Standard Deviation Calculator

Last updated: June 15, 2026

Sample & population standard deviation.

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The Standard Deviation Calculator turns a list of numbers into instant statistics: paste values separated by commas, spaces or line breaks and it returns both the sample standard deviation (s) and population standard deviation (σ), plus the mean, count and variance. Everything runs locally in your browser, so it is free, needs no sign-up, and your data never leaves your device. Results show to four decimal places.

How to use Standard Deviation Calculator

Standard deviation measures how spread out your numbers are around their average. This calculator does the arithmetic for you in real time, so there is no formula to type and no spreadsheet to set up. Just enter your dataset in the box and the sample and population figures update with every keystroke, alongside the mean and count that explain them.

Read the full guide: How to Calculate Standard Deviation (Sample vs Population)

  1. 1Type or paste your numbers into the box, separating them with commas, spaces or new lines (for example 10, 12, 23, 16).
  2. 2Read the sample std dev (s) if your data is a subset, or the population std dev (σ) if it covers the whole group.
  3. 3Check the mean, count and sample variance shown below to confirm the calculator read every value you intended.
  4. 4Edit, add or remove numbers and watch all five results recalculate instantly to four decimal places.

Sample and population at once

It returns both s (dividing by n−1) and σ (dividing by n) side by side, so you never have to guess which divisor your assignment or report expects.

Flexible number input

Commas, spaces and line breaks all work as separators, so you can paste a spreadsheet column or a messy list without reformatting it first.

Shows the working values

Seeing the mean, count and variance next to the answer lets you sanity-check that no stray text or duplicate was silently dropped from your dataset.

Check homework statistics answers

Students working through a stats assignment can paste their dataset to confirm the mean, variance and standard deviation they calculated by hand. Because the tool reports both the n and n−1 versions, you can match whichever your textbook or instructor specifies and see the four-decimal value to spot rounding slips in your own working.

Measure spread in lab measurements

Researchers and science students often repeat a measurement several times and need the standard deviation to express precision or error bars. Enter the repeated readings to get the sample standard deviation instantly, which quantifies how tightly your trials cluster around their average without opening spreadsheet software.

Analyse test scores or grades

Teachers can paste a column of class scores to see how widely results vary around the mean. A small population standard deviation signals that students performed consistently, while a large one flags a wide gap between high and low achievers, helping you judge whether an exam was fair or too hard.

Assess investment return volatility

Standard deviation is a common proxy for risk in finance. Paste a series of periodic returns to gauge how much they swing from the average return. A higher sample standard deviation indicates a more volatile, less predictable asset, letting you compare two holdings on consistency before committing capital.

Standard Deviation Calculator — frequently asked questions

What is the difference between sample and population standard deviation?

Population standard deviation (σ) divides the summed squared deviations by n and applies when your numbers represent the entire group. Sample standard deviation (s) divides by n−1 (Bessel's correction) and is used when your numbers are a sample drawn from a larger population, giving a less biased estimate.

What formula does this calculator use?

It finds the mean, sums the squared difference of each value from that mean, then divides by n for population variance or n−1 for sample variance. The standard deviation is the square root of each variance. For 10,12,23,23,16,23,21,16 the mean is 18, σ is 4.8990 and s is 5.2372.

Why does the sample standard deviation show a dash?

Sample standard deviation and sample variance need at least two values because they divide by n−1, which is zero when only one number is entered. Add a second number and both fields populate; the population figures appear as soon as there is one value.

Are my numbers uploaded anywhere?

No. The entire calculation runs in JavaScript inside your own browser tab. Nothing is sent to a server, stored, or logged, so you can safely paste sensitive financial, lab or grade data.

Does it matter what units my data is in?

Standard deviation carries the same units as your input, so seconds give seconds and dollars give dollars. The calculator treats every value as a plain number and ignores units, currency symbols or text, which it filters out before computing.

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