Standard deviation measures how spread out values are around the mean. A small value means data cluster tightly; a large value means they are widely scattered.
How to use the Standard Deviation Calculator
- Data
Results update as you type, and every field accepts the units shown in its menu.
How it works
Subtract the mean from each value, square the differences, add them, divide by n − 1 (sample) or n (population) and take the square root.
What each result means
- Sample standard deviation (s) = stdev([Data])
- Population standard deviation (σ) = pstdev([Data])
- Sample variance = variance([Data])
- Mean = mean([Data])
- Count = count([Data])
Formula
Sample s = √(Σ(x − x̄)² ÷ (n − 1))Population σ = √(Σ(x − μ)² ÷ n)Worked example
Inputs — Data: 4, 8, 15, 16, 23, 42.
Results — Sample standard deviation (s) = 13.4907; Population standard deviation (σ) = 12.3153; Sample variance = 182; Mean = 18; Count = 6.
Key terms
- Variance
- The square of the standard deviation.
Frequently asked questions
Sample or population?
Use sample (n − 1) when your data are a sample from a larger group; population when you have every value.
Why n − 1?
It corrects the bias of estimating spread from a sample (Bessel’s correction).
What formula does the Standard Deviation Calculator use?
Sample s = √(Σ(x − x̄)² ÷ (n − 1)).