Standard Deviation Calculator
Calculate mean, variance, and standard deviation for a set of numbers.
The standard deviation of your 6 values is 4.6655 with a mean of 16.17.
Why This Calculation Matters
The Standard Deviation Calculator gives you a fast, accurate answer for standard deviation, useful for homework, coursework, or inside a larger problem. The formula is shown below so you can see exactly what the tool is doing and verify it against a textbook or other reference.
How to Use This Calculator
- Enter your values in the input fields, each one has a label and help text explaining what to type.
- Results appear instantly as you type; there's no "calculate" button to press.
- Change any input to compare scenarios side by side.
All math happens in your browser. Nothing you type is sent to a server, saved, or shared.
Standard Deviation
Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means values cluster near the mean; a high standard deviation means values are more spread out.
Steps
- Calculate the mean
- Subtract the mean from each value and square the result
- Average the squared differences (variance)
- Take the square root (standard deviation)
Formula
Population SD: σ = √(Σ(x − μ)² / N). Sample SD: s = √(Σ(x − x̄)² / (n − 1)). Sample SD uses n − 1 (Bessel's correction) to correct bias.
When to Use This Calculator
- Check homework, textbook problems, or coursework answers.
- Explore how the result changes as you vary inputs, great for intuition building.
- Verify a calculation inside a larger engineering, research, or data workflow.
Limitations & Common Mistakes
- Results are only as accurate as the inputs, double-check rounding and units.
- Numeric precision is limited by JavaScript floating-point arithmetic.
Frequently Asked Questions
What does standard deviation tell you?
Standard deviation measures the amount of variation in a data set. About 68% of values fall within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 (for normally distributed data). It's the most common measure of statistical dispersion.
What is the formula used by the Standard Deviation Calculator?
The formula and a worked example are shown on this page. Results are computed with standard floating-point arithmetic and are accurate to several decimal places for typical inputs.
Can I use this for homework or standardized tests?
Yes, it's an excellent check-your-work tool. Always show your work and understand the underlying method, not just the final number.
Is this calculator free to use?
Yes. The Standard Deviation Calculator is free, requires no signup, and runs entirely in your browser, your inputs are never sent to a server.
How often is this calculator updated?
Formulas are reviewed against authoritative sources, and any rate or price data is refreshed on an automated schedule. Check the "as of" date on any live data panel for the most recent refresh.
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Key terms
- Standard DeviationA measure of how spread out a dataset is around its mean, expressed in the same units as the data. For a normal distribution, about 68% of values fall within on…
- Mean, Median, and ModeThree measures of central tendency. The mean is the arithmetic average (sum ÷ count). The median is the middle value when the data is sorted, the 50th percentil…