# Variance Calculator Calculate sample variance, population variance, and optional standard deviation for a numeric dataset > Canonical page: https://elysiatools.com/en/tools/variance-calculator - **Category:** Math & Numbers - **Keywords:** variance, sample variance, population variance, statistics, standard deviation, spread ## Overview Calculate variance for a numeric dataset. Population variance divides by n: sigma^2 = sum((x - mu)^2) / n Sample variance divides by n - 1: s^2 = sum((x - xbar)^2) / (n - 1) Use it to measure spread in measurements, scores, experiments, quality data, and descriptive statistics. ## Inputs - **Dataset** (textarea): e.g. 2, 4, 4, 4, 5, 5, 7, 9 - **Variance Type** (select) - **Decimal Places** (number) - **Include Standard Deviation** (checkbox) ## When to use - Analyzing the spread or dispersion of data points in statistical research and academic studies. - Evaluating quality control metrics to ensure manufacturing processes remain within acceptable limits. - Comparing the volatility of different financial assets or investment portfolios based on historical returns. ## How it works - Enter your numeric dataset into the text area, separating values with commas, spaces, or newlines. - Select whether you want to calculate the sample variance, population variance, or both. - Choose the number of decimal places for your results and toggle the standard deviation option if needed. - The tool instantly computes the variance using standard statistical formulas and outputs the results in a structured format. ## Use cases - Academic researchers calculating descriptive statistics for experimental data. - Financial analysts measuring the historical volatility of stock prices. - Quality assurance engineers tracking variations in product dimensions. ## Frequently asked questions ### What is the difference between sample and population variance? Population variance divides the sum of squared differences by the total number of data points (n). Sample variance divides by n-1 to provide an unbiased estimator for a larger population. ### Can I calculate standard deviation with this tool? Yes, you can check the 'Include Standard Deviation' option to automatically compute the square root of the variance alongside your results. ### How should I format my input data? You can enter numbers separated by commas, spaces, or newlines. The tool will automatically parse the numeric values from your input. ### How many decimal places can I output? You can configure the output to display anywhere from 0 to 10 decimal places using the decimal places setting. ### Is my data processed securely? Yes, all calculations are performed locally in your browser. 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