Calculators
Standard Deviation Calculator
Calculate population or sample standard deviation for a numeric dataset locally in your browser.
Enter numbers separated by commas, spaces, or new lines. Choose population to divide by N, or sample to divide by N − 1. Calculations run locally in your browser; your values are not uploaded or stored.
Measure how spread out a numeric dataset is.
Enter numbers separated by commas, spaces, or new lines, then choose population or sample standard deviation. Population mode divides the sum of squared differences by N; sample mode uses N − 1 to estimate variation from a sample. A larger result means values are more spread out around their mean, but standard deviation does not explain why the values vary or whether a dataset is representative. Invalid entries and a one-value sample are rejected. Everything runs locally in your browser, so your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What formula does the standard deviation calculator use?
It finds the mean, adds the squared difference between each value and that mean, divides by N for a population or N − 1 for a sample, then takes the square root. Population standard deviation is √(Σ(x − x̄)² ÷ N); sample standard deviation is √(Σ(x − x̄)² ÷ (N − 1)).
When should I use population or sample standard deviation?
Use population mode when your values are the entire group you want to describe. Use sample mode when the values are a sample used to estimate a larger population; it needs at least two values because it divides by N − 1.
How should I interpret standard deviation?
A smaller standard deviation means the values are closer to their mean, while a larger one means they are more spread out. It does not show why values vary, prove a distribution is normal, identify outliers on its own, or establish that a sample represents a wider population.
Do my dataset values stay private?
Yes. The calculation runs locally in your browser. CodeASystem does not upload or store the values you enter.