acalculator

What is the RSD of my data?

Paste your measurements. The RSD calculator divides the standard deviation by the size of the mean and multiplies by 100, the %RSD that laboratories use to judge how repeatable a set of results is.

Your numbers

Read as: 98.2; 101.5; 99.7; 100.4; 100.9; 99.3
Data are a
Relative standard deviation (RSD)
1.18659%

The relative standard deviation of the 6 values is 1.18659%.

Coefficient of variation (CV)
1.18659%
CV as a ratio
0.0118659
Mean (x̄)
100
Standard deviation (s)
1.186592
Count (n)
6

Relative standard deviation (RSD): 1.18659%. The relative standard deviation of the 6 values is 1.18659%.

How to calculate

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.

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%.

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

  • 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.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Data values 98.2, 101.5, 99.7, 100.4, 100.9, 99.3, Data are a Sample (n − 1) gives Relative standard deviation (RSD) 1.186592%, Mean (x̄) 100, Standard deviation (s) 1.186592, Count (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. Data values 10, 12, 23, 23, 16, 23, 21, 16, Data are a Population (N) gives Relative standard deviation (RSD) 27.216553%, Mean (x̄) 18, Standard deviation (s) 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. Data values -4, -6, -8, Data are a Sample (n − 1) gives Relative standard deviation (RSD) 33.333333%, Coefficient of variation (CV) -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)

How it works

For n values x₁ … xₙ:

  • Mean x̄ = (x₁ + … + xₙ) ÷ n
  • Standard deviation s = √(Σ(xᵢ − x̄)² ÷ d), with d = n − 1 for a sample and d = n for a population
  • Relative standard deviation = 100 × s ÷ |x̄| percent
  • Coefficient of variation = s ÷ x̄ (a ratio, negative when the mean is), also shown as 100 × s ÷ x̄ percent

The values are first divided by a power of two near the largest |x|, which changes no digit, so very large or very small values do not overflow when squared. The ratio does not depend on that scale.

Rules

  • 2 to 1,000 values.
  • When every value is 0, or the mean is 0 (or so close to 0 that the ratio is not a finite number), there is no answer.
  • A mean or standard deviation past the largest double (about 1.8 × 10³⁰⁸) is left out; the RSD is still shown.

Output format. The RSD and CV percents and the ratio to 6 significant digits; the mean and standard deviation with up to 6 decimals.

Worked examples by hand

98.2, 101.5, 99.7, 100.4, 100.9, 99.3 as a sample. Sum 600, so x̄ = 100. Deviations −1.8, 1.5, −0.3, 0.4, 0.9, −0.7; squares 3.24 + 2.25 + 0.09 + 0.16 + 0.81 + 0.49 = 7.04. s = √(7.04 ÷ 5) = 1.186592. RSD = 100 × 1.186592 ÷ 100 = 1.18659%.

10, 12, 23, 23, 16, 23, 21, 16 as a population. x̄ = 144 ÷ 8 = 18; squared deviations add to 192. σ = √(192 ÷ 8) = √24 = 4.898979. RSD = 100 × 4.898979 ÷ 18 = 27.2166%.

−4, −6, −8 as a sample. x̄ = −6, s = √((4 + 0 + 4) ÷ 2) = 2. RSD = 100 × 2 ÷ |−6| = 33.3333%; the CV is −33.3333%.

Other questions people ask

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.