Standard Deviation Calculator

About the Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is around their average — a small value means the data clusters tightly around the mean, a large one means it's widely scattered. This calculates it, along with variance and the mean, from any list of numbers. It's a staple for statistics coursework, lab and survey data, quality control, and anyone summarising the variability of a data set.

How it works — the formula

1. Find the mean (average) of the numbers.
2. For each value, take its squared difference from the mean, and add them all up.
3. Variance = that sum divided by n (population) or by n−1 (sample).
4. Standard deviation = the square root of the variance.

It shows both sample standard deviation (dividing by n−1) and population standard deviation (dividing by n), since which one you need depends on your data.

Sample vs population

• Use the population standard deviation (σ, divide by n) when your numbers are the entire group you care about.
• Use the sample standard deviation (s, divide by n−1) when your numbers are a sample drawn from a larger population, and you're estimating the population's spread. The n−1 ("Bessel's correction") compensates for the fact that a sample tends to underestimate the true spread.

Most real-world statistics use the sample version, which is why it's shown as the headline figure.

Assumptions and behaviour

• Numbers can be separated by spaces, commas or new lines; non-numeric text is ignored.
• Sample standard deviation needs at least two values (you can't divide by n−1 = 0 with one number).
• Both sample and population figures are shown so you can pick the right one.
• Results are rounded to six decimals for display.

Limitations

• Choosing sample vs population matters — using the wrong one gives a subtly wrong answer, especially for small data sets. Match it to whether your numbers are a full population or a sample.
• Standard deviation assumes a meaningful mean; it's sensitive to outliers, which inflate the spread — check for anomalies in skewed data.
• It computes descriptive statistics for the numbers as entered; it doesn't do grouped/frequency data or weighted values.
• Very large data sets are handled in your browser's memory.

Privacy

The calculation runs entirely in your browser. Your data is never uploaded or stored.