# Standard Deviation Calculator Calculate sample and population standard deviation, variance, coefficient of variation, and sigma intervals > Canonical page: https://elysiatools.com/en/tools/standard-deviation-calculator - **Category:** Math & Numbers - **Keywords:** standard deviation, sample standard deviation, population standard deviation, statistics, variance, sigma ## Overview Calculate standard deviation for a numeric dataset. Population standard deviation divides variance by n. Sample standard deviation divides variance by n - 1 before taking the square root. Use it to understand spread around the mean, compare sample and population formulas, and inspect one-, two-, and three-sigma intervals. ## Inputs - **Dataset** (textarea): e.g. 600, 470, 170, 430, 300 - **Standard Deviation Type** (select) - **Decimal Places** (number) - **Include Sigma Intervals** (checkbox) ## When to use - When you need to measure the volatility or risk of financial returns over a specific period. - When analyzing experimental or survey data to determine the reliability and variance of your results. - When comparing the spread of two entirely different datasets using the coefficient of variation. ## How it works - Paste your numeric dataset into the input field, separating numbers with commas or spaces. - Select whether to calculate the sample standard deviation (n-1), population standard deviation (n), or both. - Choose your desired decimal precision and toggle the inclusion of sigma intervals. - The tool instantly processes the numbers and outputs the mean, variance, standard deviation, and statistical intervals in a structured format. ## Use cases - Quality control managers evaluating manufacturing consistency and defect rates on an assembly line. - Financial analysts assessing the historical volatility of stock prices or investment portfolios. - Students and educators verifying manual statistics homework and visualizing data distribution. ## Frequently asked questions ### What is the difference between sample and population standard deviation? Population standard deviation is used when your dataset includes the entire population, dividing the variance by 'n'. Sample standard deviation is used when your data is just a subset of the population, dividing by 'n-1' to provide an unbiased estimate. ### What are sigma intervals? Sigma intervals (one, two, and three sigma) represent specific ranges around the mean. In a normal distribution, roughly 68%, 95%, and 99.7% of data points fall within the first, second, and third sigma intervals, respectively. ### How should I format my dataset? You can enter raw numbers separated by commas, spaces, or newlines. The calculator will automatically parse the text and extract the numeric values. ### What is the coefficient of variation? The coefficient of variation is the ratio of the standard deviation to the mean. It is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different. ### Can I adjust the precision of the results? Yes, you can use the Decimal Places setting to round the calculated statistics to your preferred level of precision, supporting up to 10 decimal places. ## Related tools - [Arithmetic Sequence Calculator](https://elysiatools.com/en/tools/arithmetic-sequence-calculator): Calculate the nth term, first terms, and finite sum of an arithmetic sequence - [Bayes Theorem Calculator](https://elysiatools.com/en/tools/bayes-theorem-calculator): Calculate posterior probability P(A given B) using prior, likelihood, and false-positive rate - [Bearing Capacity Calculator (Terzaghi)](https://elysiatools.com/en/tools/bearing-capacity-calculator): Calculate the Terzaghi ultimate bearing capacity of a shallow foundation: q_ult = c·Nc·sc + q·Nq·sq + 0.5·γ·B·Nγ·sγ. 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