Standard Deviation Calculator
Population and sample standard deviation & variance.
Amortization schedule
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Showing first 12 of months.
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Introduction
Standard Deviation Calculator — Population and sample standard deviation & variance. Enter Numbers (comma separated), Type to get an instant, accurate result.
Formula
Sample SD: √(Σ(x−mean)² / (n−1)). Population SD: √(Σ(x−mean)² / n).
Step-by-step
- Enter the Numbers (comma separated).
- Enter the Type.
- Click Calculate to see your result instantly.
Real-world example
Example: With Numbers (comma separated) = 2, 4, 4, 6, 8, Type = sample, the Standard Deviation Calculator gives Mean: 4.8, Variance: 5.2, SD: 2.2804.
Frequently Asked Questions
Should I use sample or population standard deviation?
Use sample if your numbers are a subset of a larger group; use population if they're the entire group you care about.
Why does sample SD divide by n−1?
It's Bessel's correction, which adjusts for the bias of estimating variance from a sample rather than the whole population.
What inputs does the Standard Deviation Calculator need?
You'll need to provide: Numbers (comma separated), Type. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Standard Deviation Calculator?
The Standard Deviation Calculator applies the formula exactly as calculated — Sample SD: √(Σ(x−mean)² / (n−1)). Population SD: √(Σ(x−mean)² / n). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Standard Deviation Calculator free to use?
Yes, the Standard Deviation Calculator is completely free, requires no signup, and runs instantly in your browser.
About the Standard Deviation Calculator
The Standard Deviation Calculator uses a real, verifiable formula — Sample SD: √(Σ(x−mean)² / (n−1)). Population SD: √(Σ(x−mean)² / n). — so results are accurate every time, not an approximation.