Standard Deviation Calculator
Standard deviation is the square root of variance — the typical distance of values from the mean.
Calculator
Use the Standard Deviation Calculator
Result
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Formula
σ = √(Σ(x − μ)² ÷ n)
Step-by-step
- 1
Enter values
List your numbers, separated by commas.
- 2
Read the σ
The result quantifies spread around the mean.
Worked example
Example input: numbers: 2,4,6
Result: 1.633
Related tools
- Variance Calculator
Squared spread of the data.
- Mean Calculator
The center the deviations orbit around.
Frequently asked questions
What does the standard deviation actually measure?
The typical distance of values from their mean: 2, 4, 6 sit around a mean of 4 with a standard deviation of 1.63, the example above. Bigger number, wider spread; zero, none at all. For bell-shaped data, about 68 percent of values land within one step of the mean.
What does a standard deviation of zero tell me?
That every value is identical — there is no spread at all. A list of 7, 7, 7 has variance 0 and its square root is likewise 0.
How does the example produce 1.633?
Mean of 2, 4, 6 is 4; squared gaps are 4, 0 and 4; averaging gives variance 8/3; its square root is about 1.633. Every step of that chain is what the calculator runs.
How do you calculate standard deviation step by step?
Five steps: find the mean, subtract the mean from every value, square each deviation, average the squares to get the variance, then take the square root. For 2, 4, 6: mean 4 → deviations −2, 0, 2 → squares 4, 0, 4 → variance 8/3 → σ ≈ 1.633.