Home > Geometry > Area And Circumference of a Circle : pi

## Area And Circumference of a Circle : pi

March 2nd, 2008

This is a basic guide to using pi to find the area and circumference of a circle using pi. And also explores why pi makes our formulae work.

area =πr2

circumference = 2πr or πd

where r = radius and d=diameter

Area

First lets look at the area of a circle, given by area =πr2. This is simple enough to use, we multiply the radius by itself and then by pi.
Does this make sense?
Well r squared is at least going to be an area but it might be a bit small so we multiply by pi. However this doesn’t explain much until we consider what pi is, the easiest way i find to do this is as follows
If we imagine a square that the circle fits inside perfectly(so it touches all four sides like the one above) r squared would give us one quadrant, so the area of that square is 4 x r2 . Of course the circle’s area is a bit smaller so we need to find the ratio between the areas of the square and circle. If we then times this value by four we have a magic constant to multiply r squared by to find the area of a circle (we times by four because we need the area of 4 quadrants and r squared gives us one).
Now this magic constant is pi (which makes sense being just over 3, meaning the area of the circle is just over 3/4 of the area of the square).
Circumference
The circumference of a circle is given by 2πr or πd. This seems simple, we just multiply the diameter (2r) by our magic constant pi.
Does this also make sense?
seeing as we only have one r this time so only one length it seems we are just finding a factor to increase the length by to make a different length(the circumference) which makes sense.
Again lets consider the square into which our circle fits perfectly, the perimeter of this square would be 4 time the length of one of the sides.
Now the length of the sides = the diameter so the perimeter is 4d.
Notice again that the value we are trying to find for the square is multiplied by 4, but for a circle we are going to need a ratio that is a bit smaller.
So we need to replace the 4, for a square, with another, smaller, number — it seems pi will do the job.
Conclusion
To me when i consider pi i don’t look at it as a magical fundamental constant, but more a magical fundamental constant multiplied by four, because when I consider how these formula work using pi this is how they seem to work.
So this new constant is really the ratio of
area of square to area of circle
perimeter of square to circumference of circle.
and it = pi/4 = 0.785398….
so if you have a value for a square and you want a similar value for the circle you just need to multiply it by this number and you’ll have your answer.
Categories: Geometry Tags:

1. March 20th, 2008 at 23:23 | #1

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2. April 20th, 2008 at 18:49 | #2

Thanks for help

Guy above sounds inteligent doesnt he?

3. May 16th, 2008 at 17:45 | #3

how do you find the circomfrance of a cirlcle, when they give you the area???

4. May 17th, 2008 at 10:52 | #4

the area is pi x r square
and the circumference is 2 x pi x r
so we can find are from square root of the area divided by pi
and times this by 2 pi to find the circumference

5. June 5th, 2008 at 06:00 | #5

Thank you, its really helped me with my maths homweork.

6. July 2nd, 2008 at 16:06 | #6

thanx 4 helpin meh

7. August 4th, 2008 at 11:55 | #7

How do i find the diameter when i am given the area?

8. August 6th, 2008 at 17:23 | #8

re arrange a=pi x rsqaured and u get
r=sqaureroot of area/pi
then double it to find the diameter

9. October 30th, 2008 at 22:02 | #9

how you get area of a cirlcle from the circumfrence

10. November 1st, 2008 at 12:18 | #10

circumference is 2x pi x r and area is pi x r x r
so, area = pi x square(circumference/2 x pi)
area = circumference squared / 4 pi

hope that helps

11. November 5th, 2008 at 13:37 | #11

what is wit the gangsta on the top??? anyway where is the answer to wat Howell says said???

12. November 5th, 2008 at 14:37 | #12

area = circumference squared / 4 pi

that part

13. November 19th, 2008 at 20:55 | #13

that was shity

14. November 19th, 2008 at 20:56 | #14

that was great

15. December 21st, 2008 at 15:59 | #15

why pi, but not 22/7

16. December 22nd, 2008 at 12:27 | #16

22/7? wasn’t that just an approximation of pi used before they invented calculators.

17. January 13th, 2009 at 00:07 | #17

this is to much work

18. January 30th, 2009 at 04:57 | #18

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19. January 30th, 2009 at 05:01 | #19

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20. January 30th, 2009 at 05:04 | #20

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21. January 30th, 2009 at 05:27 | #21

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22. February 4th, 2009 at 01:45 | #22

WOW i like the math nerds haha no seriously whos in math clubs its all about baseball =) ya son!

23. February 20th, 2009 at 23:52 | #23

how do you find the area of 3/4 of a circle?
also how do you find the area of 1/4 of a circle?

24. February 21st, 2009 at 11:32 | #24

just multiply the area of the whole circle by 3/4 or 1/4. For any part of a circle where you know the angle at the middle you can multiply the area of the whole circle by that angle divided by 360 (or 2pi if your using radians)

25. February 22nd, 2009 at 07:11 | #25

why is the pi of 500 decimal number different from that of 10 or maybe 100

26. March 15th, 2009 at 02:08 | #26

hey um if there is a circle inside a square and the radius is 14 but the square has no measurement how do i find the anwser (all angles are right angles)

27. March 15th, 2009 at 11:25 | #27

well the radius of the circle will be 1/2 the length of on of the sides so each side will be of length 28

assuming the circle touches all four sides of the sqaure

28. March 24th, 2009 at 20:42 | #28

why in the world we use Pi to calculate area of a circle?

29. March 24th, 2009 at 21:58 | #29

how do u find the area of the diameter.

30. March 24th, 2009 at 21:58 | #30

xD

31. March 24th, 2009 at 22:00 | #31

thank you so much it really help me thank you again =D know i can do my homework better than i did before.

32. March 24th, 2009 at 22:14 | #32

i really love math but i didnt get that part

33. March 24th, 2009 at 23:00 | #33

hey guys wat u doing this is my nices guys i ever met =)

34. March 25th, 2009 at 11:53 | #34

if you have a method not involving pi please tell me

35. April 4th, 2009 at 23:00 | #35

THANKS

36. April 10th, 2009 at 01:31 | #36

Hi All,

Would you know the latest new exact formula for calculating Pi Number? If so please visit to this link:

At the link I’ve been posting general exact formula for Pi Number in form of the sum two arcsin. Maybe useful for you.Thx.

Best Regards,
Rohedi.

37. March 18th, 2010 at 07:57 | #37

true value of pi is (14-root 2)/4=3.1464466… i will send my work if you let me know your postal address.
thank you sir
yours sincerely
rsj reddy

38. February 22nd, 2009 at 17:08 | #38

what do you mean by the “pi of 500″?