Aisha K.
Mar 12, 2026
Clean layout and the results update instantly. Exactly what I needed for a quick planning check.
Statistics, Probability & Advanced Math
How to Calculate Standard Deviation and Variance
Instant math result
Variance and standard deviation describe how dispersed values are around the mean. Provide n, sum, and sum of squares to compute both measures.
Inputs
21000
-1000001000000
01000000000
01
Smart analysis
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Tailored to your live inputs and result—guidance only, not professional advice.
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Plain-English guide
Terms & how it works
Confused by a field? Read the short definitions here while you use the tool.
Sample Size (n)
The “Sample Size (n)” value used in this tool’s formula. Adjust it to see results update live.
Sum of Values
The “Sum of Values” value used in this tool’s formula. Adjust it to see results update live.
Sum of Squares
The “Sum of Squares” value used in this tool’s formula. Adjust it to see results update live.
Sample (1) or Population (0)
The “Sample (1) or Population (0)” value used in this tool’s formula. Adjust it to see results update live.
- μ
Mean
Average of observations.
- σ
Std. deviation
Spread around the mean.
When to use this Standard Deviation and Variance
Common use cases
- Check homework results with transparent formulas
- Estimate probability for common distributions
- Convert between related statistical measures quickly
Localized examples
- Classroom and exam-prep workflows
- Business analytics back-of-envelope checks
What you get
- Formula-backed outputs with clear labels
- Step-friendly defaults for learning
- Free online calculator — no sign up
How to Calculate Standard Deviation and Variance Step-by-Step
- 1Enter the number of observations.
- 2Input the sum of values and sum of squared values.
- 3Choose sample or population mode and review results.
Governing formula
σ² = Σ(xᵢ − μ)² / N · σ = √σ²
Population variance and standard deviation of the provided values.
Example: set Sample Size (n) = 10, Sum of Values = 500, Sum of Squares = 26,000, then read the result.
Variable definitions
- μ
Mean
Average of observations.
- σ
Std. deviation
Spread around the mean.
- Sample variance would divide by N−1 instead of N.
Frequently Asked Questions
Bessel’s correction reduces bias when estimating population variance from a sample.
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4.8
out of 5.0
4 reviews
Daniel R.
Feb 28, 2026
Very usable on mobile. Would love a save/export option later, but the math feels solid.
Priya S.
Feb 3, 2026
The FAQ section answered my questions before I even had to search. Smooth dark mode too.
Marcus L.
Jan 19, 2026
Simple inputs, clear outputs. This replaced three bookmarks I used to juggle.
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