# table 8

#### kimrichi

##### Member
what is the difference betweem circular mill and square inch in the code code chapter 9 table 8?

#### kwired

##### Electron manager
Interesting, I have always known circular mils to be a unit of area but never gave any thought to the "circular" part.

If one were to place several same sized circles inside the area to be measured you still have gaps between the circles - how are these gaps included in the actual area - or is it offset by what gets cut off around the edges when measuring a circular area? Similar to measuring with square units, but corners of the units will be cut off when measuring a circular area.

#### charlie b

##### Moderator
Staff member
If one were to place several same sized circles inside the area to be measured you still have gaps between the circles - how are these gaps included in the actual area. . . ?
The areas of each individual strand in a multi-stranded conductor will collectively add up to a smaller number than the circular mil area of the conductor as a whole, for the very reason you name. The circular mill area of the conductor is not the sum of the areas of the strands, but rather the area of the smallest circle that can completely contain the entire conductor.

When we use each

#### kimrichi

##### Member
When we uxse each

#### don_resqcapt19

##### Moderator
Staff member
... The circular mill area of the conductor is not the sum of the areas of the strands, but rather the area of the smallest circle that can completely contain the entire conductor.
This table shows the combined circular mil area of the strands about the same no matter how few or how many strands you have in the conductor. The OD of the conductor changes based on how many or how few strands you have.

#### Smart \$

##### Esteemed Member
The areas of each individual strand in a multi-stranded conductor will collectively add up to a smaller number than the circular mil area of the conductor as a whole, for the very reason you name. The circular mill area of the conductor is not the sum of the areas of the strands, but rather the area of the smallest circle that can completely contain the entire conductor.
Umm... I believe you have that backwards. The circular mil area of a stranded conductor is the sum of the circular mil area of the individual strands.

For example, a 12AWG copper conductor has the same amount of copper per length whether it is solid or stranded.

#### kwired

##### Electron manager
The areas of each individual strand in a multi-stranded conductor will collectively add up to a smaller number than the circular mil area of the conductor as a whole, for the very reason you name. The circular mill area of the conductor is not the sum of the areas of the strands, but rather the area of the smallest circle that can completely contain the entire conductor.

If you are using square blocks as a measuring device you can lay one next to the other and fill all the area with no gaps between your measuring devices.

If you have 100 circles all the same size and lay them out in any dimension right next to each other you will have gaps within the area, how are these accounted for in the total circular mils of an object being measured?

Or if you were to assume several same sized circular objects as measuring gauges, does the amount of material cut off the gauges that shape the outer edge of the object being measured end up equaling the needed area to fill the remaining gaps inside the area being measured?

I am not that advanced of a math wiz, and just asking how you measure area with a base unit that can not be laid out with no gaps in between simple base units.

#### dicklaxt

##### Senior Member
The areas of each individual strand in a multi-stranded conductor will collectively add up to a smaller number than the circular mil area of the conductor as a whole, for the very reason you name. The circular mill area of the conductor is not the sum of the areas of the strands, but rather the area of the smallest circle that can completely contain the entire conductor.
True as you state,,,,,to prove charlie's point if you use the figures shown in Table 8 for overall diameter to get to the square inches,,,,,you would use the established math formula pi x radius squared,,,,,when you extend that formula the answer is square inches and matches the number shown in Table 8 for area.

The confusion is we are dealing with cross sectional area and not linear area.

dick

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#### kwired

##### Electron manager
True as you state,,,,,to prove charlie's point if you use the figures shown in Table 8 for overall diameter to get to the square inches,,,,,you would use the established math formula pi x radius squared,,,,,when you extend that formula the answer is square inches and matches the number shown in Table 8 for area.

The confusion is we are dealing with cross sectional area and not linear area.

dick
Maybe I am wrong but isn't cross sectional area mentioned in the conductor property tables simply the amount of area of the circular side of a cylinder shaped object? The result being a two dimensional circle. Area of a two dimensional object is area, the definition of circular mil that I read is simply the area of a circle with a diameter of 1/1000 inches. Lay how many circles of that size across the surface of the object being measured gives you how many circular mils of area that object has. Now if we were measuring with squares, triangles, or other multi sided objects it is usually possible to cover all the measured space with no gaps between the objects used to make the measurement. Circles is not possible to lay out without voids between them in places. How does this work out to include the spaces not covered in the net total area?

#### dicklaxt

##### Senior Member
Don't worry about the created gaps made by the individual circles(conductor strands)

We only want to deal with the overall diameter of a group of stranded bare conductors formed/wrapped into a particular shape in this case a circular shape,we don't care how many gaps it may have.

When a cable is manufactured it has a predetermined number of strands for a given size required,once this amount of copper(total copper in each strand) is wrapped around each other to give a circular(tubular) shape then a jacket is put around it.The outer diameter of the jacket is the diameter shown in Table 8.The cross sectional area is only the area across the sliced plane,,,it has no other dimension

hope that helps

dick

#### dicklaxt

##### Senior Member
TYPO!!!!!!!That should have read inner diameter of the jacket.

dick

#### Smart \$

##### Esteemed Member
Maybe I am wrong but isn't cross sectional area mentioned in the conductor property tables simply the amount of area of the circular side of a cylinder shaped object? The result being a two dimensional circle. Area of a two dimensional object is area, the definition of circular mil that I read is simply the area of a circle with a diameter of 1/1000 inches. Lay how many circles of that size across the surface of the object being measured gives you how many circular mils of area that object has. Now if we were measuring with squares, triangles, or other multi sided objects it is usually possible to cover all the measured space with no gaps between the objects used to make the measurement. Circles is not possible to lay out without voids between them in places. How does this work out to include the spaces not covered in the net total area?
I think it is easier to think of circular mil area measurement as a ratio to the area of a one mil circle. See table below. Note the circular mil area is just the square of the diameter in mils. The resulting measure still covers the area of concern (the shape doesn't really need to be circular). In measuring multiple circular areas, such as stranded conductor crosssection, only the circular areas are measured. The gaps are not included.

 mil diameter area (in?) circular mil area 1 0.000000785398 1 2 0.000003141593 4 3 0.000007068583 9 4 0.000012566371 16 5 0.000019634954 25 6 0.000028274334 36 7 0.000038484510 49 8 0.000050265482 64

#### Smart \$

##### Esteemed Member
... Note the circular mil area is just the square of the diameter in mils. ...
If you want to verify my assertion, go to Table 8 and choose any conductor having single stranding (18-8AWG). Take the square root of the circular mils and divide by 1000. The result will be the conductor diameter.

#### dicklaxt

##### Senior Member
As was said before,circular mil is one way of expressing area when using mm and circular inch is area when using inches.This is apples to apples but measured in mm one time and inches the next time,either will work but the summation of all the circular mils you can cram into a given circle is not what we are after we want to know the size of the circumscribed area of the circle that is around them.The answer would be all the little circles along with all the gaps they formed.

dick

#### Smart \$

##### Esteemed Member
If you want to verify my assertion, go to Table 8 and choose any conductor having single stranding (18-8AWG). Take the square root of the circular mils and divide by 1000. The result will be the conductor diameter.
If you want to verify with stranded simply divide the circular mils by the number of strands before taking the square root and dividing by 1000.

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#### Smart \$

##### Esteemed Member
...The answer would be all the little circles along with all the gaps they formed.
You need to rethink that statement

If you have a 1000 circular mil circle and try to cram 1000 one mil circles into it, you cannot do so without overlapping them.

That's why the overall diameter in Table 8 for stranded conductors is larger than single strand overall diameter (also why there is a "—" in the stranding column).

FWIW, circular mil measurement of circular objects simply take pi out of the diameter-area equation.

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#### dicklaxt

##### Senior Member
You need to rethink that statement

If you have a 1000 circular mil circle and try to cram 1000 one mil circles into it, you cannot do so without overlapping them.

That's why the overall diameter in Table 8 for stranded conductors is larger than single strand overall diameter (also why there is a "?" in the stranding column).

FWIW, circular mil measurement of circular objects simply take pi out of the diameter-area equation.

LOL.....I didn't say you could put 1000 little circles in a 1000big circle ,you did....

No pi remains in the formula, use 1000MCM as the example,it has a diameter of 29.26mm,using pi radius squared formila we expand thusly 29.26/2 squared X pi equals 672 mm which matches the area listed of 673mm.:thumbsup:

dick

#### Smart \$

##### Esteemed Member
LOL.....I didn't say you could put 1000 little circles in a 1000big circle ,you did....
I added the 1000 value. Other than that, you said...
...the summation of all the circular mils you can cram into a given circle is not what we are after we want to know the size of the circumscribed area of the circle that is around them.The answer would be all the little circles along with all the gaps they formed.
The red text is incorrect.

Regarding the green text, I can't see how that relates. If you "stack" a bunch of one-mil diameter circles inside a larger circle, what would be the count and how do you include the gaps both amid the circles and the periphery?

No pi remains in the formula, use 1000MCM as the example,it has a diameter of 29.26mm,using pi radius squared formila we expand thusly 29.26/2 squared X pi equals 672 mm which matches the area listed of 673mm.:thumbsup:

dick
That's an entirely different issue. You are converting to a different unit of measure: Cmil -> mm?