Standard Deviation Calculator
🎲 Statistics & probability. Use the Standard deviation (from the variance) formula to find standard deviation σ, σx², n, mean x̄: pick the value you want, type the others, and the answer updates as you go.
Standard deviation σ2
Pick the ○ next to the value you want to find, fill in the others, and it solves as you type.
What each letter means
| Quantity | Unit |
|---|---|
| Standard deviation σ | no unit |
| Σx² | no unit |
| n | no unit |
| Mean x̄ | no unit |
Worked example
Find the standard deviation σ when Σx² = 232, n = 8, Mean x̄ = 5.
Using σ = (Σ x²)/n - x²: Standard deviation σ = 2.
Frequently asked questions
What is the formula for Standard deviation (from the variance)?
σ = (Σ x²)/n - x².
What do the letters stand for, and what units are used?
Standard deviation σ, Σx², n, Mean x̄.
How do you calculate standard deviation σ?
Put the values into σ = (Σ x²)/n - x². For example, with Σx² = 232, n = 8, Mean x̄ = 5, standard deviation σ = 2.
Can I solve for a different value?
Yes. In the calculator above, pick the circle next to any value (standard deviation σ, σx², n, mean x̄) and fill in the others: it rearranges the formula for you.
