Standard Deviation Calculator
Calculate population and sample standard deviation, variance, and coefficient of variation for a dataset.
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How to use this calculator
- 1
Enter your data values (up to 8 fields shown; all are used).
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The calculator automatically computes both sample and population standard deviation.
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Use sample SD (s) if your data is a sample from a larger population.
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Use population SD (σ) if your data represents the entire population.
Frequently asked questions
What is standard deviation?
Standard deviation measures how spread out data is from the mean. A low SD means data points are close to the mean; a high SD means they are spread out. Mathematically, it is the square root of variance.
What is the difference between population and sample standard deviation?
Population SD (σ) divides by n (used when you have all data). Sample SD (s) divides by n−1 (used when your data is a sample — the correction makes the estimate unbiased). Use sample SD for most real-world data analysis.
What is the 68-95-99.7 rule?
For normally distributed data: 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD. A value more than 3 SDs from the mean is statistically rare (0.3% chance).
What is coefficient of variation (CV)?
CV = (SD / Mean) × 100%. It expresses variability as a percentage of the mean, making it possible to compare dispersion across datasets with different units or scales.
Standard deviation and variance explained
How to use the standard deviation
Use this standard deviation to population and sample standard deviation, variance, and coefficient of variation for a dataset. Enter your values above and get your result in seconds. The tool is free, works on all devices, and keeps your data private — nothing is stored or shared.
How the standard deviation works
The standard deviation calculator uses standard formulas used in mathematics, science, and engineering. Enter your inputs, and the tool calculates the result instantly in your browser. No server-side processing means your data stays on your device. Results update in real time as you change inputs.
Why spread matters
Two investments with the same average return can have very different risk profiles. Investment A returns exactly 7% every year. Investment B returns −10%, +5%, +30%, −5%, +21% for the same average. Investment B has far higher standard deviation — same mean, much more risk. SD is the most common measure of volatility and risk.
The formula step by step
1. Calculate the mean. 2. Subtract the mean from each value and square the result. 3. Sum all squared differences. 4. Divide by n (population) or n−1 (sample) to get variance. 5. Take the square root to get standard deviation.
Standard deviation in the real world
Finance: stock volatility, portfolio risk. Quality control: manufacturing tolerance. Education: grading on a curve. Science: measurement uncertainty. Medicine: clinical trial results. Sports analytics: consistency of player performance. SD is a universal language for describing uncertainty.
Standard deviation: how it works
Built on well-established mathematical principles, this tool delivers accurate results for students, researchers, and professionals. Enter your values and get instant clarity without specialist software or manual arithmetic.
Who uses this tool?
Teachers, students, engineers, and data analysts use it to verify calculations, check homework, and solve problems faster. It is intuitive enough for beginners while comprehensive enough for professional use.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →