Standard Deviation Calculator
Calculate standard deviation and variance for any data set. Get both sample and population values, plus the mean, sum, and count.
| Count (n) | 6 |
| Sum | 108 |
| Sample variance (s²) | 182 |
| Population variance (σ²) | 151.667 |
Use sample (s) when your data is a sample of a larger group; use population (σ) when it's the entire set.
How to use this calculator
Paste or type your numbers separated by commas, spaces, or new lines. The calculator returns the sample and population standard deviation, the variance for each, and the mean, sum, and count.
How standard deviation works
Standard deviation quantifies spread. After finding the mean, you measure how far each value sits from it, square those distances (so negatives don't cancel out), average them, and take the square root to return to the original units. The bigger the result, the more variable the data.
Worked example
For 4, 8, 15, 16, 23, 42, the mean is 18. The population standard deviation is about 12.3 and the sample standard deviation about 13.5 — a fairly spread-out set.
The formula
σ = √( Σ(x − mean)² ÷ n ) · s = √( Σ(x − mean)² ÷ (n − 1) )
Frequently asked questions
How do you calculate standard deviation?
Find the mean, subtract it from each value and square the result, average those squared differences to get the variance, then take the square root. The result is the standard deviation.
What's the difference between sample and population standard deviation?
Population standard deviation (σ) divides by n and is used when you have every data point. Sample standard deviation (s) divides by n − 1 and is used when your data is a sample of a larger group. This calculator shows both.
What does standard deviation tell me?
It measures how spread out the data is around the mean. A small standard deviation means values cluster close to the average; a large one means they're widely scattered.
What is variance?
Variance is the average of the squared differences from the mean — the square of the standard deviation. It's shown here for both the sample and population.