Standard Deviation Calculator

The Standard Deviation Calculator is a free online tool that compute population and sample standard deviation, variance, mean, median, mode, and range with a full step-by-step deviation table. csv export.. It runs entirely in your browser with no installation or sign-up needed.

Population divides by N (entire population). Sample divides by N-1 (Bessel correction) for an unbiased estimate when the data is a sample from a larger population.

Paste numbers separated by commas, spaces, tabs, semicolons, or newlines. Blanks and non-numeric tokens are ignored, so you can paste from spreadsheets or CSVs directly.

Sample stddev divides by N-1, which is 0 when n=1. Add at least a second value, or switch to Population mode which is defined for n >= 1.

Yes, the Standard Deviation Calculator is 100% free with no registration, no hidden fees, and no usage limits. All processing happens locally in your browser, ensuring complete privacy.

Yes, the Standard Deviation Calculator is fully responsive and works on smartphones and tablets. You can use it on any device with a modern web browser -- no app download required.

No account or registration is needed. Simply open the Standard Deviation Calculator in your browser and start using it immediately. There are no sign-up walls or usage restrictions.

The Standard Deviation Calculator uses industry-standard formulas and algorithms to ensure accurate results. However, for critical financial or medical decisions, always consult a qualified professional.

The Standard Deviation Calculator works in all modern browsers including Chrome, Firefox, Safari, Edge, and Opera. For the best experience, use the latest version of your preferred browser.

Variance and standard deviation both measure how spread out a data set is, and they are directly linked: the standard deviation is simply the square root of the variance, and the variance is the standard deviation squared. The key practical difference is units. Variance is expressed in squared units, so if your data is in dollars, the variance is in "dollars squared" — hard to interpret. Standard deviation undoes that squaring and returns to the original units, which is why it is the figure most people actually report and compare. This calculator shows both side by side for population and sample modes, so you can see the relationship directly. Paste your numbers above and the headline card displays the variance and its square-rooted standard deviation together, with the substituted formula spelled out.

A low standard deviation means values cluster tightly around the mean, so the data is consistent and predictable; a high standard deviation means values are widely scattered, signaling more variability or risk. There is no universal cutoff for "high" or "low" — it only makes sense relative to your mean and context. A standard deviation of 5 is large for data averaging 10 but tiny for data averaging 10,000, which is why analysts often compare the standard deviation to the mean rather than reading it alone. Two data sets can share an identical average yet behave completely differently in spread. Enter your numbers above to see the standard deviation alongside the mean, range, min, and max, giving you the full context needed to judge whether your spread is tight or wide.

The empirical rule, also called the 68-95-99.7 rule, describes how data falls around the mean in a roughly normal (bell-shaped) distribution. About 68 percent of values lie within one standard deviation of the mean, about 95 percent within two standard deviations, and about 99.7 percent within three. This is why standard deviation is so widely used: once you know the mean and the standard deviation, you can estimate where most of your data should fall and flag unusual outliers beyond two or three deviations. The rule underpins quality-control limits, confidence intervals, and grading curves. It assumes an approximately normal shape, so it is a guide rather than a guarantee for skewed data. Calculate your mean and standard deviation above, then apply these percentages to understand your data's typical range.

The mode is the value that appears most often in your data set, and unlike the mean or median, it is not always unique. If every number appears exactly once, there is no most-frequent value, so the calculator reports "No mode." If two or more values tie for the highest frequency, the data is multimodal and the tool lists all of them — for example, a set where both 7 and 12 appear three times shows "7, 12." This behavior is statistically correct: a data set can legitimately have zero, one, or many modes. The mode is most useful for spotting repeated readings or the most common category, while the mean and median better describe the center of numeric data. Paste your values above and the descriptive-statistics grid reports the mode alongside mean, median, and range automatically.

Standard deviation is computed in stages: find the mean, subtract it from each value to get the deviation, square each deviation, sum those squares, divide by N (population) or N−1 (sample), then take the square root. This tool exposes every stage in a step-by-step table so you can verify the work rather than trust a single number. Each row shows the original value xᵢ, its deviation from the mean (xᵢ − μ), and the squared deviation (xᵢ − μ)², with the summed squared deviations totaled at the bottom — exactly the figure that feeds the variance formula. Seeing each line makes it easy to catch a typo, confirm homework, or follow the method while learning it. Enter your data above, then export the full table and summary to CSV to keep a record or check it in a spreadsheet.