Standard Deviation Calculator
Please enter at least two valid numbers.
What Is Standard Deviation?
Standard deviation measures how spread out a set of numbers is from the mean. A low standard deviation means values are clustered close to the average, while a high standard deviation means values are more spread out.
Formulas Used
Population Standard Deviation: σ = √[Σ(x − μ)² / N]
Sample Standard Deviation: s = √[Σ(x − x̄)² / (n − 1)]
The key difference is the denominator — population standard deviation divides by N (total count), while sample standard deviation divides by n−1 (Bessel's correction), which adjusts for the fact that a sample tends to underestimate the true population variability.
How to Use This Calculator
Choose whether your data represents a full population or a sample, enter your numbers separated by commas or spaces, then click "Calculate" to see standard deviation, variance, mean, and count.
Population vs. Sample — Which Should You Use?
Use "Population" when your data includes every member of the group you're studying (e.g., test scores for an entire class). Use "Sample" when your data is a subset used to estimate a larger population (e.g., a survey of 100 people representing a city).
Frequently Asked Questions
Why does sample standard deviation give a higher result than population?
Dividing by n−1 instead of n makes the result slightly larger, which corrects for the tendency of a sample to underestimate true variability.
What does a standard deviation of zero mean?
It means all the numbers in your data set are identical — there's no variation at all.
How many numbers do I need minimum?
At least two numbers are required. Sample standard deviation is undefined for a single data point.
Is variance the same as standard deviation?
No, variance is the standard deviation squared. Standard deviation is more commonly used because it's in the same units as the original data.