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HomemathStandard Deviation

Standard Deviation

Calculate mean, variance, and standard deviation for a set of numbers — both population and sample.

Our free Standard Deviation lets you calculate mean, variance, and standard deviation for a set of numbers — both population and sample. It is built for students, teachers, engineers, and professionals who need fast, reliable math results who need fast, reliable results without installing software or creating an account.

Standard Deviation runs entirely in your browser on CalculatorsPlus — enter your values, get instant results, and copy or share your output in one click. Your data never leaves your device; we do not store inputs on any server.

Use the standard deviation to verify manual work, explore "what if" scenarios, and save time on repetitive calculations. For learning, try solving the problem by hand first, then check your answer here.

Results update in real time as you change inputs, so you can explore "what if" scenarios — adjust one variable at a time to see how it affects the outcome before committing to a purchase, plan, or decision.

This page includes step-by-step instructions, frequently asked questions, and practical tips below the calculator. Bookmark it for repeat use — many math tasks come up weekly during projects, studies, or financial planning.

Common Uses

  • Homework verification and exam preparation
  • Quick checks during work, shopping, or DIY projects
  • Teaching demonstrations and classroom examples
  • Engineering and spreadsheet formula validation

How to Use the Standard Deviation

  1. 1

    Enter your data

    Input your numbers separated by commas or spaces.

  2. 2

    Choose population or sample

    Select whether your data is the full population or a sample.

  3. 3

    View statistics

    See mean, variance, standard deviation, and data summary.

💡 Tips & Tricks

  • Use sample SD when your data is a subset of a larger population (most real-world cases).
  • Outliers dramatically affect standard deviation — consider removing or investigating them.
  • SD is most meaningful for normally distributed data.

Frequently Asked Questions

What is standard deviation?
Standard deviation measures how spread out data points are from the mean. A low SD means data clusters near the average; a high SD means data is widely dispersed.
What is the difference between population and sample SD?
Population SD (σ) divides by N (total count). Sample SD (s) divides by N-1 (Bessel's correction) to give an unbiased estimate when working with a sample of a larger population.
What is variance?
Variance is the square of the standard deviation. It measures dispersion but in squared units, making it less intuitive. SD = √Variance.
What does the 68-95-99.7 rule mean?
In a normal distribution: 68% of data falls within ±1 SD of the mean, 95% within ±2 SD, and 99.7% within ±3 SD. This is the empirical rule.