Standard Deviation Calculator

Calculate population and sample standard deviation, mean, variance, and full summary statistics for any data set. See the step-by-step math breakdown.

Separate values with commas, spaces, or new lines.

Enter Numbers to Get Started

Type or paste your data set above, then hit Calculate.

Measure Data Spread with Precision

Enter your data set and instantly calculate population or sample standard deviation, mean, variance, and more. Every step of the math is shown so you can verify or learn the process.

Population · Sample · Variance

Why Use This Calculator?

Population & Sample Modes

Switch between population (σ) and sample (s) standard deviation depending on whether your data covers the full group or a subset.

Step-by-Step Breakdown

See every deviation and squared deviation in a table so you can follow the formula and double-check the result against your own work.

Full Summary Statistics

Get mean, variance, sum, count, min, max, and range alongside standard deviation — everything you need in one place.

Privacy-First Processing

All calculations run inside your browser. Your data is never uploaded, stored, or shared with any server.

How this Standard Deviation Calculator works

This calculator computes both the population and sample standard deviation of any numeric data set directly in your browser. Standard deviation measures how spread out numbers are from their average value. A low standard deviation means most of the numbers are close to the average, while a high standard deviation indicates that the numbers are spread out over a wider range.

You can paste a comma-separated list of values, or enter one number per line. The tool parses the data and immediately calculates the mean (average). For each number, it finds the difference from that mean and squares the result to remove negative values. The sum of these squared differences is divided by the total count (for population) or the total count minus one (for sample) to find the variance. Taking the square root of that variance gives the standard deviation.

A step-by-step breakdown table displays every intermediate calculation — the individual values, their deviation from the mean, and the squared deviation. This transparency is crucial for students verifying their manual math homework or professionals wanting to understand exactly how the summary statistics were derived.

How to use this Standard Deviation Calculator

1

Enter your data

Type or paste a list of numbers separated by commas, spaces, or new lines into the input box.

2

Choose the type

Select population (σ) if your data covers the full group, or sample (s) if it represents a subset.

3

View the results

Hit Calculate to see standard deviation, mean, variance, and a step-by-step breakdown of every computation.

Example Usage

Calculating standard deviation for a set of 8 numbers:

Input
4, 8, 6, 5, 3, 7, 9, 2
Output
Mean: 5.5 Population SD (σ): 2.2913 Sample SD (s): 2.4495 Variance (σ²): 5.25 Count: 8 | Range: 7

Frequently Asked Questions

What is standard deviation?
Standard deviation is a measure of how spread out values are from the mean (average) of a data set. A low standard deviation means values are clustered close to the mean, while a high one means they are spread over a wider range.
What is the difference between population and sample standard deviation?
Population standard deviation (σ) divides the sum of squared deviations by N (the total count). Sample standard deviation (s) divides by N−1, which corrects for the bias that occurs when you estimate from a subset rather than the full group. Use population when you have every data point; use sample when you have a representative subset.
How many numbers do I need to calculate standard deviation?
You need at least two numbers. With a single data point, there is no spread to measure, so standard deviation is undefined.
Can I enter negative numbers or decimals?
Yes. The calculator accepts positive numbers, negative numbers, and decimals in any combination. Just separate each value with a comma, space, or new line.
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 simply the square root of the variance. Variance uses squared units, while standard deviation returns to the original unit of measurement, which makes it easier to interpret.
Is my data sent to any server?
No. All calculations run locally inside your browser using JavaScript. Nothing you type or paste ever leaves your device.
What formula does this calculator use?
For population SD: σ = √(Σ(xᵢ − μ)² / N). For sample SD: s = √(Σ(xᵢ − x̄)² / (N − 1)). The step-by-step breakdown table shows every term so you can follow along.
Can I use this for school or university assignments?
Yes, the calculator is a helpful study tool. The step-by-step breakdown shows each deviation and squared deviation, which mirrors the manual process your instructor expects. Always understand the math before relying on the tool for graded work.
What does a high standard deviation indicate?
A high standard deviation means data points are widely spread from the mean. In practical terms, it suggests high variability — for example, test scores with a high standard deviation show a wide gap between the highest and lowest performers.
How do I interpret standard deviation in real life?
In a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three. This is the 68-95-99.7 rule used in quality control, finance, grading curves, and scientific research.

Related Tools

Try It

Scientific Calculator

Run trigonometry, logarithm, power, and root calculations in your browser.

Try It

Algebra Calculator

Solve linear and quadratic equations, simplify expressions, and work through systems of equations with the steps shown.

Try It

Percentage Calculator

Work out what percent of a number, what percent one number is of another, percentage increase and decrease, and discounts or markups. Five calculators on one page.

Try It

Percentage Change Calculator

Find the percentage increase or decrease between two numbers, work back to the original value, and check percentage difference or percent error.

Try It

Credit Card Calculator

Calculate credit card payoff time.

Try It

Age Calculator

Calculate exact age in years, months, days.

The Standard Deviation Calculator is maintained by CodeItBro. We aim to provide the best free developer tools on the web. If you have feedback or suggestions, please visit our contact page.

Comments

Questions, corrections, and useful tips are welcome. Comments are reviewed before publication.

Loading comments...

Comments are stored and moderated using Cusdis Cloud. Email is optional. Privacy Policy

As featured on

CodeItBro - Free dev tools + practical guides to help you ship faster | Product HuntCodeItBro - Free Online Developer Tools badgeCodeItBro badge