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Standard Deviation Calculator

Find the standard deviation of a dataset in seconds. Enter your numbers to get the mean, population and sample standard deviation, plus variance — free, no sign-up.

About this tool

Standard deviation tells you how spread out a set of numbers is around their average. Two classes can both average 70 marks, yet feel completely different — one tightly grouped, the other all over the place. The standard deviation is the number that captures that difference.

Our free calculator takes any list of numbers and instantly returns the mean, the population and sample standard deviations, and the variance. Students, researchers, analysts and the simply curious all use it the same way: paste, calculate, done.

How to use

Paste or type your numbers into the box, separated by commas, spaces or line breaks — any mix works, and you need at least two values. Press Calculate SD to see the count, mean, both standard deviations and the variance.

Read the population figure when your numbers are the entire dataset (every exam score in the class). Read the sample figure when they are a sample drawn from something bigger (a survey of 200 voters). For large datasets the two are nearly identical.

The math behind it

The math: first find the mean, then measure how far each value sits from it. Square those distances (so negatives cannot cancel out), average them, and take the square root to return to the original units. That average of squared distances is the variance; its square root is the standard deviation.

Population SD divides by N (the whole group). Sample SD divides by N−1, a small correction called Bessel’s correction that removes the bias of estimating from a sample. Example: 2, 4, 4, 4, 5, 5, 7, 9 has mean 5, population SD exactly 2.00 and sample SD about 2.14.

Frequently asked questions

What is standard deviation in simple terms?
It measures how spread out numbers are around the average. A low standard deviation means values cluster tightly near the mean; a high one means they scatter widely. Two datasets can share the same average yet tell very different stories — the standard deviation is what reveals the difference.
What is the difference between population and sample standard deviation?
Population SD describes an entire group and divides by N — use it when your numbers are the complete dataset, like every sale your shop made this year. Sample SD divides by N−1 to correct the bias of estimating from a part of the group, like a poll of 500 voters. With big datasets the two answers barely differ.
Can standard deviation be negative?
No. It is always zero or positive, because it is built from squared differences and squares are never negative. A standard deviation of zero simply means every value equals the mean — there is no spread at all.
What is a good standard deviation?
There is no universal good value; it depends on what you measure. In manufacturing a tiny SD means consistent quality, while in exam scores a moderate SD is perfectly normal. Always compare it to the mean: an SD of 2 is small next to a mean of 100, but huge next to a mean of 5.
Why do we square the differences instead of just averaging them?
Plain differences cancel out — by definition, distances above and below the mean always sum to zero. Squaring makes every distance positive and gives extra weight to outliers, which are usually what you want to notice. The final square root converts the result back into the original units.

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