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Standard Deviation Calculator

Measure spread in a list of numbers using sample or population standard deviation.

Exact method explained belowEditable inputs

Set up your calculation

Runs on your device

SOLUTION

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter numbers, treat values as.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Variance is the sum of squared distances from the mean divided by N for a population, or N − 1 for a sample. Standard deviation is the square root of variance. The calculation uses an incremental algorithm to reduce numerical error.

A WORKED EXAMPLE

For 2, 4, 4, 4, 5, 5, 7 and 9, the mean is 5. Population variance is 4 and population standard deviation is 2. Sample deviation is approximately 2.13809.

What to keep in mind

Sample mode needs at least two observations. Separate values with commas, spaces or semicolons; use dots for decimals, not thousands separators. This is an unweighted calculation.

Common questions

Which mode should I choose?

Choose population if these are all values you want to describe. Choose sample when estimating population variability from a sample.

What units does the result use?

Standard deviation uses the original measurement unit. Variance uses that unit squared.

Methodology maintained by ClarityKit. How these tools are built and checked.