Checks Out
All calculators
MathsLive

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.

Calculation method, coverage and version

Inputs used
List of numbers.
Calculation approach
The calculator applies the rules and assumptions described in “How it works” to the values you enter. Rounding can cause small differences from an official or provider calculation.
Coverage
Maths. UK nations, tax treatment, local rules and provider criteria can differ; check the official sources shown below before acting.
Content version
No page-specific review date is currently published. Treat the result as indicative and verify current rules independently.
Not included unless explicitly requested: personal circumstances not entered, provider discretion, future rule changes, professional fees and case-specific exceptions. Read the full calculator methodology.

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 →