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Standard Deviation Calculator
Paste a list of numbers to get the standard deviation, variance and mean of your dataset.
Enter at least two numbers to measure the spread.
Formula
Sample: s = √(Σ(x − x̄)² ÷ (n − 1)) · Population: σ = √(Σ(x − x̄)² ÷ n)
How to calculate
- 1Compute the mean of your data set.
- 2Subtract the mean from each value and square the difference.
- 3Add up all the squared differences.
- 4Divide by n − 1 for a sample (or n for a population), then take the square root.
How to use this calculator
- 1Paste or type your numbers, separated by commas or spaces.
- 2Choose sample or population standard deviation.
- 3See the standard deviation, variance, mean and count at once.
- 4Use sample mode unless you truly have every value in the group.
Examples
Test scores
70, 75, 80, 85, 90 → mean 80, sample SD ≈ 7.9 — scores typically sit within 8 points of the average.
More spread
60, 70, 80, 90, 100 also averages 80, but the SD ≈ 15.8 — twice as spread out.
Common questions
Sample or population standard deviation?
Sample divides by n − 1 and is right whenever your data represents a sample of a larger group — the common case. Population (÷ n) only applies when you have every value.
What does standard deviation tell me?
How spread out values are around the mean. For roughly normal data, about 68% of values fall within one SD and 95% within two.
Can standard deviation be negative?
No — it is a square root, so it is never negative. Zero means every value is identical.
