The Area of a Circle


One of the first proficiencies you need is to be able to compute the area of a circle.  This information is used to figure out everything from force exerted against the pipe, to computing volumes and deducing other important information.

Most people have heard “Area equals Pi times radius squared” [A = π r2] this is what most people would remember from school – well there is a much easier way !

Somebody along the way figured out that you can just figure this out for an imaginary circle that has a radius of 1, and then apply that to any circle you come across, and Presto! you can compute the area much more easily. Let me show you…

The radius of a circle with a diameter of 1 is .5
Now take .5 x .5 and you get .25

3.14159 x .25 = .7854

.7854 is easy to remember on a calculator because once you hit the . key (point) .. you just go counter-clock-wise starting at 7, then 8, 5, 4  – [ it kind of forms a backward C shape ]


If you now take the Diameter of any circle and multiply it by itself (square it) you can then multiply by .7854 and get the Area.

This is easier because most of the time we are working with irrational numbers, that are easy to remember, for example 5.5″ 17# casing has an inside diameter of 4.892″ – if we try to use the Pi-R-squared method we have to divide by two, try to remember that number and then multiply by PI … or we can just take 4.892 x 4.892 x .7854 = 18.7959 in2

Try it the old fashioned way and see which method you prefer.

So here comes the really cool part…  you can take two different diameters and figure out the annular area by squaring the first Diameter, and then subtracting the square of the second diameter, then multiply by .7854, and you get the area of the space between.

[(d1 x d1) – (d2 x d2)] x .7854 = Annular Area

Lets try it….

A common problem would be to compute the volume between two pieces of pipe, say we want to fill the area between 4.5″ 11.6# casing and some 2-3/8″ tubing….

The inside diameter (ID) of 4.5″ 11.6# casing is 4.0″
The outside diameter (OD) of 2-3/8″ tubing is 2.375″

4.0 x 4.0 = 16.0
2.375 x 2.375 = 5.6406
[16.0 – 5.6406] x .7854 = 8.1362 in2

8.14 in2 x 12 = 97.64 in3 = there are 97.64 cubic inches in a one foot annular between 4″ casing and 2-3/8″ tubing.
Divide that by 231 cubic inches in a gallon…

97.64 / 231 = 0.4227 Gallons per foot.

let’s say we have 6,784 feet of pipe, so multiply that to get

0.4227 x 6,784 = 2867.6 Gallons.

divide by 42 (gallons per barrel) and you have 68.3 Bbls.

you may want to look at these links to find out more.

Barrels of oil
in3 per Gallon