Area of a Circle
Area of a Circle
The area of a circle is important to electricians in the calculation of
conduit fill. Area of a circle equals PI or p (3.14) times the radius of the circle
squared or r2.
The radius used for conduit fill is the interior diameter divided by
A=pr2 is the algebra looking formula to be
So if you needed to calculate the area of a 1/2 inch electrical metallic
tubing raceway, you will seek the internal radius from Table 4 in Chapter 9 of
the National Electrical Code. Note the table gives diameter. So the diameter is
twice the radius. To find the radius, divide by two.
You would find the diameter measurement given as .622 inches. First, .622
divided by 2 equals .311. Then on with the calculation.
So 3.14 times .311 squared is .096721 square inches. Times 3.14 equals
.3037 square inches. The Table 4 gives this area as .304.
If you happen to use the PI p key on the calculator rather than 3.14, your
answer would be .30385 square inches. Depending on the accuracy needed, the PI
p key might be a better choice.
Find practice problems HERE.
Find answers to practice problems HERE
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Extras For Experts
A circle's area is found
using the formula:
But where does this formula
come from? Let's
find out ...
What we're going to do is break up a circle
into little pieces, and then reassemble it into a shape that we know the
area formula for ... the rectangle.
Maybe you're wondering how on earth you
can rearrange pieces of a circle to make a rectangle! Well, just
watch ... it's easy!
We'll start with the circle that we want to break
split the circle into quarters: Then
reassemble them to try to make a rectangle: Not
exactly a rectangle, is it? But we're not done yet!
Let's break the circle into eighths instead:
and arrange these pieces into a rectangular shape: This
is certainly starting to look like a rectangle ... but we're not
there yet! The next step is to go back and try splitting the circle into
sixteenths. Here are the pieces:
time when we put them together, they are much closer to looking like a
rectangle! See what you think: The
goal is to make a shape that is as close to a rectangle as possible, so
that we can find its area using the rectangle formula A = L x W
... but this shape does not have straight sides, so the formula
wouldn't be very accurate.
Let's go one step further, and break up the
circle into a whole bunch of little pieces. When we rearrange all
the pieces, the shape would look something like this:
is very close to a perfect rectangle! But you can see that the top and
bottom are still not perfectly straight ... they are definitely a
Can you visualize what would happen if we kept
going? If we continued to break the circle up into tinier and tinier
Eventually, the bumps would become so small that
we couldn't see them, and the top and bottom of the shape would appear
perfectly straight. This is what we would see:
perfect rectangle! Now all we have to do is find its area, using the
formula A = L x W The
next question is, 'How long are the length and width of our rectangle
made from circle parts?'
Let's go back to an earlier picture, so you can
see the circle parts more clearly: The
original circle's outside length was the distance around, or the
circumference of the circle: Half
of this distance around, ,
goes on the top of the 'rectangle',
and the other half of the circle, also length ,
goes on the bottom
In other words, all of the red and blue pieces
add up to ,
the circumference. The sides are just the radius
of each of the pieces, or the radius of the circle, r.
So we know the length is
and the width is r
Now we can find the area of the shape, using the
and there we have the formula for the area of the circle we started