What is Pi. Includes formulas, equations, examples.

Pi is the ratio of a circle’s Circumference to its Diameter, i.e., π = C/D = 3.14159...

Most formulas and equations reference the diameter as two times the radius. In other words, D = 2r.

The Symbol for Pi. What Is Pi Used for in Math : 3.14159265...
The Symbol for Pi. What Is Pi Used for in Math : 3.14159265... | Source

What Is and About Pi

If you are looking for the constant, the first few digits are 3.1415926535.

3.14159 or even just 3.14 will do fine for the majority of calculations.

For the first 771 digits of pi, you will find them further down the page.

And at the end of the page is a video, What Is the Sound of Pi.

What is Pi used for in math - The Basics:

Pi is a mathematical constant that we discovered approximately 4000 years ago. If there is something that has anything to do with circles and arcs, we can use pi to figure things out that relate to it.

An example:

The formula for Circumference is C = 2πr.

If we know the radius of a circle (half the diameter), we can figure out its circumference by multiplying two times pi times the radius.

So, if the circle has a radius of 5 units, then the circumference would equal 2 x pi x 5 = 10 X 3.14159 = 31.4259 units.

Another example:

The formula for the Area of a circle is A = πr².

We can figure out the area of a circle by multiplying pi times the radius-squared.

If the radius equals 5 units, then the area equals 3.14159 x 25 = approximately 78.54 square units.

Volume formulas:

There are more pi formulas having to do with calculating volume further down the page.

Algebra tutorial:

For a beginner guide to algebra, here is an algebra tutorial.

What Is Pi Used for in Math - Intermediate:

Pi is what's called an irrational number. This means that the numbers representing it never repeat and never end. It can only be approximately represented as a fraction. Pi is not just restricted to that which has to do with geometry and trigonometry. Pi also plays a major role in calculus and integrals.

What Is Pi Used for in Math - Advanced:

Pi is not just restricted to the concept of pure mathematics. The constant of pi shows up everywhere in our universe and in almost every branch of physics.

Pi can also show up when least expected. As an example, if you multiply the straight-line distance of the start-end-points of a river by pi, you will get the the approximate meandering distance that the water traveled to get there. Thus, if the straight-line distance of a river is 1000 miles, the water actually traveled approximately 3,142 miles to accomplish that trip.

Pi - Metaphysical:

Whenever the disciplines of chaos theory, random numbers, or metaphysics comes into play; pi invariably shows up. Almost as if pi is the true key to everything. Some theorize that pi is a look into the mind of the creator of the universe.

What and When is Pi Day?

Born March 14, 1879. He was awarded the Nobel Prize in Physics in 1921. Albert Einstein was a United States citizen from 1940 to 1955.
Born March 14, 1879. He was awarded the Nobel Prize in Physics in 1921. Albert Einstein was a United States citizen from 1940 to 1955. | Source

Pi Day is the day that celebrates the mathematical constant of pi. It is on March 14th of each year. What with March being a 3 and the day being 14; we have 3.14, the first three digits of pi.

March 14 also happens to be Albert Einstein's birthday.

How to celebrate Pi Day? Eating pie of course. And doing a bunch of other stuff.

If you work at a tech company, there could very well be an office pie/pi/pie party.

At colleges and universities, various forms of rowdiness might also be included in the celebrations.

Pi Day can also be used to celebrate mathematics in grade schools, middle schools, and high schools. It all depends on how inspired the teachers and parents are to make it happen.

All in all, Pi Day is a day to have fun.

And with any luck, you might even get some pie.

Pi Approximation Day

If Pi Day did not fulfill all your pi needs, then there is Pi Approximation Day. This occurs on July 22. The 22nd day of the 7th month gives you 22/7, the fractional approximation of pi. What with it being an approximation, it is not celebrated as much as Pi Day. However, if you look hard enough, there will be people celebrating it. Or initiate something yourself; wise people have no problem coming up with an excuse to have fun.

Pi in Decimal and Hexadecimal

Pi in Decimal, Base 10

Here's the first 771 digits, so as to encompass the Feynman Point of 999999.

Base 10:


1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837

Pi in Hexadecimal, Base 16

Pi – Here's the first 501 digits in Hexadecimal.

Base 16:


243F6A8885 A308D31319 8A2E037073 44A4093822 299F31D008 2EFA98EC4E
6C89452821 E638D01377 BE5466CF34 E90C6CC0AC 29B7C97C50 DD3F84D5B5
B547091792 16D5D98979 FB1BD1310B A698DFB5AC 2FFD72DBD0 1ADFB7B8E1
AFED6A267E 96BA7C9045 F12C7F9924 A19947B391 6CF70801F2 E2858EFC16
636920D871 574E69A458 FEA3F4933D 7E0D95748F 728EB65871 8BCD588215
4AEE7B54A4 1DC25A59B5 9C30D5392A F26013C5D1 B023286085 F0CA417918
B8DB38EF8E 79DCB0603A 180E6C9E0E 8BB01E8A3E D71577C1BD 314B2778AF
2FDA55605C 60E65525F3 AA55AB9457 48986263E8 144055CA39 6A2AAB10B6
B4CC5C3411 41E8CEA154

Basic Pi and some non Pi Volume Formulas

Four volume formulas.
Four volume formulas. | Source

And four slightly more advanced pi formulas.

Four pi formulas
Four pi formulas | Source


What Is the Sound of Pi

Last, but not least. Here is a video, The Sound of Pi. Becomes quite mesmerizing after awhile. Kind of spooky.

May all your pi days be prosperous ones.

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Comments 7 comments

Katharella profile image

Katharella 4 years ago from Lost in America

I love the movie Pi! While I'm bad at math I can still always come up with a reason people and things are linked by 8. Which, as I'm sure you know is on it's side represents infinity. I see 8's in everything.

CWanamaker profile image

CWanamaker 4 years ago from Arizona

Hmm, I have never seen the binary and hexadecimal forms of Pi before...pretty neat!

logic,commonsense 4 years ago

Sounds like Pi in the sky to me! :)

Bedbugabscond profile image

Bedbugabscond 4 years ago from United States

My sister takes my kids and hers on Pi day. They make lots and lots of pies and then measure pi of every one! Pi day is a wonderful day to teach the kids a little math in a fun way. Voted up for mentioning pi day!

Glenn Stok profile image

Glenn Stok 4 years ago from Long Island, NY

You brought back a lot of memories for me with this hub. I used Pi so often in my college days that I never forgot it to the ninth place. 3.14159265 and even that isn't accurate because, like you say, it's an irrational number.

I wish they taught things in college when I was in my 20s the way you teach.  I never knew the things you mentioned and you make Pi all that much more meaningful.  I'll never forget Einstein's birthday now. And to calculate the meandering of water in a river is awesome. It makes me start wondering if Pi  might have some association with the laws of gravity?  So much to think about!

I never knew about Pi Approximation Day. I'll have to examine that a little more, but it looks like I missed it by one day since today is July 23.

Katharella profile image

Katharella 4 years ago from Lost in America

We have the Gregorian calendar as we all know, and some (not me) believe that the Mayans have the true calendar of the world. But if it's true that our calendar will be off the equinox in about 10,000 years, and the Mayan calendar ends 12.23.12 then I think there should be made a Pi calendar. After all the world is round, and there's no proof of it ever ending.

mariexotoni profile image

mariexotoni 2 years ago

Wow- blew my mind with that river example!

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