Standard Deviation Calculator
Enter your data set to find the standard deviation and variance — both sample and population — along with the mean and count.
Reviewed by the WorldCalcs team · Methodology · Last reviewed: June 2026
Result
- Count (N)
- 8
- Mean
- 5
- Sample variance
- 4.57143
- Sample SD
- 2.13809
- Population variance
- 4
- Population SD
- 2
What is standard deviation?
Standard deviation measures how spread out a set of numbers is around their mean. A small standard deviation means the values cluster close to the average; a large one means they are more scattered. It is the square root of the variance and is expressed in the same units as the data, which makes it easier to interpret.
How standard deviation is calculated
First find the mean. Then, for each value, subtract the mean and square the result, and add these squared differences together. For the population standard deviation, divide that sum by the number of values, N, and take the square root: σ = √(Σ(x − μ)² / N). For the sample standard deviation, divide by N − 1 instead of N — this is Bessel's correction, used when your data is a sample of a larger group: s = √(Σ(x − x̄)² / (N − 1)).
Example
For 2, 4, 4, 4, 5, 5, 7, 9: the mean is 40 ÷ 8 = 5. The squared differences from the mean add up to 32. Dividing by N = 8 gives a population variance of 4, so the population standard deviation is √4 = 2. Dividing by N − 1 = 7 gives a sample variance of about 4.571, so the sample standard deviation is about 2.138.
All calculations happen in your browser. Nothing is sent, stored, or tracked.
Results are estimates and may contain errors — for general information only, not professional advice. Always verify before relying on them. Disclaimer
How to use
Type your numbers separated by commas, spaces or new lines. Decimals and negatives are fine.
The calculator shows the mean, count, and both sample and population variance and standard deviation. Sample figures need at least two values.