StatisticsFree

Standard Deviation Calculator

Use this free online standard deviation calculator to find the standard deviation and variance of any dataset. Enter your numbers to measure how spread out your data is.

Standard Deviation

Add numbers to measure data spread

Add at least one number to see results.

AI Assistant

Ask about this calculator

I can help you understand the standard deviation calculator formula, interpret your results, and answer follow-up questions.

Try asking

Formula

Core Formula

\sigma = \sqrt{\frac{\sum (x_i - \bar{x})^2}{N}}

How it works: Find the mean, calculate the squared difference of each value from the mean, average those squared differences, and take the square root.

Review and Methodology

Updated Mar 17, 2026

This calculator runs locally in your browser. Inputs are converted into the units required by the formula, and the result is paired with supporting references so you can verify the method before using it for planning or estimates.

Worked Example

Dataset: 2, 4, 4, 4, 5, 5, 7, 9

1Step 1: Mean = 40/8 = 5

2Step 2: Squared differences: 9, 1, 1, 1, 0, 0, 4, 16

3Step 3: Variance = 32/8 = 4

4Step 4: SD = sqrt(4) = 2

Result: Standard Deviation = 2

What Is Standard Deviation?

Standard deviation is a measure of how spread out the values in a dataset are from the mean. A low standard deviation means data points are clustered close to the mean, while a high standard deviation means data is spread over a wider range of values.

A standard deviation of 0 means all values are identical
About 68% of data falls within one standard deviation of the mean (in normal distributions)
About 95% falls within two standard deviations, and 99.7% within three (the 68-95-99.7 rule)
Variance is the square of the standard deviation and is useful for statistical calculations

Standard deviation is essential in finance (measuring investment risk), quality control (manufacturing tolerances), science (experimental precision), education (grading curves), and any field that needs to quantify variability or consistency.

You can also calculate changes using our Average Calculator or Mean Median Mode Calculator.

Frequently Asked Questions

What does standard deviation tell you?

It measures the spread or dispersion of data points from the mean. A low SD means data is clustered near the mean (consistent). A high SD means data is spread out (variable).

What is the difference between population and sample SD?

Population SD divides by N (the total count). Sample SD divides by N-1 (Bessel's correction) to provide an unbiased estimate of the population SD when working with a sample.

What is variance?

Variance is the square of the standard deviation. It represents the average of the squared differences from the mean. While harder to interpret directly (since its units are squared), it is useful in many statistical formulas.

What is the 68-95-99.7 rule?

In a normal (bell-shaped) distribution, approximately 68% of values fall within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. This is also called the empirical rule.

How is standard deviation used in finance?

In finance, standard deviation measures investment volatility (risk). A stock with a high SD has unpredictable returns. Portfolio managers use SD to balance risk and return across investments.

How do I add this Standard Deviation Calculator to my site?

Absolutely. Use the "Embed" option above to tailor the dimensions, color scheme, and styling to match your site. Copy the generated iframe snippet and drop it into your HTML, WordPress editor, or any CMS. There is no cost and no account required. See calculory.com/services/embed-calculators for a step-by-step walkthrough.

AI Assistant

Ask about this calculator

I can help you understand the standard deviation calculator formula, interpret your results, and answer follow-up questions.

Try asking

Related Calculators

Average Calculator Mean Median Mode Calculator

More Statistics Calculators

View all

Average Calculator

Calculate the arithmetic mean of numbers.

Mean Median Mode Calculator

Find mean, median, and mode of a dataset.

Standard Error Calculator

SEM from standard deviation and sample size with confidence ranges.

Confidence Interval Calculator

Calculate confidence intervals with adjustable levels.

All articles

$Best Math Training Apps in 2026: 12 Picks for Students, Adults, and Speed Enthusiasts$

Maths9 min

Best Math Training Apps in 2026: 12 Picks for Students, Adults, and Speed Enthusiasts

We tested 12 math training apps across four categories: academic support, logical reasoning, mental math speed, and gamified learning. See which apps actually improve your skills in 2026.

Read article

$Guide to Interactive Math Games for Kids and Classrooms 2026$

Maths5 min

Guide to Interactive Math Games for Kids and Classrooms 2026

Interactive math games in 2026 blend adaptive online platforms with low-prep classroom activities. Use this guide to pick the best game format by age, goal, and time.

Read article

Regional9 min

Seattle Sales Tax vs NYC, Chicago, LA, and SF: 2026 Guide

Seattle's sales tax is 10.25% in 2026, tied with Chicago and LA for the highest of any major US city. See how it stacks up against NYC, SF, Houston, and Portland.

Read article

Business5 min

Agentic ROI Blueprint: Replacing Roles in 2026

In 2026, teams are measuring total capability, not just headcount. Learn how to model the cost of replacing or augmenting full-time roles with an AI agent stack.

Read article