The cross sectional area of wire
John Dunn - November 15, 2016
Most wire is made with a circular cross section of some particular radius and diameter. The area of
that cross section is the well known A = pi*R² which is colloquially pronounced as "pie are squared."
We will put aside the old joke that "Pie are not squared; pie are round" but we have to admit to
ourselves that expressing area and having to work with the irrational number "pi" can get
numerically awkward.
The number "pi" is the irrational number 3.14159265 ... which makes the exact numerical value of
cross sectional area of a wire an endless string of numbers too. To make matters easier, we can use
a different description of cross sectional area called "circular mils" which are described as follows.
First, we define that the diameter of our wire is taken in thousandths of an inch where one onethousandth of an inch is called "one mil." Thus, 0.001 inch = 1 mil, 0.01 inch = 10 mils and so forth.
Then we define the cross sectional area simply as the square of the wire's diameter in mils and call
that our area in units of "circular mils." This makes number handling ever so much easier.
Thus, if R is the wire's radius in mils for which the diameter is D in mils, then the true area is pi*R²
while the convenient area in circular mils is simply D². This is really easy and it all looks like this:
There are many wire tables available online, but we can examine a modified excerpt of one of them
such as seen on PowerStream, where we notice a seemingly odd fact about current carrying
capabilities versus wire size.
The reason it generally takes more circular mils per ampere for the heavier gauges is that wire
circumference varies linearly versus the radius and diameter while the cross sectional area varies as
the square of the radius and diameter. As a result, there is less wire surface area per unit of wire
volume for the heavier gauge wires than for the lighter gauges. That makes getting heat out of
larger wires become more of a challenge.
I understand that the really large dinosaurs (think Brontosaurus and the like) had the same skin
surface area to body volume ratio issues and therefore, body cooling issues. The skin area to body
volume ratio for a Brontosaurus was very much smaller than for a little thing like Compsognathus, a
dinosaur that was roughly the size of a modern day chicken.
Also see:
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Bad crimp, bad news
What size and type of output wires should I use?