Standard Deviation Calculator
Free standard deviation calculator. Enter a list of numbers to get sample and population SD, variance, mean, median, and range instantly.
What is a standard deviation?
Standard deviation measures how spread out a set of numbers is around their mean. A low standard deviation means values cluster tightly together; a high one means they’re scattered widely. It’s the most common measure of variability in statistics.
How this calculator works
- Paste or type your numbers separated by commas, spaces, or newlines — it reads any of them.
- It calculates the mean, then the squared difference of every value from that mean.
- Sample standard deviation divides by n−1 (for a sample from a bigger population); population SD divides by n.
- It also returns variance, median, and range for a fuller picture.
How to use the result
- Pick sample vs. population SD. Sample is correct when your numbers are a random subset; use population when they’re the complete set.
- Combine mean and SD to describe your data: most values sit within roughly one SD of the mean if the distribution is roughly bell-shaped.
- Compare SDs across groups to see which one varies more — e.g. which sales team’s results are more consistent.
- Use the median too if outliers are present — the mean skews, the median holds.
What’s the difference between sample and population standard deviation?
Population standard deviation treats your numbers as the entire universe of interest — all exam scores in the class. Sample standard deviation treats them as a sample, and divides by n−1 to correct for the fact that a sample underestimates true spread. For most real-world data that isn’t a complete census, the sample version is the one to report.
Common mistakes
- Using population SD on sample data. It biases the spread slightly low; use n−1 for samples.
- Mixing units or missing values. A stray comma or non-numeric entry silently drops that value.
- Ignoring outliers. Standard deviation is sensitive to them — one extreme value can inflate the SD dramatically.
Standard deviation is the spread counterpart to the percent change calculator’s relative measures — absolute spread vs. relative change each tell a different part of the story. For quick spot checks of your data, the basic calculator is always at hand.