We are independent & ad-supported. We may earn a commission for purchases made through our links.
Advertiser Disclosure
Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.
How We Make Money
We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently of our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.

What Is Sigma Notation?

By Richard Nelson
Updated May 21, 2024
Our promise to you
All The Science is dedicated to creating trustworthy, high-quality content that always prioritizes transparency, integrity, and inclusivity above all else. Our ensure that our content creation and review process includes rigorous fact-checking, evidence-based, and continual updates to ensure accuracy and reliability.

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

Editorial Standards

At All The Science, we are committed to creating content that you can trust. Our editorial process is designed to ensure that every piece of content we publish is accurate, reliable, and informative.

Our team of experienced writers and editors follows a strict set of guidelines to ensure the highest quality content. We conduct thorough research, fact-check all information, and rely on credible sources to back up our claims. Our content is reviewed by subject-matter experts to ensure accuracy and clarity.

We believe in transparency and maintain editorial independence from our advertisers. Our team does not receive direct compensation from advertisers, allowing us to create unbiased content that prioritizes your interests.

The concept of sigma notation means to sum up all terms and uses three parts to form math statements, like i ai. The Greek letter is the summation operator and means the sum of all, i is called the index number, and ai refers to a series of terms to be added together. This mathematical notation is used to compactly write down the equations in which summing all terms is required. It can be used, for example, to show the addition of all employees’ hours at a company. If ai is the hours worked by a certain employee and there are n employees, then i ai means to add a1+a2+a3+a4…an .

Understanding the associative, distribution and commutative properties allows for more uses of these mathematics. The associative and commutative properties will allow any number to be multiplied by all terms of the summation. Instead of performing the multiplication for each term, it can be done once at the end with the sum of all terms. If every employee earned k per hour, the notation is written compactly as k i ai. The distribution property changes the sum of two series of numbers into two sigma notation formulas.

Sigma notation, often referred to as summation notation, can be used in many common situations. For example, it can be used to calculate the sum of deposits for a bank account. Banks add together all deposits and withdrawals to determine the current balance. A grocery receipt shows all the items to be added and subtracted to calculate a checkout total. All of these examples can be written in a short formula.

There are many complex examples of the use of the notation as well. Many college students need sigma notation to make equations to solve difficult problems. Computer programmers use sigma notation for finance, business and gaming software. Scientists use it often in statistical analysis of their experiments.

The history of sigma notation was changed by Carl Friedrich Gauss in the late 18th century. He was asked to calculate the sum of the first 100 integers. He returned moments later with the correct answer, 5050. He realized a new theorem, that i ai is the same as adding the first and last numbers, such as 100+1 then 99+2, which always gives the same answer, 50 times over. He was a young child when he discovered this theorem and went on to become a renowned mathematician.

All The Science is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Discussion Comments
By TanGoddess — On Oct 29, 2014

I had to do a paper on Carl Friedrich Gauss some time ago. Despite his mind for math, he was an interesting character. You want to imagine a Sheldon Cooper type of guy when thinking of a mathematician and he was, at least to some degree. He was a young genius, a perfectionist and a school kid who could misbehave and produce correct arithmetic answers within seconds. I’m sure his instructors loved him!One famous Gauss story is the one where he was interrupted in midsts of a problem to be told his wife was dying. Supposedly he replied,"Tell her to wait a moment till I'm done.” No doubt the guy loved his math!

All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.

All The Science, in your inbox

Our latest articles, guides, and more, delivered daily.