How do I calculate the square inches of the surface of a circle

Question

Good afternoon,

I am trying to find an easy way to calculate the surface of a circle (in square inches) to calculate the amount of paint needed to do a special painting technique.

The calculation for a square/oblong surface is L x W / 25 = fluid ounces of paint.

For example for an 18" x 18" square canvas, it's 18 x 18 / 25 = 12.96 ounces of paint (give or take a bit)

However, not being a math wiz at all, (I'm an artist, not a mathmatician) I googled "What is the surface of an 18" circle". It returned the answer of 1,017.9. I thought that was an awfully big number, but I plugged into the above formula: 1,017.9 sq inches / 25 = 40.716 fluid ounces of paint. From experience, I know that that is WAY TO MUCH paint.

I know that this calculation has something to do with Pi, but I flunked Algebra I in college 4 semesters in a row. I don't understand mathematical calculations at all.

If I were to use Google (as an example) what would I type in the search bar to get the correct answer? I have been working on this for DAYS and DAYS and still have not found a fairly easy way to calculate this number.

Any help you could give me would be greatly appreciated.

Regards,

Eric Van Marter

Answer 1

The formula for the area of a circle is Pi*r^2, where r is the radius of the circle. If your circle is 18 inches across, then 18 is the diameter of the circle. The radius is equal to half of that, or 9 inches. So the area you have to paint is Pi*9^2 ~ 3.14*81 = 254.34 square inches.

The answer that google gave you is for a circle with a radius of 18 inches, which would be 36 inches across.

Note that a circle that is 18 inches across has an area that is roughly 78% of a square that is 18 by 18, so the circle will need a little more than 3/4 the amount of paint that the square needs.