Statistics

Standard Deviation Calculator

Calculate mean, variance, population standard deviation, and sample standard deviation from a list of numbers.

Count

Mean

Variance (population)

Std Dev (population)

Variance (sample)

Std Dev (sample)

Tool guide

How to use Standard Deviation Calculator

Standard Deviation Calculator gives you a focused way to handle one small task quickly. Calculate mean, variance, and population and sample standard deviation. It is free to use, requires no login, and is built for quick checks when you need a practical result.

Useful for

Check everyday numbers before making a purchase, quote, or budget decision.
Compare inputs quickly when you do not want to open a spreadsheet.
Verify math for work, school, invoices, ads, or personal planning.

Example

For example, use Standard Deviation Calculator to enter the values from a receipt, estimate, campaign report, or planning note, then copy the result into your document or message.

Good to know

Results are meant for quick planning and double-checking. For legal, tax, or financial decisions, review the numbers with a qualified professional.

How it works

The standard deviation calculator takes a list of numbers and computes the count, mean, population variance, population standard deviation, sample variance, and sample standard deviation.

Population std dev = √(sum of squared deviations / n). Sample std dev = √(sum of squared deviations / (n - 1)).

Practical examples

A data set of 45, 50, 55, 60, 65, 70, 75 has a mean of 60 and a population standard deviation of 10.
Use population standard deviation when you have data for every member of a group.
Use sample standard deviation when working with a sample of a larger population.

Common mistakes

Do not use population standard deviation for a small sample that represents a larger group. Use sample standard deviation for that.
Standard deviation can be sensitive to outliers. Consider checking your data for extreme values.

Questions

What is the difference between population and sample standard deviation?

Population divides by n (all data points). Sample divides by n-1 to give an unbiased estimate of a larger population.

When should I use each type?

Use population when you have the complete dataset. Use sample when your numbers are a subset of a larger group.