Online Tool Store
Standard Deviation Calculator
Calculate sample or population standard deviation, variance, mean, range, sum, and value deviations from a pasted number list.
🔒 This tool runs entirely in your browser. Your files are never uploaded to a server.
Separate numbers with commas, spaces, or new lines.
Standard deviation
2.73
Variance
7.43
Mean
14.38
Count
8
Sum
115
Range
8
Value deviations
| Value | x − mean | Squared deviation |
|---|
Sample statistics use n − 1 in the variance denominator.
How to calculate standard deviation
- Paste the numerical dataset.
- Choose whether the data represents a sample or complete population.
- Review standard deviation, variance, mean, count, sum, range, and individual deviations.
Formula
Subtract the mean from each value, square those differences, and sum them. Population variance divides by n; sample variance applies Bessel’s correction and divides by n − 1. Standard deviation is the square root of that variance.
FAQ
What does standard deviation measure?
It summarizes how far values typically spread from their mean. A smaller result indicates tighter clustering; a larger result indicates greater dispersion.
When should I choose sample?
Choose sample when the entered observations are a subset used to estimate a larger population. The calculation divides squared deviations by n − 1.
When should I choose population?
Choose population when the values represent every member of the population you intend to describe. Its variance denominator is n.
What is variance?
Variance is the average squared distance from the mean using the selected denominator. Standard deviation is the positive square root of variance.
Can I enter negative values and decimals?
Yes. Integers, decimals, negative values, and scientific notation can be separated with commas, spaces, semicolons, or line breaks.
How we compare
| Feature | Online Tool Store | Calculator.net | Omni Calculator |
|---|---|---|---|
| Sample and population modes | Included | Included | Included |
| Per-value deviation table | Included | Formula guidance | Step guidance |
| Confidence interval tools | Not included | Approximation included | Related calculators |
Choose Calculator.net for confidence-interval approximations or Omni Calculator for an extended learning walkthrough. Choose Online Tool Store for direct pasted data, full summary statistics, and a per-value deviation table.