Math the king of the sciences , without math our lives couldn't be like we know them .

Without math the school wouldn't have that thrill you like , you like math don't you .

Yet, math is a dare that everybody should acomplish ,even if we don't want to .

In this Instructable i will tell you the 2 most common methods to obtain the area of any circle .

Step 1: Before We Start....

You'll need a small number of implements to determine the area of a circle :

First you need to know the basic value of pi

By basic I mean the first 5 digits , it won't deliver a result as perfect when we compare to the trillion of numbers that really is .

Here's a small paragraph about the numerical value of pi (Thx a lot wikipedia!)
The numerical value of pi truncated to 50 decimal places is:[11]

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
See the links below and those at sequence A000796 in OEIS for more digits.

While the value of pi has been computed to more than a trillion (1012) digits,[12] elementary applications, such as calculating the circumference of a circle, will rarely require more than a dozen decimal places. For example, a value truncated to 11 decimal places is accurate enough to calculate the circumference of the earth with a precision of a millimeter, and one truncated to 39 decimal places is sufficient to compute the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom.

Because pi is an irrational number, its decimal expansion never ends and does not repeat. This infinite sequence of digits has fascinated mathematicians and laymen alike, and much effort over the last few centuries has been put into computing more digits and investigating the number's properties.[15] Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of pi, no simple pattern in the digits has ever been found.[16] Digits of pi are available on many web pages, and there is software for calculating pi to billions of digits on any personal computer.

Original Article here

Don't worry we will be using a truncated 5 digit value : 3.1416
We'll get a (mostly) accurate number with this value

Step 2: ...Something Else...

And you'll need three more things .

something to measure your circle (ie. Ruler , measuring tape ...)
A writing instrument and a writing surface (ie. a good pencil and a notebook)
A calculator or really good mind

Step 3: Formulae

Basically you can obtain the area knowing one measurement of the circle The Radius

The Radius is the measure from the center of the circle to any part of the circunference , see image below

Step 4: REMEMBER THIS !

I've failed several exams by forgetting to add the exponent to the result , Always remember
It's Area !

Step 5: Assuming You Know the Diameter...

Before anything , you may need to measure the circle's length from side to side , from edge to edge , This measure is called Diameter and is two time the radius (r *2 not r²!)

Here is an example , You have a small wheel , it measures from side to side 16 centimeters , you need to know the area so you can determine how much material you need for making 3 more .

So it goes like this :
Diameter is equal two times the radius
16 cm is the diameter , 16 equals to two times the radius
16 over 2 equals to the radius
16 over two is 8
the radius is 8

Area= is pi by radius squared
Area = 3.1416 by 8 squared
8 squared (The Calc may come in handy here) is 64
So, The area is 3.1416 by 64 ( use the Calc here)
the Area is 201.0624 square cm

It was easy ain't it ?

Step 6: Assuming You Know the Radius ...

If you can obtain the Radius ( measure from the center to any point of the circunference ) , It's better !

The Formula is easy A=pi*R²

Now , Your mom told you to build her a knitting loom of 10 cms , as you know 5 is the half of 10 , so , you need to determine how much wood you need to make her what she wants.

So , you do this :
the Area is pi by radius by radius
So , is 3.1416 by 5 by 5
5 by 5 is 25 (Yep , use the calc here)
So the area is 25 by 3.1416
The Area is 78.54 cm²
Now you can go to buy 80 cm worth of wood !

Don't forget to write that the result is square ( add the exponent)