Standard Deviation Calculator
Paste your numbers, choose sample or population, and get the standard deviation, variance, mean and the steps. Choose sample if your numbers are part of a bigger group, and population if they are the whole group.
Example loaded: 2, 4, 4, 4, 5, 5, 7, 9. Select Clear to enter your own numbers.
Your numbers
Your results
Standard Deviation: the quick answer
Standard deviation measures how spread out numbers are around their mean. A small value means they sit close together, and a large value means they are far apart.
Example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the population standard deviation is 2. The sample standard deviation is about 2.14.
What standard deviation tells you
Standard deviation shows how spread out your numbers are around the mean. A small value means the numbers sit close to the mean. A large value means they are more spread out. It is never negative, and it is 0 only when every number is the same.
The formulas
- Population: standard deviation = square root of (sum of squared distances from the mean / n).
- Sample: standard deviation = square root of (sum of squared distances from the mean / (n – 1)).
- Variance is the same calculation before the square root.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The squared distances from the mean are 9, 1, 1, 1, 0, 0, 4 and 16, which add up to 32. As a population: variance = 32 / 8 = 4, so the standard deviation is 2. As a sample: variance = 32 / 7 = 4.571, so the standard deviation is 2.138.
Sample or population?
Use population when your numbers are every item in the group, such as all the scores in one class. Use sample when they are only some of a larger group, such as 30 customers out of thousands. Dividing by n – 1 for a sample corrects for the fact that a sample tends to underestimate the spread.
Related: the mean calculator and the median calculator.
Frequently asked questions
What is standard deviation?
It measures how far numbers typically fall from their mean. The bigger it is, the more spread out the numbers are.
Should I choose sample or population?
Choose population if you have every value in the group, and sample if your values are only part of a larger group. When unsure, sample is the usual choice.
Why does the sample formula divide by n – 1?
A sample tends to show less spread than the full group, so dividing by n – 1 instead of n corrects for that.
Can standard deviation be negative?
No. It is 0 or more, and 0 means every number is identical.
What is the difference between standard deviation and variance?
Variance is the standard deviation squared. Standard deviation is in the same units as your data, which makes it easier to read.
How do I find standard deviation in Excel or Google Sheets?
Use =STDEV.S(A1:A10) for a sample and =STDEV.P(A1:A10) for a population.
What counts as a high standard deviation?
There is no single cut-off. Compare it with the mean and with what is normal for your data.
About this calculator
Written by Umar Khan. The calculator finds the mean, adds up the squared distances from it, divides by n (population) or n – 1 (sample), then takes the square root. Results are shown to up to 10 decimal places (6 for standard deviation) with trailing zeros dropped, and your numbers stay in your browser. Last updated November 9, 2026. Questions or corrections: [email protected].
Written by Umar Khan
Umar Khan is a PhD student in engineering at NTNU, the Norwegian University of Science and Technology, in Norway. Every formula and worked example on this page is shown in full so you can check each result yourself. Corrections are welcome at [email protected].
Related calculators
For information only, not professional advice.
Written by Umar Khan. Last updated: November 9, 2026.