Coefficient of Variation Calculator

The coefficient of variation (CV), also called relative standard deviation (RSD), expresses the standard deviation as a percentage of the mean. It lets you compare variability between data sets with different units or scales.

5 values read.

Coefficient of variation
2.7115%
As a ratio
0.0271
s
0.2739
Mean
10.1
n
5
±1 SD9.89.91010.110.210.310.410.5
▲ mean 10.1 · ◆ median 10.1 · shaded band = mean ± 1 SD (9.8261 to 10.3739)

Step-by-step working

  1. Count the valuesn = 5
  2. Add the values and divide by the count to get the meanx̄ = (10.2 + 9.8 + 10.5 + 10.1 + 9.9) ÷ 5 = 50.5 ÷ 5 = 10.1
  3. Subtract the mean from each value, then square the result (see the table)(x − x̄)² for each x, e.g. (10.2 − 10.1)² = 0.01
  4. Add up the squared deviations (the sum of squares)SS = Σ(x − x̄)² = 0.3
  5. Divide by n − 1 for the sample variance (Bessel’s correction)s² = 0.3 ÷ 4 = 0.075
  6. Take the square root to get the standard deviations = √0.075 = 0.273861
  7. Divide the standard deviation by the mean and multiply by 100CV = 0.273861 ÷ 10.1 × 100 = 2.7115%
Deviation table
xx − x̄(x − x̄)²
10.20.10.01
9.8−0.30.09
10.50.40.16
10.100
9.9−0.20.04
Σx = 50.5≈ 0SS = 0.3

Formula CV = (s ÷ x̄) × 100%

Ask the tutor about your result

An AI tutor reads your inputs and results above and explains them in plain English. The numbers come from the calculator; the explanation is AI-written, so check it against your notes.

When to use it

A standard deviation of 5 g is huge for a 20 g sample but tiny for a 5 kg one. Dividing by the mean removes the scale. In analytical chemistry, RSD is the standard way to report the precision of replicate measurements; an RSD under a few percent is usually expected for good technique.

CV only makes sense for ratio data with a true zero and a positive mean (mass, length, concentration). It is meaningless for temperatures in °C or for data that can be negative.

Frequently asked questions

Is CV the same as RSD?

Yes. RSD is usually quoted as a percentage; CV is sometimes written as a decimal (0.05) and sometimes as a percentage (5%).

Should I use sample or population SD?

Sample SD for replicate measurements or any sample; population SD only if you have the entire population.