Percentages to angles, using trig calculator

[oldminer]

This is copyrighted by Michael Cowing, a buddy of mine, highly educated, technical and very much a real gemologist.
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Ever wonder how to find the important pavilion and crown
main angles from measurements of pavilion depth or table
size and crown height?

Here is how to get those angles with the help of a couple
of buttons on a $16 scientific calculator. It’s as easy as
1 2 3, abc do ra me.

You can use these steps to check the measurement
consistency between angle and percentage results from
devices like the Sarin, OGI or your GIA proportion scope
measurements. You may be surprised.

If you have measured or obtained the pavilion depth % and
the culet % you:

1. Double the pavilion depth %
2. Subtract the culet % from 100
3. Divide the result from step 1 by the result from step 2
and push the tan-1 button to obtain the pavilion angle

For example What exact pavilion angle corresponds to the
ideal depth percentage of 43.1% when there is no culet?

1. 43.1 times 2 equals 86.2
2. 100 minus 0 equals 100
3. 86.2 divided by 100 equals .862 and tan-1(.862) equals
40.761 degrees

So the exact pavilion depth percentage corresponding to
Tolkowsky’s 40.75 is actually 43.083%, not the rounded off
43.1%. Close enough.

If you have measured or obtained the table % and the crown
height % you:

1. Subtract the table % from 100 and divide the result by 2
2. Divide the crown height % by the result from step 1
3. Push the tan-1 button to obtain the crown angle

If you can measure the table % but not the crown height %,
the crown angle can be obtained by measuring the length of
the kite shaped, bezel facet. Divide its length by the
diamond diameter times 100 to get the bezel length %. You
then:

1. Subtract the table % from 100 and divide the result by 2
2. Divide the result from step 1 by the bezel length %
3. Push the cos-1 button to obtain the crown angle

If you have measured the table % and the bezel %, the crown
height % can be obtained by:

1. Subtract the table % from 100 and divide the result by 2
2. Square the bezel % and subtract the square of the result
from step 1
3. Take the square root of the result from step 2 to obtain
the crown height %

Find the tan-1 and the cos-1 on your scientific
calculator. On this Casio you push the shift button and
then the tan or cos to obtain the tan-1 and cos-1

Copyright © 2004 by Michael Cowing

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Provided as a public service to those who are in need of this information. I can''t tell you how many times I have been asked these questions and did not have the full answer.

 

[Garry H (Cut Nut)]

Good stuff Dave and Mike.

Any volunteers to do a little study?
Find as many Sarin and Ogi scanned stones and check the reported angle vs the calculated angle from the pav depth %.

I will bet there is an understatement of pavilion angle by 0.1 or 0.2 degrees.
Also halving the culet is not quite right - it would be for a stone with a 45 degree pavilion angle - but not a 40-41 degree pav. Can an engineer explain / calculate what the correct figure should be please?

 

[niceice]

Oh, now that is VERY cool! We have been asked that question many times as well Dave and have always had a devil of a time trying to explain it... Thanks for sharing the information in such a concise format and please thank your friend Michael for taking the time to figure it out and write it down!

However, we would like to 'remind' people that the Sarin and OGI machines actually measure the Crown & Pavilion ANGLES and only estimate the percentage measurements... And this is the equipment used by the majority of the major gemological laboratories, so if you are trying to figure out the Crown or Pavilion Angle from the Crown Height or Pavilion Depth Percent measurement as stated on a lab report which only discloses that information, you are already at a disadvantage because you are trying to work a formula to obtain an estimate of the angle based upon an estimate of the depth percentage

 

[valeria101]

Hoping one Q is not one too many:

Why is said around here that using measured angles is more accurate ?

As far as I understand, one can get results far from reality with these calculations if the culet and girdle size is not known (as in: big culet allows for steep pavilion angles even if the actual pavilion depth is shorter than a stone with pointed culet and the same pavilion angle would have).

 

[niceice]

----------------
On 3/5/2004 2:24:18 PM valeria101 wrote:

Hoping one Q is not one too many:

Why is said around here that using measured angles is more accurate ?

As far as I understand, one can get results far from reality with these calculations if the culet and girdle size is not known (as in: big culet allows for steep pavilion angles even if the actual pavilion depth is shorter than a stone with pointed culet and the same pavilion angle would have).
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Looks like this one was posted while we were editing our post above, read our edited post and the answer has been provided... Your message posted at the same time we were editing ours...

 

[valeria101]

Thank you very much Niceice! this was a fast moving thread...


No need to cut the culet in two; are the angles marked black in the picture below the ones ?

 

[Garry H (Cut Nut)]

Sarin measure angles by placing some imaginary x's on imaginary graph paper - hence the pavilion being the longest facet gets the most accurate angle - which is good because it is also the most critical cut quality factor.

The angle is then used to calculate the %

I repeat the accuracy of Ogi may appear better on polished stones because the results are often closer to the measured parameters - but the scanner is not as accurate. The best evidence of this is in the use of planning scanners for cutting rough - Sarin costs more but is more widely used by factories working with bigger better goods.

 

[Buena Girl]

Thanks for info!

Had to buy a scientific calc. last month. FYI for any bargain hunters:
Target: $4.50 for cheapest scientific calc
Best Buy: $7 for cheapest scientific calc

 

[caratgirl]

Thanks a bunch! I am going to try plugging in all of my numbers and see how they match up (as if some are 'unknowns'). Maybe I can get a reasonable estimate on the angles of my other stone. It's not worth it to me to get it fully appraised, so this will be a fun experiment!

 

[Superidealist]

----------------
On 3/5/2004 2:21:34 PM Cut Nut wrote:


Also halving the culet is not quite right - it would be for a stone with a 45 degree pavilion angle - but not a 40-41 degree pav. Can an engineer explain / calculate what the correct figure should be please?
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The procedure is correct as written.

 

[alexah]

Is it true that there isn't really any ideal crown/pavillion angles for a princess cut diamond? - I think I read that somewhere....

Is there any number which should cause concern?

Thanks

 

[Nicrez]

Anything about the measurement of a perfectly square stone, like a radiant, EC, Cushion or Flanders? Doubting it, but just curious....

 

[oldminer]

There are numbers associated with well cut fancy shapes. However, these numbers do not predict brightness. You need to search out a well cut AND bright stone to get a truly fine one. You may find relatively poorly cut fancy shapes with lots of brightness, but they may have other problems of being overly deep or fragile due to cutting deficiencies.

Light return does not tell the whole story alone. Neither does cut parameters when used alone. Together these two components tell a great deal about any given diamond.