What this calculator does
Standard deviation measures how far values spread around the mean. It is one of the most important statistics in education, research, quality control and finance.
This calculator accepts numbers separated by commas, spaces or line breaks and returns the mean, median, variance, standard deviation and range.
Standard deviation
s = √( Σ(xᵢ − x̄)² ÷ (n − 1) ) The sample formula divides by n−1; the population formula divides by n. More spread-out values produce a larger standard deviation.
How this calculator works
- 01
Paste your numbers
Commas, spaces and line breaks are all accepted.
- 02
Choose sample or population
Most everyday data is a sample from a larger population.
- 03
Interpret the spread
Compare the standard deviation with the mean and range.
Frequently asked questions
When should I use n versus n−1?
Use n−1 when the data is a sample from a larger population. Use n when you have the entire population.
What does a high standard deviation mean?
Values are more spread out around the mean, which implies greater variability and uncertainty.
Do outliers affect the result?
Yes, strongly. One extreme value can change both the mean and the standard deviation, so inspect the data first.
Data basis: 2026 · Annual constants live in structured JSON files and are updated once a year.
Results are unverified model calculations and do not replace tax, legal or financial advice.