Standard Deviation Calculator
Data Variance Analysis
The variance is the average of the squared differences from the Mean. The standard deviation is the square root of the variance.
s = √( Σ(xi - x̄)² / (n - 1) )How to Use the Standard Deviation Calculator
Using our online Standard Deviation Calculator is the fastest way to understand the variance and dispersion within your dataset. Whether you are analyzing student test scores, financial returns, or scientific data, this tool handles the complex math instantly.
- Input your data: Type or paste your numbers into the input field, separating each value with a comma (e.g., 4, 8, 15, 16, 23, 42).
- Select your formula: Choose Sample if your data is just a portion of a larger group. Choose Population if your data represents every possible member of the group you are studying.
- Calculate: Click the calculate button. The tool will automatically compute the standard deviation, variance, mean, and item count.
Mathematical Principles: Sample vs. Population
The standard deviation formula changes slightly depending on whether you are working with a population or a sample. This standard deviation calculator accounts for both to ensure absolute accuracy.
Population Standard Deviation (σ)
When you have collected data from every single member of the population, you use the population standard deviation formula. You calculate the mean (μ), subtract the mean from each data point to square the result, sum these squared differences, and divide by the total number of data points (N). Finally, take the square root.
Sample Standard Deviation (s)
When you only have a subset of data (a sample), you use the sample standard deviation formula. This uses Bessel's correction, dividing the sum of squared differences by n - 1 instead of just N. This correction yields a slightly larger, more unbiased estimate of the true population variance.