Home › Calculators › Standard Deviation Calculator

Standard Deviation Calculator

Averages hide how spread out your data really is. This free standard deviation calculator finds the standard deviation, variance, mean and count for any data set, choosing between the population and the sample formula, so you can measure spread correctly for whatever you are analysing.

Numbers (comma or space separated)

Data type

What is a Standard Deviation Calculator?

A standard deviation calculator measures how spread out a set of numbers is around their mean. A low standard deviation means the values cluster closely together, while a high one means they are scattered widely. Together with the mean and variance, it is one of the most important summary statistics in analysis.

The tool supports both forms. The population standard deviation (σ) divides by the number of values N and is used when your data is the whole group you care about. The sample standard deviation (s) divides by N − 1 and is used when your data is a sample meant to estimate a larger population — the minus one (Bessel’s correction) makes the estimate unbiased.

Analysts, students and anyone working with data use standard deviation to understand consistency, to find outliers, to assess risk and volatility, and to report how reliable an average is. Because the calculations run in your browser, you can throw sensitive or confidential figures in without uploading them anywhere.

How to use the Standard Deviation Calculator

Enter your data set in the input box, separated by commas, spaces or new lines.
Choose whether your data is a full population or a sample.
Click Calculate to run the analysis.
Read the results: count, mean, variance, and the standard deviation are all shown, with the formula displayed.
Clear and enter a new set to compare another data set.

Example

Data set: 2, 4, 4, 4, 5, 5, 7, 9

Count = 8, Mean = 5, Variance = 4.

Population standard deviation σ = 2.0.

Sample standard deviation s = ≈ 2.14.

Who is this standard deviation calculator for?

Standard deviation is the language of variability, and it shows up in coursework, finance, quality control and everyday analysis. This calculator helps students, couples, professionals and retirees make sense of how spread out a data set is.

Students and young adults: Statistics assignments, lab reports and exam prep all depend on standard deviation. Students enter any data set and instantly see the mean, variance and the sample or population deviation with the right formula applied.
Couples: Comparing prices, budgets, or how much your monthly spending varies is a real-life use of spread. A couple can enter a list of monthly bills or grocery costs and see how consistent — or erratic — their expenses really are.
Salaried professionals: Analysts and managers use standard deviation to measure risk and variability in sales, quality, or performance data. Enter a data set to spot outliers and gauge how reliable an average really is.
Retirees: Tracking the ups and downs of an investment or a budget is easier with a number for volatility. Retirees enter a series of returns or prices to understand how much a value swings over time before they decide anything.

Standard deviation table — a worked data set

This table walks through the sample default 12, 15, 18, 20, 24, 30, 35, showing each value's distance from the mean and the squared deviation used to compute variance and standard deviation.

Value	Deviation (value − 22)	Squared deviation
12	−10	100
15	−7	49
18	−4	16
20	−2	4
24	+2	4
30	+8	64
35	+13	169

With n = 7 and a mean of 22, the squared deviations add to 406. Population variance = 406 ÷ 7 = 58, giving σ ≈ 7.62; sample variance = 406 ÷ 6 = 67.67, giving s ≈ 8.23.

Common use cases

Measuring the consistency of test scores survey responses or repeated measurements.
Assessing volatility and risk in finance, like how much returns vary.
Finding outliers and understanding how tightly a process performs.
Completing statistics problems and reports for study or work.

Pro tips

Use the sample formula whenever your data is part of a larger group — it gives an unbiased estimate of the population.
The standard deviation shares the units of your data, while the variance is in squared units, so report the standard deviation for real-world interpretation.
Range and mean alone miss patterns; a combined look at mean plus standard deviation tells you far more about a data set.
A spike in standard deviation often signals an outlier, so check the values on either side of the mean when it rises suddenly.

FAQ

What is standard deviation?

Standard deviation is a measure of how spread out a set of values is around the mean. A lower value means the data is tightly clustered; a higher value means it is scattered.

What is the difference between the sample and population formulas?

The population formula divides by the number of values N, while the sample formula divides by N − 1. Use the sample version when your data is a sample meant to estimate a larger population.

What is variance?

Variance is the average of the squared differences from the mean. Standard deviation is simply the square root of variance.

What does a high standard deviation mean?

It means the values are widely spread around the average, so the data is less consistent and more variable.

How do I enter my data?

Type the numbers separated by commas, spaces or line breaks — the parser splits them automatically.

Why do I get a different answer for sample versus population?

Because the sample calculation applies Bessel’s correction (dividing by N − 1) to avoid underestimating the spread of a larger population.

Is it private and free?

Yes. It runs entirely in your browser, so your data is never uploaded, and it is completely free.

What units is standard deviation expressed in?

The same units as your data. If your values are in dollars, the standard deviation is in dollars too.