Math calculator
Standard Deviation Calculator
Calculate population and sample standard deviation.
About the standard deviation calculator
The standard deviation calculator finds both population and sample standard deviation for a dataset.
How to use this calculator
- 1
Enter numbers
Enter numbers separated by commas.
- 2
View results
See population σ, sample s, variance, and mean.
How the calculation works
Population σ = √(Σ(x−μ)²/N). Sample s = √(Σ(x−x̄)²/(n−1)).
Example: 5,10,15,20: σ≈5.59, s≈6.45.
When to use a calculator vs. mental math
Simple operations like percentages and proportions are great for mental math. Complex problems — quadratic equations, standard deviation, and base conversions — benefit from calculator precision. Always estimate the answer first to catch input errors, and verify results with a second method when possible.
Important limitations
This tool provides a mathematical estimate based only on the values entered. It does not account for regulations, taxes, lender fees, market conditions, or individual circumstances. Results are for planning purposes only — consult a qualified professional for regulated, medical, financial, or construction decisions.
Frequently asked questions about standard deviation calculator
How accurate is the standard deviation calculator?+
The calculation follows the displayed formula and retains full numeric precision before formatting the result.
Can I use the result professionally?+
Use it as a planning estimate. Confirm regulated, medical, financial, or construction decisions with a qualified professional.