Variance Calculator
Calculate the population and sample variance of a dataset from summary statistics. Variance measures the average squared deviation from the mean and is fundamental to ANOVA and regression.
This free online variance calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
Sum of all data values.
Sum of each data value squared.
Total count of data points.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Variance Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Variance Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Variance Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Variance Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
- •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
- •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
- •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.
About This Calculator
The Variance Calculator is a free, browser-based calculation tool for engineers, students, and technical professionals. Calculate the population and sample variance of a dataset from summary statistics. Variance measures the average squared deviation from the mean and is fundamental to ANOVA and regression. It implements standard formulas and supports both metric (SI) and imperial unit systems with automatic unit conversion. All calculations are performed instantly in your browser with no data sent to a server. Use this calculator as a quick reference and sanity-check tool during design, analysis, and learning. Always verify results against primary engineering references and applicable standards for any safety-critical application.
About Variance Calculator
The variance calculator computes the average squared deviation from the mean for a dataset. Variance is the fundamental measure of dispersion in statistics and is the basis for standard deviation, ANOVA, regression analysis, and portfolio theory. While standard deviation is often preferred for interpretation because it shares the same units as the data, variance has mathematical properties that make it indispensable: it is additive for independent random variables, it decomposes naturally in analysis of variance, and it is the key parameter in the normal distribution. This calculator provides both population variance and sample variance with Bessel's correction.
The Math Behind It
Formula Reference
Population Variance
sigma^2 = sum((x_i - mu)^2) / N
Variables: sigma^2 = population variance; mu = population mean; N = population size
Sample Variance
s^2 = sum((x_i - x_bar)^2) / (n - 1)
Variables: s^2 = sample variance; x_bar = sample mean; n = sample size
Worked Examples
Example 1: Homework scores
Scores: 80, 85, 90, 95, 100. Calculate sample variance.
The sample variance is 62.5 points squared.
Example 2: Daily temperatures
Temperatures (C): 20, 22, 21, 20, 22. Calculate population variance.
The population variance is 0.8 degrees Celsius squared.
Common Mistakes & Tips
- !Interpreting variance in the original units; variance is in squared units, so take the square root for standard deviation.
- !Using population variance for sample data, which underestimates the true variability.
- !Comparing variances of datasets with different units or scales without standardizing first.
Related Concepts
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
Why is variance in squared units?
Because variance averages the squared deviations from the mean. Squaring ensures all deviations are positive but changes the unit. Take the square root to get standard deviation in the original units.
Can variance be negative?
No. Variance is always non-negative because it is a sum of squared values. A negative result indicates a calculation error.
What is the relationship between variance and standard deviation?
Standard deviation is the square root of variance. Variance is the square of standard deviation. They convey the same information but in different units.