SD Calculator
Sd calculator works out Standard deviation and Variance from Data values, Frequencies (optional) and Data represents. The default figures on this page give standard deviation of 2.13809; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
5 steps
- n = 8, Σx = 40
- Mean = 40 / 8 = 5
- Σ(x − mean)² = 32
- s² = 32 / (8 − 1) = 4.571429
- s = sqrt(4.571429) = 2.13809
Deviation tabletable
| value | frequency | deviation | squaredDeviation |
|---|---|---|---|
| 2 | 1 | -3 | 9 |
| 4 | 1 | -1 | 1 |
| 4 | 1 | -1 | 1 |
| 4 | 1 | -1 | 1 |
| 5 | 1 | 0 | 0 |
| 5 | 1 | 0 | 0 |
| 7 | 1 | 2 | 4 |
| 9 | 1 | 4 | 16 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the sd calculator calculates
Computes sample and population standard deviation and variance from a data set or a frequency table, showing every deviation and squared deviation.
How to use this sd calculator
Enter Data values, Frequencies (optional), Data represents and Report. Standard deviation updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Standard deviation, Variance and Sample standard deviation (s).
The method follows OpenStax, Introductory Statistics 2e, section 2.7 "Measures of the Spread of the Data" and NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.6 "Measures of Scale".
Textbook set 2,4,4,4,5,5,7,9 (population) example
With Data values: 2,4,4,4,5,5,7,9, Data represents: population, the calculator returns Mean: 5, Sum of squared deviations: 32, Population variance (σ²): 4. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Standard deviation, Variance and Sample standard deviation (s). The inputs you can vary are Data values, Frequencies (optional), Data represents and Report.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to do SD on a calculator?
Computes sample and population standard deviation and variance from a data set or a frequency table, showing every deviation and squared deviation. Open “How this is worked out” beside the result to see each step for your own figures.
How do we calculate SD?
It needs Data values, Frequencies (optional), Data represents and Report. Nothing else is required, and the figures stay in your browser.
What is SD mode on a calculator?
Computes sample and population standard deviation and variance from a data set or a frequency table, showing every deviation and squared deviation. On this page it is computed from Data values, Frequencies (optional) and Data represents and shown as Standard deviation, Variance and Sample standard deviation (s).
How do I calculate SD in Excel?
The result gives Standard deviation, Variance, Sample standard deviation (s), Sample variance (s²), Population standard deviation (σ) and Population variance (σ²), each labelled with its unit so the figure can be read on its own.
What information do I need for the sd calculator?
You need Data values, Frequencies (optional), Data represents and Report. The page opens with default figures that give standard deviation of 2.13809, so you can see the scale before entering your own.
What does this sd calculator show?
It shows Standard deviation, Variance, Sample standard deviation (s), Sample variance (s²), Population standard deviation (σ), Population variance (σ²), Mean and Data points entered, with the working and any warnings for your entries.