Free Standard Deviation Calculator (+ Guide)

What is a standard deviation calculator?

A standard deviation calculator measures how spread out a list of numbers is.

A small standard deviation means the values sit close to the mean. A large one means they're scattered.

How to calculate standard deviation

Here's the formula as the NIST handbook gives it, in steps:

The calculator does each step and shows them in a table you can download.

Sample or population?

Use the sample standard deviation when your numbers are part of a bigger group, like 50 customers out of thousands. Dividing by N − 1 corrects for the sample being small.

Use the population standard deviation only when you have every value, like every student in one class.

A worked example

Here's the example the calculator loads: 2, 4, 4, 4, 5, 5, 7, 9, as a population.

The mean is 40 ÷ 8 = 5. The squared distances from 5 add up to 32.

Divided by 8, the variance is 4, and its square root is 2. As a sample, dividing by 7 instead, it's 2.14.

Mistakes to avoid

These are the ways the answer comes out wrong.

• Dividing by N for a sample, which understates the spread
• Forgetting to square the differences, so the positives and negatives cancel out
• Forgetting the square root, which leaves the variance
• Comparing standard deviations of data in different units

Who is the standard deviation calculator for?

It's for students, researchers and analysts, and these tools help around it.

• Statistics calculator – for every statistic at once
• Mean, median and mode calculator – for the center of your numbers
• Probability calculator – for chances and odds

Know the spread, and the mean means more.