Post subject: Pentagonal Cut Stone MM to Carat Formula
Posted: Fri Sep 22, 2017 4:04 pm
New to the Forum or The Quiet Type
Joined: Fri Sep 22, 2017 3:39 pm Posts: 1
Good Afternoon All!
First post, but I've been reading through the forums for a while waiting for a worthy question to post! Today is the day that I have been stumped. I have run across a pentagonal cut smokey quartz that is set, and I was wondering if anyone had a formula for estimating carat weight. I don't want to remove the stone, and just need a good estimate. None of my resources, or google have shown any hint of a formula....
You're not likely to find one since this is not a standard cut, and even if you did it wouldn't give accurate results because the window indicates the stone has been cut shallower than would be ideal. Hate to say it but it's not likely to be an easy estimate, though someone might have a trick for doing it.
Post subject: Re: Pentagonal Cut Stone MM to Carat Formula
Posted: Fri Sep 22, 2017 10:24 pm
Gold Member
Joined: Mon May 26, 2014 9:42 pm Posts: 1031
If I had to guess, I would estimate it as though it was a round stone with same area. The area of a pentagon isabout 1.72a*a, where a is the length of a side. the area of a circle is Pi*r*r
so a circle with equivalent area has a radius of r=sqrt(1.72/pi)a or .74a
The diameter would then be 1.48a
Don't know how well it will work, but that is what I would do, using the formula for a circular stone.
(after all the volume of a cone with a polygonal base is (1/3)h*base area, regardless of it is a circle or a pentagon. )
Post subject: Re: Pentagonal Cut Stone MM to Carat Formula
Posted: Fri Sep 29, 2017 1:44 am
Valued Contributor
Joined: Tue Nov 04, 2014 12:12 pm Posts: 180
The design looks similar to Marco's Pentagonal minibarion with perhaps a shallow pavilion. I'd adjust the Marco's gemcad file to say a 40 degree culet and then run the formula -
carats = Vol./W^3 x W x W x W x 0.005 x s.g.
where Vol./W^3 is from the adjusted gemcad file, W is the width of the gem; and s.g. is the specific gravity of the gem (approx. 2.65 for smoky quartz)
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