Relative Standard Deviation Calculator
Find the relative standard deviation (RSD, the standard deviation as a percentage of the mean) from data or from a known SD and mean.
Change the values and press Calculate to work out your own figures.
From data
Enter numbers and say whether they are a whole population or a sample.
Show the working
- Mean = 178 ÷ 8 = 22.25
- Sum of squared deviations = Σ(x − mean)² = 1,059.5
- s² = 1,059.5 ÷ (n − 1) = 151.357142857
- s = √151.357142857 = 12.3027290817
- CV = s ÷ |mean| = 12.3027290817 ÷ 22.25 = 0.55293164412 = 55.293164412%
From a standard deviation and mean
Enter a standard deviation and mean you already know.
Show the working
- RSD = SD ÷ |mean| × 100% = 2.5 ÷ 50 × 100% = 5%
How to use it
Enter numbers and say whether they are a whole population or a sample. Enter a standard deviation and mean you already know.
Paste or type the numbers separated by commas, spaces or new lines. Results are worked out exactly and shown to 12 significant figures; Show the working lists each step.
Key facts
RSD = SD ÷ |mean| × 100%
Where RSD is used
Laboratories use RSD to report precision: an RSD of 2% means repeat measurements typically vary by about 2% of their average.
Questions
How do I calculate RSD?
Divide the standard deviation by the mean and multiply by 100%.
What does a low RSD mean?
Measurements are close together relative to their size.
Formulas
RSD = SD ÷ |mean| × 100%
Sources
Limitations
- Up to 5,000 values. Values are separated by commas, spaces or new lines, so write 1250 rather than 1,250.