Spread Index

[Superidealist]

An easy way to compare the relative spread of diamonds of different wieghts is to calculate a number I call spread index. The spread index of a diamond is the diameter it would have if it were rescaled to weigh exactly one carat.

Spread Index = (average diameter)/(carat weight)^(1/3)

In ideal-cut diamonds the spread index should be very near 6.50. A smaller spread index indicates a less spready diamond, a larger spread index indicates a spreadier diamond. Keep in mind, however, that a larger spread index is not always better since a very large number may indicate a too-shallow cut.

The spread index can also be used with princess cut or modified square or octagonal cut diamonds.

It cannot be used to compare diamonds of different shapes.

 

[Garry H (Cut Nut)]

Diamcalc has a spread index that compares every shape to a tolkowsky diamond.
It is the little number in the lower right corner.
Marquise and oval do well - it works on scanned stones as well.
It tells you how much heavier / lighter the stone is in ct wt as well as + or - % variance.

Cool huh?

 

[Mikesgirl]

Interesting. My diamond comes up 6.484, and on the HCA cut advisor it scored excellent on spread. Makes me want to try it on a bunch of stones and compare. Gotta admit, the math/geometry of the optics fascinates me.

 

[Mara]

I'm a dunce at math...is that ^(1/3) supposed to represent multiplying the # by 1/3 or ????

 

[smaggard]

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On 10/3/2003 12:29:28 AM Mara wrote:


I'm a dunce at math...is that ^(1/3) supposed to represent multiplying the # by 1/3 or ????
----------------

No Mara, imagine there are parentheses around the 2nd part of the equation so do that first. And ^(1/3) means raised to the power of 1/3.

So take the carat weight and raise that to the power of (1/3), keep that answer and then divide the average diameter by that answer. Does that make sense?

Edited to add: I've never understood how the HCA gives you a score on "spread or diameter for weight" when it never asks for with the diameter OR the weight????

 

[Giangi]

Edited to add: I've never understood how the HCA gives you a score on "spread or diameter for weight" when it never asks for with the diameter OR the weight????

I think they give a result basing on depth %.

 

[magna2]

By raising a number to the power of 1/3 basically is stating to take the cube root of the number. The Spread Index proposed by Superidealist would be more meaningful if his formula was then divided by 6.5:

[(avg Diameter)/(ct weight)^1/3]/6.5

Thus it would be desireable to have an index number as close to "1" as possible.

 

[Mara]

Doing it the Magna way got me .60 ....appropriate I guess since my stone is shallow?

 

[Superidealist]

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On 10/3/2003 10:27:32 AM magna2 wrote:


By raising a number to the power of 1/3 basically is stating to take the cube root of the number. The Spread Index proposed by Superidealist would be more meaningful if his formula was then divided by 6.5:

[(avg Diameter)/(ct weight)^1/3]/6.5

Thus it would be desireable to have an index number as close to '1' as possible.

----------------

Yes raising to the 1/3 power is taking the cube root, so the spread index is the average diameter divided by the cube root of the carat weight. This gives the average diameter of the diamond if it were rescaled to weigh exactly one carat while keeping all its angles (that is, its shape) exactly the same.

I considered dividing by an "ideal" quantity at one point but abandoned it because it makes a judgement that I think is best left to the individual. I don't want to say that there is a "perfect" value, which is what this essentially says. Of course, my pointing out that ideals are around 6.50 does pretty much the same thing.

By the way, Ive seen both 6.500 mm and 6.502 mm listed as the "ideal" diameter for a one carat round. Does anyone know which is correct?

By the way, dividing any linear quantity (the measurement of any length, not just the diameter) by the cube root of the carat weight will give the equivalent quantity for a diamond rescaled to weigh exactly one carat.

 

[Superidealist]

----------------
On 10/3/2003 12:26:16 PM Mara wrote:


Doing it the Magna way got me .60 ....appropriate I guess since my stone is shallow?


----------------

I'm guessing a mistake was made in the calculation since this number seems very low. It would correspond to a one carat diamond with a 3.6 mm diameter.

 

[Mara]

Hmm I had the fiance do it

He's supposed to be smarter than me.

My stone's average diameter is 7.15mm


Carat weight is 1.23c




?

 

[Superidealist]

These numbers result in a spread index of 6.67 or 1.03 on Magna's scale.

 

[Mara]

So if I had a 1c stone then my diameter would be 6.67mm instead of the ideal 6.50mm.




Sounds about right I guess.




on the DiamCalc my stone had a spread index of .12c...so its a 1.23c that looks like a 1.35c. A 1.23 well cut stone would have a diam of around 7mm. A 1.35c stone would have around 7.15mm.

 

[Garry H (Cut Nut)]

HCA knows the weight of the pavilion cone, and it subtracts the calculated crown heght from pav depth arriving at a girdle thickness (calc the wt of a cylinder) and the crown is a frustrum of a cone which is calcualted.

Leonid's wonderful work

Very accurate.
We have considered a more complex factor that accounts for verticle spread - a stone with a flat crown is penalised and a steep crown small table gets a bonus.

 

[Lynn B]

Just ran across this old thread, and am resurrecting it to see if any kind soul who is better in math than me (and that would probably include Rhino's DOG!

) could give me the spread index of my stone?

The diameter is 7.49 x 7.51 x 4.53. The carat weight is 1.53. Any other numbers needed?

THANKS!

Lynn (the Math Moron)

 

[AndyRosse]

Lynn,

6.518...very nice!!!

Michelle

 

[quaeritur]

ok... I'm a complete math idiot. So my .79 ct 6.03mm diameter has a spread index of approximately 6.523? Or 1.0035 with magna's adjustment?

Cool, I think

 

[Garry H (Cut Nut)]

This is the spread factor that is not taken into account - the more light return (especially near the girdle) the larger the same diameter (as shown) better cut diamond will look.

A Princess cut with the same surface area as a well cut round brilliant will always appear smaller.

 

[researcher]

Interesting formula! I'll have to see if I get the same results using it. The formula I use is as follows:

[(Carat weight)^(1/3)]*x, where x equals the average diameter/width for a 1ct stone(6.5 for a round, 5.6 for a princess).

If you go to Calculator and enter the formula as:

[Power(Carat weight,1/3)]*x

entering in the carat weight of your stone and the appropriate average diameter you should get the right result!

 

[Superidealist]

Just multiply both sides of the equation in the original post by (carat weight)^(1/3) and you will see it is the same.

The formula can be used in a variety of ways:


Since spread index is defined as it is, to find the diameter a diamond would have if it were rescaled to weigh exactly one carat, use:
Rescaled diameter = (average diameter)/(carat weight)^(1/3)


Since a well-cut one carat round has an "ideal" diameter of 6.50mm, to find the "ideal" diameter for a diamond of a given weight, use:
"Ideal" diameter = (6.50mm)*[(carat weight)^(1/3)]


Since a well-cut one carat round has an "ideal" diameter of 6.50mm, to find the "ideal" carat weight for a diamond of a given diameter, use:
"Ideal" carat weight = [(given diameter)/(6.50mm)]^3


To find "ideal" numbers for other cuts, substitute the appropriate "ideal" value for 6.50mm in the above formulas.

 

[wonka27]

Just figured out my spread index on the four diamonds I just bought.

Ering diamond: .789 ct / Index = 6.01 / Mine =5.97
Pendant diamond: .323 ct / Index = 4.46 / Mine = 4.43
Earring diamond 1: .235 ct / Index = 4.01 / Mine = 4.02
Earring diamond 2: .237 ct / Index = 4.02 / Mine = 4.05

That's pretty cool. I guess I could have done better on the first two. But the important thing to me is they are high performing diamonds!

So if 6.5mm is an ideal 1ct, what would a lower performing diamond be in millimeters? I guess it could go bigger or smaller? Any thoughts?

 

[Rowan]

I am still stumped. I'm completely math-challenged. Would someone mind?
My stone is .52ct 5.23-5.24 diameter.
Thanks!

 

[wonka27]

Rowan -

Looks like your spread index is 5.23 (rounding up of course). So you should be right in line!

 

[lsmathis1]

I used the formula above and I still feel like mine's coming up wrong - I'm sorry to be a mooch, but could someone help/do mine as well?

1.81 ct 7.83 avg. diamter

Thanks in advance

Much appreciated.

 

[Rowan]

Thanks Wonka!

 

[wonka27]

----------------
On 8/19/2004 10:40:25 AM lsmathis1 wrote:

I used the formula above and I still feel like mine's coming up wrong - I'm sorry to be a mooch, but could someone help/do mine as well?

1.81 ct 7.83 avg. diamter

Thanks in advance

Much appreciated.----------------

I come up with 7.92mm for your diamond.

 

[lsmathis1]

Thanks Wonka

I trust your numbers...I thought I was good at math, but looks like I was waaaay off.

~Lisa

 

[lsmathis1]

I'm still a bit confused though (sorry a little slow with this) our diamond is an AGA Ideal cut 1B...would you say that my spread is a little high at 7.92mm? Maybe someone can give me some insight? I've read a few articles on "spread" and understand what it means, but just more curious about how our diamonds number falls?

EDIT: 1.81ct Avg. diameter 7.83

 

[Todd07]

Interesting thread.

I use two simple indexes to compare diamonds in my spread sheet. They help balance the $/c figure which makes a well cut diamond look less attractive.


Spread Index: (smallest diameter)/(carat weight).


- I think the SI clearly shows which diamond made best use of their weight.


Cost/mm Index: (smallest diameter)/(total price)


- This is probably the best way to identify which stone is the best value when comparing similar quality.




The ave dia may be a better way but I kept it simple and used smallest dia.

 

[Superidealist]

To eliminate any confusion that may exist, Wonka is using the term "spread index" to mean something other than what I defined in the first post of this thread. The numbers he has generated are what I have called "ideal" diameters for a given carat weight. That said, here are the numbers for the various stones listed:

Rowan:
Spread Index: 6.51 (If your diamond weighed one carat, its diameter would be 6.51mm.)
"Ideal" Diameter for 0.52ct: 5.23mm (This is the value Wonka calculated.)
"Ideal" Weight for 5.235mm: 0.52ct
Percent Body Fat: 0.0%

lsmathis1:
Spread Index: 6.42
"Ideal" Diameter for 1.81ct: 7.92mm
"Ideal" Weight for 7.83mm: 1.75ct
Percent Body Fat: 3.3%

For the record, I don't think it is wise to use spread index as a measure of cut quality. It's just a fun diversion.