Standard Deviation Calculator

Standard Deviation Calculator Guide

Use this standard deviation calculator to measure how spread out a data set is. A small standard deviation means values are close to the mean. A large standard deviation means values are more spread out.

What Is Standard Deviation?

Standard deviation is based on the distance of each value from the mean.

Variance = average of squared deviations from the mean
Standard deviation = square root of variance

How to Use This Calculator

1. Paste your data values into the input box.
2. Separate values with commas, spaces, or new lines.
3. Click Calculate.
4. Review the mean, variance, and standard deviation.

Worked Example

Data set:

2, 4, 4, 4, 5, 5, 7, 9

Mean:

40 / 8 = 5

The values are compared with the mean, squared, averaged, and square-rooted to get the standard deviation.

Population vs Sample Standard Deviation

Population standard deviation is used when your data set includes every value in the group. Sample standard deviation is used when your data is only a sample from a larger group. This calculator is designed for straightforward population standard deviation checks.

Mistakes to Avoid

Do not compare standard deviations from data sets with different units or very different scales unless the comparison makes sense.

Important Note

The current tool calculates population standard deviation for straightforward comparison.

Frequently Asked Questions

What does a high standard deviation mean?

It means the values are spread farther from the mean.

What does a low standard deviation mean?

It means the values are clustered close to the mean.

Is standard deviation always positive?

Yes. Standard deviation is never negative.

Why is variance squared?

Squaring removes negative signs and gives more weight to larger deviations.