Standard Deviation Calculator
Compute sample or population standard deviation and variance for a list of numbers.
Last updated: 2026-06-03
This calculator uses generic assumptions. Use advanced mode to override them for a more accurate result.
Inputs
Formula transparency
Source: defaultsample = √(Σ(x−x̄)²/(n−1)) · population = √(Σ(x−μ)²/N)
How to use it
- Paste your numbers.
- 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.