A formula for accurately calculating diamond carat please?

[gm89uk]

I've become fixated on maths and diamonds and find it fascinating.
Does anyone have a formula for calculating diamond carat weight based on:
Girdle Diameter, Table %, Crown Deg, Pav Deg and Girdle Width (assuming the culet is pointed)?
I am aware of the estimating formula W^2*D*0.0061*GC% but was hoping for something more accurate. There is an app available on my android phone that can do this (which I won't share due to forum rules) and I cannot for the life of me find the formula to calculate it!

I realise all formulas will be estimates but some are more accurate than others. I've read sarin machines estimate carat based on the measurements?

The closest I've come is this educational PDF which requires upper and lower-half lengths.
http://www.wtocd.be/nl/DiamondInfo/articlesPDF/The_Brilliant_Cut.pdf

Many thanks in advance!

 

[Garry H (Cut Nut)]

Re: A formula for accurately calculating diamond carat pleas

I prefer the 0.0061 constant to be 0.00625 because it accounts for the average girdle.

DiamCalc is the best tool but costs around $400 - however you get loads of other tools as well.
Sarin and all scanners work out a diamonds volume and multiply by the SG or weight constant (which is very tight for diamond).

 

[oldminer]

Re: A formula for accurately calculating diamond carat pleas

I use the formula with .0061 as Garry H does. With practice and allowing for adjustments such as girdle thickness, culet size, crown angle which are visual observations, I can get very close to exact weight, especially for rounds and square shapes. Those stones with curved sides that have potentially bulging or less curved sides are a bit less accurately done by formula. Importantly, the formula's constant for round, ".0061" Is different for other shapes. Each shape's formula's constant is a combination of the fixed specific gravity of diamond multiplied by a number that calculates the cubic volume of the stone from the product of length, width and depth. That number is different for every shape and so the constant for rounds is not the same as for other shapes.

A formula need not be more accurate than a point or two anyway. If the exact weight is crucial on a mounted diamond, nothing substitutes for weighing the stone. OEC diamonds tend to weigh 5% to 10% more than the modern cut round formula depending on the angles and culet size. Really old mine cut cushions weigh close to 20% more than by round measurements and sometimes even more in extreme cases.

 

[gm89uk]

Re: A formula for accurately calculating diamond carat pleas

Thank you both for your replies.

I am more interested in the formula itself because I was making a program (for myself with no commercial interest) for calculating carat more accurately using crown & pav, table, GD, girdle % compared to the traditional methods you have described above, and how it compares to reported carat weight on certificates. I am aware of the rounding of angles on GIA certificates and the inaccuracy this will output in carat weight. I would love a formula that does not need 'correction' but is tailor made for that diamond.

It may be the only way is to calculate volume and convert to carat (although there isn't enough information on certificates to calculate volume accurately).

 

[oldminer]

Re: A formula for accurately calculating diamond carat pleas

I use a very nice app which works well with colored gems and diamonds. It is called Gemstone Weight Estimator and it was created by Anchor Cert. It has an iOS functionality, but I am not sure about Windows or Android. It does allow and make adjustments according to the outline and pavilion bulges some stones might have.

 

[gr8leo87]

Re: A formula for accurately calculating diamond carat pleas

I have thought about doing something like this when I was studying Econometrics. Basically you enter a lot of existing information (data) and then run a panel data regression analysis and see how it goes from there. But then couldn't get around to actually doing it. Do share with us your findings.

 

[drk14]

Re: A formula for accurately calculating diamond carat pleas

I am more interested in the formula itself because I was making a program (for myself with no commercial interest) for calculating carat more accurately using crown & pav, table, GD, girdle % compared to the traditional methods you have described above, and how it compares to reported carat weight on certificates. I am aware of the rounding of angles on GIA certificates and the inaccuracy this will output in carat weight. I would love a formula that does not need 'correction' but is tailor made for that diamond.

It may be the only way is to calculate volume and convert to carat (although there isn't enough information on certificates to calculate volume accurately).

This is a quick approximation that I worked out for you, not sure how accurate it is.



It approximates the MRB pavilion as a cone, the girdle as a cylindrical disk, and the crown as the frustum of a cone. Thus, it will probably overestimate the weight somewhat, but at least it takes into account the depth fraction (d), table fraction (t), crown angle (theta_c) and pavilion angle (theta_p). The computed mass m would have to be divided by a conversion factor (e.g., 0.2 g/ct) to yield carat weight, and you'd have to be careful to use a consistent set of measurement units for the conversion factor, the width (W) and the diamond density (rho).

Disclaimer: I have not checked my work or done any test calculations, so use at your own risk...

 

[gm89uk]

Re: A formula for accurately calculating diamond carat pleas

That's exactly what I was trying to find the time to sit down and write! Thanks a lot for that. I'm away at the moment but will report back on what I find when I get back and have a play with it.

 

[gm89uk]

Re: A formula for accurately calculating diamond carat pleas

I am more interested in the formula itself because I was making a program (for myself with no commercial interest) for calculating carat more accurately using crown & pav, table, GD, girdle % compared to the traditional methods you have described above, and how it compares to reported carat weight on certificates. I am aware of the rounding of angles on GIA certificates and the inaccuracy this will output in carat weight. I would love a formula that does not need 'correction' but is tailor made for that diamond.

It may be the only way is to calculate volume and convert to carat (although there isn't enough information on certificates to calculate volume accurately).

This is a quick approximation that I worked out for you, not sure how accurate it is.



It approximates the MRB pavilion as a cone, the girdle as a cylindrical disk, and the crown as the frustum of a cone. Thus, it will probably overestimate the weight somewhat, but at least it takes into account the depth fraction (d), table fraction (t), crown angle (theta_c) and pavilion angle (theta_p). The computed mass m would have to be divided by a conversion factor (e.g., 0.2 g/ct) to yield carat weight, and you'd have to be careful to use a consistent set of measurement units for the conversion factor, the width (W) and the diamond density (rho).

Disclaimer: I have not checked my work or done any test calculations, so use at your own risk...

I derived the formulas myself and came up with the same values as yourself. Then I put them in an excel sheet to compare against the actual volume calculations in the article I quoted in the first post.

The formulas were remarkably accurate without any correction. The Girdle and Pavilion calculations were overestimations as you predicted but interestingly the crown, assuming it's the a frustum of a cone, underestimates the true volume of the crown.

I could then apply a fudge factor to the girdle, pavilion and crown to very closely represent the average diamond (assuming star length and half lengths are 50% and 77% respectively). At the extremes of lower halves and star lengths this would only account for roughly a +/- 0.0125 in carat difference.

To correct the above formulas:
Girdle 'fudge factor': 0.994941378164058
Pavilion 'fudge factor': 0.991556538121318
Crown 'fudge factor': 1.0174092561863

If you multiple all of those above volumes by the fudge factors and total them, then multiple by 0.017575 (to convert from volume to carats) you have a accurate result which is a far better estimator than 0.0061 x (average w)^2 x d.