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# An easy way of calculating crown and pavilion angles

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#### asblackrock

##### Shiny_Rock
If you know the Pavilion depth, the Crown depth and the Table of a diamond (all given as a % of average diameter), the “all so important “ Pavilion Angle and Crown angle can be calculated easily.

PAVILION ANGLE:
1. Enter the Pavilion depth into your calculator.
2. Divide this by 50.
3. There is a button on many calculators labelled “Tan –1”, or it may be written in small writing above the “Tan” button. Press the “Tan –1” button (or if it is written above the “Tan” button, press the shift button, then the “Tan” button). This is the exact pavilion angle in degrees.

Eg. Pavilion depth = 43.1
43.1/50 = 0.862
“Tan –1” 0.862 = 40.76. This is the exact pavilion angle in degrees

CROWN ANGLE:
1. Divide the Table by 100
2.Subtract this from 1
3. Multiply this by 50
4. Store this figure
5. Divide the Crown depth by the above figure
6. Press the “Tan-1” key. This is the exact crown angle in degrees

Eg. Table = 53 Crown depth=16.2
53/100 = 0.53
1-0.53 = 0.47
50x0.47 = 23.5
16.2/23.5 = 0.68936
“Tan –1” = 34.58. This is the exact crown angle in degrees

Note: This formula only works for round brilliant cut diamonds with no culet (ie pointed). If a culet is present, use the crown angle formula to work out the pavilion angle, plugging in culet rather than table (if you flip a stone upside down, the culet becomes a mini "table").

#### asblackrock

##### Shiny_Rock
PS For "crown depth" read "crown height"

#### Richard Sherwood

##### Ideal_Rock
Great post Angela. You can also account for change in the pavilion angle caused by an open culet by figuring it for the pavilion like you figured the table for the crown (subtracted from 1, etc.).

This is probably the same trigonometry that the HCA uses in converting percentages to angles.

The only caveat is that usually the angle information provided by a Sarin or OGI report is more accurate than percentages reported. Percentages reported on many reports are often estimated or rounded off.

#### kevinraja

##### Shiny_Rock
Excellent post. I bought a princess diamond this week, the sarin report of which is given below. The angles that I computed based on your calculation doesn't match with the one given in the sarin report. Is the Sarin report wrong? Or the formula you provided is wrong? Thanks

#### JC

##### Shiny_Rock
NICE! Thanks for the tip Angela....

#### Carolynw

##### Shiny_Rock
Can you help me to determine if this is a well cut stone?

SARIN
diam. 7.47mm (7.43 - 7.50 ) x 4.56
depth 61.0%
crown 34.6 ' 15.2 %
pavil. 40.9 ' 43.0%
table 4.12mm 55.1%
cutle 0.9 % Small
girdle 1.4 % (0.9 - 1. %

GIA
VS2 E
1.53 size
Dep 61.4
Table 56
Cul NN
Pol Ex
Sym Ex
Grd TN-M F

#### oldminer

##### Ideal_Rock
This was very nice of Angela to post these formulas. It is certainly not rocket science, but it is the kind of math that eludes many of us. I have force fed this into my head for years, but many of you will never need to have this at hand, so a place to refer to is excellent.

Once you get to a fancy shape, this all goes bad. The formula is for rounds. Think a moment. On the pricness cut that someone else posted, the crown angles could be different on all four sides. It does not have the necessary symmetry of a round outline. This is exactly why the AGA Cut Class system does not utilize crown or pavilion angles for any fancy shapes. The crown height and pavilion depth can be measured properly on fancy shapes, but it is a wasted effort to concern yourself with them on fancy shapes. How do you propose to use these angles, anyway? What reference chart exists that will work with fancy shapes and these two angles? I don't think there is anything out there.

Anyway, for rounds, the formulas will be useful for filling in the HCA.

#### quaeritur

##### Brilliant_Rock

----------------
On 10/21/2004 12:06:14 PM Carolynw wrote:

Can you help me to determine if this is a well cut stone?

SARIN
diam. 7.47mm (7.43 - 7.50 ) x 4.56
depth 61.0%
crown 34.6 ' 15.2 %
pavil. 40.9 ' 43.0%
table 4.12mm 55.1%
cutle 0.9 % Small
girdle 1.4 % (0.9 - 1. %

GIA
VS2 E
1.53 size
Dep 61.4
Table 56
Cul NN
Pol Ex
Sym Ex
Grd TN-M F

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

#### asblackrock

##### Shiny_Rock
Hi Kevinraja
I am up (6am in Australia). The formula I gave does only apply to round brilliant cuts. I did not think to specify this, sorry.

#### Bagpuss

##### Brilliant_Rock
Thank you for some real solid help Angela. I have cut and saved this invaluable formula.

nice post Angela
Johan

#### asblackrock

##### Shiny_Rock
Hi Rich
Good point (forgive the pun - it is very early!)

For those of you not quite following, if you flip a stone upside down, the culet becomes a mini "table". Use the crown angle formula to work out the pavilion angle, plugging in culet rather than table (still works if you plug in 0 if the stone has no culet).

eg. With Carolyn's stone, (pav 43%, culet 0.9%) ignoring the culet gives a pav angle of 40.7. Taking the culet into account, the pav is 40.95. It is specified as 40.9. The small discrepancy is caused by rounding off the pav% (ie could have really been 42.96-43.04 and still be called 43.0)

#### asblackrock

##### Shiny_Rock
I have just looked at the crown angle figures for Carolyn's stone.
With a crown height of 15.2 and table of 55.1 the crown angle works out as 34.1. It is specified as 34.6!

I have worked out all the variations allowing for rounding off (ie crown could actually be 15.16-15.24 and table 55.06-55.14). The extreme measurements are 34.00-34.19. Has Carolyn just typed in the wrong numbers? The formula is definitely correct.

I was also surprised to see so much difference between GIA and Sarin specifications (61 compared to 61.4 for depth and 55.1 compared to 56 for table). Can anyone explain this?

#### Carolynw

##### Shiny_Rock
Ill type it again.
OGI

depth 61.0%
crown 34.6 ' 15.2 %
pavil. 40.9 ' 43.0%
table 4.12 mm 55.1%
cutlet 0.9%
girdle 1.4%

Not sure if i typed it wrong before.
Is there something wrong with this OGI report, is
it not accurate?

#### Richard Sherwood

##### Ideal_Rock
Sarin and OGI machines measure the angles and estimate the distances (percentages).

Sometimes the percentages will be slightly off, while the angles are usually more accurate.

This shows up when you compare a Sarin/OGI report with a GIA report, in which the distances were obtained through direct measurement (GIA), instead of distance measurement estimation after computation and extrapolation of angles (OGI/Sarin). Usually the GIA estimate for a table percentage, for example, is more accurate than a Sarin's or OGI's estimate.

The Sarin/OGI's are more accurate where it really counts though, in the measurements of the crown/pavilion angle, whose relationship is the primary determing factor of the brilliance of a diamond.

In the later Sarin/OGI models this is not as much of a problem, as the photo resolution has increased, allowing for even more accurate measurements. I've just ordered one of these hummers (the OGI Novascope), and am looking forward to see if it performs as well as the Israelis are claiming. It measures and reports all the minor facets as well.

#### Garry H (Cut Nut)

##### Super_Ideal_Rock
oh Rich you should have talked to me first.

Ogi does not work with any octoNus products - did you know that?

There are things happening....

#### Garry H (Cut Nut)

##### Super_Ideal_Rock
Angela the least accurate scan measurements are table size (also always rounded to whole #'s) and culat size.

Therefore reliance on conerting % to angles is not something I would advise anyone do other than to deciide if a stone warrants further investigation.

Presumably the need is for entering into HCA - the calculator does it for you - but typically there is about a 0.15 degree understatement of pavilion angle because most scans miss the culet. This can have devestating impact on HCA scores.

#### asblackrock

##### Shiny_Rock
Hi Carolyn
As far as I can see, something is definitely not quite right with the diamond’s OGI specifications. For the crown angle to be 34.6 degrees, the table calculates 55.9 (this would tie in much better to the GIA specification of 56). If OGI "measures the angles and estimate the distances" surely the would have estimated 55.9, not 55.1. Maybe Rich can comment on this.

BUT, having said this, I don't think this actually makes any difference. I have entered the specifications of your stone in the HCA (Holloway Cut Adviser) found in this website. The score is EXACTLY the same for table % of 55.1 and 55.9. I quote:

"Light Return Excellent
Fire Excellent
Scintillation Very Good
Spread or diameter for weight Very Good
Total Visual Performance 1.5 - Excellent

A score below 2 (Excellent) means you have eliminated known poor performers (more than 95% of all diamonds).

Even though HCA grades cut more effectively than systems like the AGS, it does not yet factor in symmetry and minor facets. Having found a diamond that scores well, you should employ an expert appraiser to examine the stone. If you decide not to, then at least compare the diamond to others and/or view it through an ideal-scope."

I am no expert, but your stone sounds fantastic. It's specificatons fall within the "ideal" range, its polish and symmetry are excellent and the HCA score is excellent. The only factor you do not mention is fluorescence. With a colour of E, strong fluorescence would make your diamond look slightly milky in natural light.

I would certainly be very happy with this diamond's cut (I am currently looking for 3 similar, but smaller diamonds for an eternity ring), but would personally still want to examine it with an ideal-scope.

#### Garry H (Cut Nut)

##### Super_Ideal_Rock
Angela be careful please. A little bit of knowledge!

Strong or even Very Strong Fluoro makes so few diamonds milky that GIA when they tried to include this issue in a major study they conducted in 1997, could not find enough milky stones (one of each color) with which to conduct a survey.
Milky stones are incredibly rare.

Many years ago DEF type colors with strong blue were called Blue White diamonds and fetched a high premium.

#### asblackrock

##### Shiny_Rock
Garry
I am sorry if I have provided incorrect advice. Perhaps you should modify your tutorial in Pricescope’s Knowledge section, so that novices like me are not confused. Your tutorial states:

“If a diamond has extremely strong flourescence it can appear oily or cloudy, and this is not good.
Another reason the trade discounts flourescent diamonds is that some laboratories use grading lights that emit a small amount of ultra violet light. This means lower grade blue flourescent diamonds are possibly assigned a better grade than they should.
Our advice is to stay away from very strong blues unless you can actually compare them side by side with non-fluorescent diamonds in shaded daylight.”

Another internet tutorial writes: “Medium to strong blue fluorescence in a diamond of D-H color may cause a foggy or milky quality in daylight with high UV lighting conditions. “

Although from what I have read it seems fluorescence improves the look of many diamonds, it degrades others. Rightly or wrongly the trade currently values most diamonds with clarity D-F less if they exhibit strong fluorescence. Surely it is necessary information to have when appraising a stone.

I would appreciate your comments on this, as it will only help to advance my self confessed limited knowledge.

#### Garry H (Cut Nut)

##### Super_Ideal_Rock
The tut says Extremely strong - the enquiry mentioned a strong, but not Very strong fluoro.

We are reviewing the tutorial at the moment and I will take that on board thanks Angela

#### Skip

##### Rough_Rock
Hello. Can someone tell me the crown angle for this diamond. I don't have a calculator with "tan" buttons.

Total depth 61.6
Table width 59
crown height 13
pavillion depth 44

Thanks in advance for the help.

#### oldminer

##### Ideal_Rock
Angela;

Diamond dealer, by the very nature of our business need to somehwat imitate horse traders, used car sellers, and arab bazaar hustlers. We aren't all that bad a group, but bartering and haggling are part of this business.

Any and all actual or perceived detriments, important or not, are to be haggled over. Ultimately, a diamond with any comment such as fluorescence, cloud, pinpoints, etc has a point over which a buyer and a seller can argue and bicker. It does not really matter if the fluorescence is visible, as the seller will insist it isn't and the buyer will insist he sees something apparent. The same with any other "fault", important or totally unimportant.

The most valuable diamonds have no arguing points. Any that have an issue are subjected to in depth quibbling. It is a natural part of the diamond game.

#### Garry H (Cut Nut)

##### Super_Ideal_Rock
----------------
On 10/25/2004 1:11:25 PM Skip wrote:

Hello. Can someone tell me the crown angle for this diamond. I don't have a calculator with 'tan' buttons.

Total depth 61.6
Table width 59
crown height 13
pavillion depth 44

Thanks in advance for the help.----------------

This is an excellent example of why people should not use this method.
The %'s are rounded - the table size is 58.5 to 59.4% and the crown height is 12.5 to 13.4%.
This gives a range of crown angle possabilities of 31 to 33.4 degrees.
But the stone is a possible stone for further consideration according to HCA because the ddp pavilion counteracts the shallow crown - it could be wort calling in

#### asblackrock

##### Shiny_Rock
Garry is correct. If both the table % and crown height% have been rounded off, the range of crown angles possible is 31.1 - 33.4. In the absence of any other information it does, however, at least still tell you that the crown angle is reasonably shallow.

Garry has, however opened up a can of worms. If figures are rounded off and only crown height% and pavilion depth% are given, in my opinion there is not enough information to use the HCA calculator at all.

For the figures given by Skip above, if the culet is 0, the measurements could actually be:
Table% 58.5, Crown height %12.5, Pav depth% 43.6, with a resulting HCA score of 1.6
or Table% 59.4, Crown height %13.4, Pav depth% 44.4, with a resulting HCA score of 5.1.
This does not even allow for errors induced in rounding off the Depth% and Culet% to within 0.1.

An actual HCA score of anywhere between 1.6 and 5.1 for the above stone is wildly inaccurate.

The HCA states: “Select angles or depth % for Crown and Pavilion”. Although it is followed by “Angles are more accurate”, I could not access the information. No words of warning are given about the possibility of figures for Total depth% and Table% and Culet% also being rounded off on certificates and the further errors that this introduces.

It is of great concern to me that decisions on diamond purchase could be made based on a possibly inaccurate HCA score if only crown height% and pavilion depth% are used. The HCA states “We recommend you use the Holloway Cut Adviser as a final check on your selection.” I think this should only be done if you have very accurate information. Even with accurate data to within 0.1 degrees, with every score given it should include a +/- figure to allow rounding off of all 5 figures entered.

Users beware.