Sigma Symbol, Its Meaning And Uses In Math and Science

As the next part of our article series about the Greek symbols, we are having a detailed look at the sigma symbol today. What does the sigma symbol mean? How is it used in math and science? The answers to all these questions and more are in this detailed post about the sigma symbol, its meaning and uses. 

What is the Sigma Symbol?  

Being the eighteenth letter in the Greek alphabet, Sigma comes right after the letter Rho and is followed by Tau. 

As is the case with most of the other alphabets, even English for that matter, two different symbols are used to represent sigma in uppercase and lowercase respectively. 

  • The symbol for uppercase sigma is Σ
  • The symbol for lowercase sigma is σ
Sigma Symbol, Its Meaning And Uses In Math and Science
Sigma Symbol, The Eighteenth Letter in Greek Alphabet – ©Niakris6 at ShutterStock

The sigma sign has been used in mathematics, chemistry, and other fields of study for a very long time. However, while it is common to see uppercase and lowercase sigma signs in science textbooks and the likes, what many people are completely unaware of is the fact that the sigma sign has a third form as well. 

This relatively unknown sigma sign is called ‘letter-final sigma.’

It can be thought of as another type of lowercase sigma symbol that is only used at the end of a word. 

  • The symbol for letter-final sigma is ς

It is a special letter used to denote the last alphabet in a Greek word, provided that the particular word in consideration does not consist only of capital alphabets. 

For example, consider the word Ὀδυσσεύς which is the Greek representation of the word ‘Odysseus.’ You will notice that the last ‘s’ in Odysseus is denoted by the letter-final sigma (ς) whereas the other two ‘s’ in the middle of Odysseus are represented by the lowercase sigma (σ) sign in the Greek variation. 

This brings us to another interesting fact about the sigma sign, which is that it is usually viewed as the equivalent of the letter ‘s’ in modern English. 

This doesn’t seem so surprising especially when you take into account the shape of the letter ‘s’ and the uppercase sigma symbol. 

Σ looks a lot like ‘S’ written in a rough typeface with sharp lines and an additional horizontal stroke at the bottom. Moreover, the enunciation of both the alphabets also has quite a similar ring to one another.  

In the Greek numerals, also known as Alexandrian numerals (a system of using Greek letters to write different numbers), sigma corresponds to a value of 200. 

Origin of the Sigma Symbol

Some semioticians suggest that the sigma symbol is derived from ‘shin.’

Shin is the twenty-first character in the Phoenician alphabet, sometimes also referred to as the Proto-Canaanite alphabet. In case you are unaware, Phoenician is the oldest known system of alphabets that dates as far back as 1050 BC. It is believed that the ancient civilizations in what constitutes modern day Lebanon, Syria and northern Israel heavily relied on this system of alphabets for communication.

The Phoenician shin looks exactly like the capital letter ‘W’ in the modern English alphabet. Rotate it 90 degrees clockwise and you get the capital version of the sigma symbol.

Uses and Meaning of the Sigma Symbol Throughout History

Historians believe that the word ‘sigma’ comes from the Greek word sig-jo which literally translates to ‘I hiss.’ 

The sigma symbol has been held in high importance since ancient times. In Ancient Greece, the sigma symbol was printed on coins. It was also used in architecture, and was displayed prominently in churches. 

Moreover, the sigma sign has been of decorative value as well. A 6th Century mosaic work in the Byzantine church of St. George in Jordan features the sigma sign on the famous Madaba Map. 

In the modern-day world, the sigma sign is renowned for its use in mathematical formulas. In the field of math, the word ‘sigma’ either means summation or standard deviation. 

This is because the uppercase sigma is used as a summation sign in mathematics, whereas the lowercase sigma refers to the square root of variance, or in simple words, the standard deviation. 

The two sigma symbols have their own distinct formulas. An example of sigma as a summation operator is given below. 

Sigma as a Summation Operator

n=03n=0+1+2+3=6

This is commonly known as the ‘sigma notation.’ In practice, the sigma operator is used in finance and accounting, managing balance sheets and in similar other instances where there is a need to add a series of numbers. 

You will also see the sigma sign as a parameter in various well-known mathematical formulas. For example, it is used in the formula for calculating the Rayleigh distribution and Maxwell distribution. When used in conjunction with certain symbols, sigma can denote other functions such as the divisor function that consists of small sigma with a ‘k’ in the subscript.   

In physics, you will often come across terms like 2-sigma, 5-sigma, and so on. This is a further extension of the use of sigma for representing standard deviation. Sigma with a bigger number as a prefix signifies a relatively lesser deviation from a set value and vice versa. It is a technique used by scientists to measure the fluctuations in a set of data, and identify whether it was caused by a certain factor or was just a random error.

In biology, the lowercase sigma symbol was initially used to demonstrate the total life span of a multicellular unit in the bone marrow. However, its use in this respect is now obsolete.  

How to Type Sigma Symbol in Word

If you are wondering how to type the sigma symbol in a Word document, then the following guide will come in handy.

There are two different ways in which you can insert the sigma symbol in Word.

Method 1 – Insert Symbol

  1. Go the Insert option in the main menu in MS Word.
  2. Click on Symbols. If you cannot find the sigma symbols in the few options shown below, then click on More Symbols. A dialog box will open up.
  3. In the ‘Subset’ bar, select Greek and Coptic from the dropdown menu.
  4. Find the uppercase and lowercase sigma symbols and double click to insert them in the file.
  5. Close the dialog box.

Method 2 – Type Directly

  1. Place the cursor where you want to insert the sigma symbol. 
  2. From the list below, type the symbol code for the appropriate sigma symbol and press Alt+X key without giving any space. The code will automatically turn into the required sigma sign.
    1. For uppercase sigma 🡪 type 03A3
    2. For lowercase sigma 🡪 type 03C3
    3. For letter-final sigma 🡪 type 03C2

Did you like our post on the sigma symbol and its meaning? Then, you might want to check out the comprehensive piece we did on Greek alphabet as well as other Greek symbols. Please, kindly use the search box at the bottom (for mobile users) or on the sidebar (for desktop users)