with two decimals, the standard deviation and mean with four.

Worked example

Five replicate readings: 98.2, 99.1, 97.8, 98.6, 99.4, treated as a sample.

  1. Mean = 493.1 ÷ 5 = 98.62.
  2. Squared deviations: 0.1764, 0.2304, 0.6724, 0.0004, 0.6084, which add up to 1.688.
  3. Sample variance = 1.688 ÷ 4 = 0.422, so s = 0.6496.
  4. RSD = 0.6496 ÷ 98.62 × 100 ≈ 0.66%.

With the population setting the divisor becomes 5, giving s = 0.5810 and an RSD of 0.59%.

Try this example →

Common mistakes

  • Writing decimals with a comma, such as 98,2. Commas and semicolons separate values, so 98,2 is read as two numbers, 98 and 2, which inflates the RSD enormously.
  • Leaving the data set on sample when you measured every item in the group, or the reverse. With few readings the choice changes the RSD noticeably, as the two results above show.
  • Applying RSD to values with an arbitrary zero point, such as temperatures in degrees Celsius. Shifting the zero changes the mean and therefore the percentage, so RSD only makes sense on ratio-scale data.
  • Typing a stray word or symbol in the list and trusting the count. Non-numeric entries are dropped without warning, so check that the Count line matches the number of readings you entered.
  • Reading a high RSD as an error when the mean is close to zero. A tiny mean makes the ratio blow up even if the spread itself is small.

Sources

About this calculator

The relative standard deviation (RSD), also called the coefficient of variation (CV), expresses a data set's standard deviation as a percentage of its mean: RSD = (standard deviation ÷ mean) × 100%. Unlike the raw standard deviation, this normalized figure lets you compare the spread of two data sets measured on completely different scales.

Analytical chemists, quality-control labs, and pharmaceutical scientists rely on RSD to judge measurement precision and instrument repeatability — lab accreditation standards such as ISO/IEC 17025 and pharmacopoeial assay-validation guidelines like USP General Chapter 1010 often set maximum acceptable RSD thresholds that a method or instrument must meet before results are considered reliable.

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Comments (1)

  • Editorial team

    An RSD from only three replicates is a shaky number, because one slightly odd reading can swing it a lot. The five readings in the guide give 0.66 percent; drop two of them and the figure can jump around noticeably. If your method sets an acceptance limit, compare against that, and collect more replicates before drawing conclusions from a single borderline result. How many replicates does your procedure normally call for?

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