📈 Standard Deviation Calculator
Paste your data set to get the standard deviation and variance for both the sample and the population, plus the mean — a clear read on how tightly your numbers cluster.
📈 Measure the Spread
What is a Standard Deviation Calculator?
It quantifies how far the values in a data set typically fall from their mean. A small standard deviation means the data hugs the average; a large one means it scatters widely. This tool reports both the population form (dividing by n) and the sample form (dividing by n − 1), along with the corresponding variances, so you can pick the right one for your context.
Reach for it whenever you need to describe consistency or risk — the repeatability of sensor readings, the volatility of a metric, or the variability of test scores. Standard deviation is the backbone of z-scores, confidence intervals, and control charts, so getting it right sets up the rest of your analysis.
❓ Frequently Asked Questions
What is the difference between population and sample standard deviation?
Population standard deviation divides the sum of squared deviations by n (the full count) and is used when your data is the entire population. Sample standard deviation divides by n − 1 (Bessel's correction) and is used when your data is a sample drawn from a larger group — it corrects the tendency of a sample to underestimate the true spread.
What is variance, and how does it relate to standard deviation?
Variance is the average of the squared deviations from the mean; standard deviation is its square root. Variance is in squared units, which is hard to interpret, so standard deviation is usually reported because it is in the same units as your data.
Why square the deviations instead of just averaging them?
The plain deviations from the mean always sum to zero, so they cancel out. Squaring makes every deviation positive and penalises larger departures more heavily, giving a stable, differentiable measure of spread that underpins much of inferential statistics.
What does a large standard deviation tell me?
A larger standard deviation means the values are more spread out around the mean; a smaller one means they cluster tightly. Because it shares the units of your data, you can read it directly — for exam scores measured in points, a standard deviation of 12 points is a wide spread, while 2 points is narrow.