Standard Deviation Calculator
Enter a list of numbers to calculate the mean, variance, and standard deviation — a measure of how spread out the values are from the average.
Show solution steps
What is the Standard Deviation Calculator?
Standard deviation tells you how spread out a set of numbers is around their average. A low standard deviation means most values sit close to the mean; a high one means the values are scattered widely — which is why it's widely used as a measure of consistency in academic scores, quality control, and as a proxy for risk or volatility in investment returns.
How to Calculate
Enter your list of numbers, then choose whether they represent an entire population or a sample drawn from a larger one — use population standard deviation when your numbers are literally everything you care about (e.g. every student in one class), and sample standard deviation when they're a subset you're using to estimate a bigger group (e.g. a survey sample). The calculator finds the mean, measures how far each number is from it, and averages those squared distances before taking the square root.
Formula
Population: σ = √( Σ(x−μ)2 / n )
Sample: s = √( Σ(x−x̄)2 / (n−1) )
Use population SD when your numbers are the entire group you care about; use sample SD when your numbers are a sample drawn from a larger population you're trying to estimate.
Worked Example
For the dataset [2, 4, 4, 4, 5, 5, 7, 9]: mean = 5, population standard deviation = 2.
How to Use
- Enter your numbers separated by commas or spaces.
- Choose population or sample standard deviation.
- Read the mean, variance, and standard deviation instantly.