Hasebah

Standard Deviation Calculator

Compute sample or population standard deviation and variance for a list of numbers.

Quick utilityFully localized assumptionsGlobal-readyInteractive chart

Last updated: 2026-06-03

This calculator uses generic assumptions. Use advanced mode to override them for a more accurate result.

Inputs

Input mode

Formula transparency

Source: default
sample = √(Σ(x−x̄)²/(n−1)) · population = √(Σ(x−μ)²/N)

How to use it

  1. Paste your numbers.
  2. Choose sample (part of a larger set) or population (the whole set).

Example

  • 5, 7, 3, 9, 6 → sample SD ≈ 2.24, population SD = 2.

What the result means

A larger standard deviation means the values are more spread out around the mean.

Common mistakes

  • Using population mode for sample data (understates spread).
  • Forgetting sample mode needs at least two values.

Limitations

  • Sensitive to outliers.
  • Assumes the numbers are comparable measurements.

Frequently asked

Sample vs population?
Sample divides by (n−1) to correct bias; population divides by N.
When to use sample?
When your data is a subset of a larger population you're estimating.
What does a large SD mean?
Wider spread of values around the mean.
Minimum values?
Sample needs at least two; population needs at least one.
Is data stored?
No — fully local.

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Results are estimates and not professional advice. Verify important decisions with a qualified professional.