Education

Standard Deviation Calculator

Paste a list of numbers and get the sample and population standard deviation, variance, mean, count, min and max — with the working shown. Accepts commas, spaces or line breaks, so you can paste straight from a spreadsheet.

Examples

Input

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

Output

Population SD 2 · Sample SD 2.138 · Mean 5

How it works

Standard deviation measures how far the numbers sit from their mean, on average. The tool finds the mean, squares each number’s distance from it, adds those squares up and divides: by n for a population, or by n − 1 for a sample. The square root of that variance is the standard deviation.

2, 4, 4, 4, 5, 5, 7, 9      mean = 5

Squared distances: 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32

Population: 32 ÷ 8 = 4       SD = 2
Sample:     32 ÷ 7 = 4.5714  SD = 2.1381

Use the population figure when your list is the whole group, and the sample figure when it is a selection from a larger group. At least two numbers are needed. Results are rounded to four decimal places, and anything in the list that is not a number stops the calculation with a message.

How to use Standard Deviation Calculator

Paste the data

Numbers separated by commas, spaces or new lines — straight from Excel or Sheets works.

Read the stats

Mean, sample SD (n−1), population SD (n), both variances, min and max update live.

Pick the right SD

Use sample SD when your data is a sample of a larger group; population SD when it is the whole group.

Why use this tool

Both sample (n−1) and population (n) standard deviation

Variance, mean, count, min and max in one view

Paste-friendly: commas, spaces, tabs or line breaks

Instant and private — data never leaves your device

Frequently asked questions

Sample or population standard deviation — which one do I need?

If your numbers are the entire group you care about, use population SD (divides by n). If they are a sample representing a bigger group, use sample SD (divides by n−1), which corrects for the underestimate.

What does standard deviation actually tell me?

How spread out the values are around the mean. For roughly normal data, about 68% of values fall within one SD of the mean and 95% within two.

What is variance?

The average of the squared distances from the mean — the standard deviation squared. SD is usually easier to interpret because it is in the same units as the data.

Found a bug or have an idea?

ToolOrbit is actively developed — feedback directly shapes what gets built next.

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