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Standard Deviation Calculator

Paste your dataset and get sample SD, population SD, variance and mean.

Short answer

Sample SD divides by (n − 1) and is used when your numbers are a sample from a larger group. Population SD divides by n and is used when you have all the data.

Numbers

Fill in the fields above to see your result instantly.

How it works

Standard deviation measures how spread out numbers are around the mean. Steps: (1) find the mean, (2) subtract the mean from each value and square the result, (3) sum the squared differences, (4) divide by n (population) or n−1 (sample), (5) take the square root.

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9 → mean = 5, population SD ≈ 2, sample SD ≈ 2.138.

Who should use this

  • •Statistics students
  • •Researchers reporting variability
  • •Anyone analysing test scores or measurements

Common mistakes

  • ×Using population SD when you only have a sample (use n−1)
  • ×Not squaring the deviations before averaging

Frequently asked questions

When do I use sample vs population SD?▾

Use sample SD (n−1) when your data is a subset of a larger group. Use population SD (n) only when you have data on every member of the group.

What does a high SD mean?▾

Values are spread far from the mean. A low SD means values cluster close to the mean.

Related calculators

Mean / Median / Mode →