Calculating Proportions

Unfortunately some dealers find it necessary to describe their diamonds as having “really nice make, fine make or excellent ideal proportions” when they’re not even close to being in the ideal range. Fortunately, Pandora managed to slam the lid shut before “Hope” escaped. No, not the Hope Diamond, just plain old Hope. Even though many diamond grading reports don’t provide you with all of the measurements necessary to determine the overall cut rating of a diamond, it’s not too late to save yourself from the perils of purchasing a poorly cut diamond that you thought was ideal. Be the first kid on your block to figure this stuff out!

This article contains the “Secret Sauce” of the McDiamond Industry! It’s your recipe for success in your attempt to whip up a spectacular diamond for your bride. Heck, if you’re a quick study, you might even be able to hold your own in a room full of jewelers! The first thing to remember is that the only way to accurately determine the overall proportions rating of a diamond is to know all of the factors which contribute to the score, the necessary parts to know are the Measurements (the minimum / maximum diameter and overall depth); the Table Diameter; the Total Depth; the Crown Angle; the Pavilion Angle (the most critical factor); the Girdle Thickness; and the Culet Size. With that in mind, let’s play!

Lab Graded Diamonds – Act One – Scene One:
Character: An analytical type
(i.e. Mathematician, Engineer, Computer Programmer, Geek, etc.)
To be read: Slowly and without feeling.

A common misconception amongst the public is the belief that if you purchase a “certified diamond” that you are getting a “quality diamond” and that’s not always the case. The reality is that a diamond grading report issued by a gemological laboratory is merely than an evaluation of the diamonds’ characteristics. A diamond grading report is not a “certification” of quality and if you read the disclaimer on the back of one of those reports that will become quite clear. The characteristics of a lab graded diamond can be good or bad, the presence of a lab report merely reflects the sellers’ willingness to pay for a report to be issued. The diamond grading laboratories will issue a report on a chunk of frozen spit, but who’s going to know it’s a piece of garbage if they can’t decipher the report?

The secret to buying a lab graded diamond is to be able to comprehend what each of the factors that contributes to the diamond as a whole. A basic understanding of the common 4C’s (Cut, Color, Clarity and Carat weight) is an absolute must. Unfortunately, many diamond grading reports do not provide complete information pertaining to the proportions of the diamond and thus you are missing several pieces of the puzzle. To complete the picture, you need to determine the table diameter, the total depth, the crown angle, the pavilion angle, girdle thickness, and the culet size.

But what do all those weird terms mean? What is a crown angle? And what does a diamonds table or culet size have to do with anything? Let’s start at the beginning by learning what each part of a diamond is called and the rest will unfold as we go.

The Modern Round Brilliant Cut Diamond

The modern round brilliant cut diamond has 58 facets separated into four basic sections known as the Crown, Girdle, Pavilion and Culet. The top portion or upper half of the diamond is called the Crown and consists of a large octagonal facet called a Table, which is surrounded by eight triangular shaped Star Facets which point downward towards the edge of the diamond; eight kite shaped Bezel Facets which radiate from the table corners to the girdle edge; and sixteen triangular shaped Upper Girdle Facets which are arranged in pairs that circle the perimeter of the crown.

The GIRDLE is the edge of the stone that rests between the upper and lower portions of the diamond. It is not to be confused with what your grandmother wears to separate her upper and lower proportions. A properly cut girdle on a diamond resembles symmetrical ocean waves that have been drawn right side up and upside down on top of each other. And no, we’re not going to further explore grandmas proportions because she’s already irritated enough – yea, we got the flaming email pertaining to our inappropriate discussion of girdles. We care. Of course we care, we’re just impertinent. Our Grammy taught us that word…

The lower portion (bottom half) of a diamond is called the Pavilion. A small facet located on the bottom of the diamond is called the Culet and finishes off what would otherwise be a sharp and brittle point. From the culet, there are eight elongated, kite shaped facets called Pavilion Mains which radiate up towards the girdles’ edge. Between each pavilion main is 1 of 16 elongated, triangular Lower Girdle Facets which are arranged in pairs.

Table Diameter:

The table facet on a round brilliant cut diamond is the large flat facet located at the top of the diamond and is pictured here with light blue arrows that we have placed on it for your viewing pleasure. The expression “Table Diameter” or “Table Width” represents the size of the diamonds’ table in relative proportion to the overall size of the stone. It is usually expressed as a percentage of the girdle diameter, such as “55% Table” which by the way is what is actually pictured here on a 1.023 carat stone. Don’t you just love the subtle accuracies of modern ray tracing software?

To calculate the table percentage of a round brilliant cut diamond, measure the minimum and maximum outer girdle diameters and the four corner-to-corner table diameters (shown here with lovely blue arrows). Then divide the longest table diameter by the average girdle diameter, and multiply the quotient by one hundred.

Say what? Okay, in English… If the diamond measures 6.48 x 6.53 millimeters in diameter with a depth of 4.00 millimeters and its largest Table Diameter is 3.58 mm, then:

Average Diameter = (6.48 + 6.53) ÷ 2 = 6.505 mm which is the average outside diameter.

Table Percentage = (3.58 table diameter divided by average outside diameter 6.505) = 0.5503458 × 100 = 55.03% which you would round off to a 55% table percentage. The table percentage is always rounded to the nearest whole percent. Of course you might have more luck plucking a piece of lint out of the crack of a refrigerator repairman (with your tweezers and rubber gloves) than you’ll have getting a jeweler to surrender his precious micrometer or StableTM Gauge if he senses that you’re an analytical soul on a quest for precision and thus you’ll find it more than a little challenging to complete this computation. Thankfully determining the table diameter of any lab graded diamond is as easy as looking at the diagram on the lab report. You’ll find that most of the round brilliant cut diamonds being sold have table diameters between 55 to 65% however the acceptable range for a true ideal cut diamond is between 52.4 to 57.5%. Too large of a table tends to create an imbalance in a diamonds’ scintillation by creating a flash that overpowers the reflections from other facets. Large tables outside of the ideal range also tend to reduce the dispersion of light.

To calculate the table percentage of a fancy shape diamond simply divide the width of the table by the width of the stone and multiply the resulting quotient by 100. Note: table diameters of fancy shape diamonds are measured at the widest point of the table in the same direction of their widths.

Total Depth:

To determine the total depth of a round brilliant cut diamond, simply divide its’ depth [measured from the top of the table to the culet - the bottom point] by its’ average girdle diameter. In other words, determine the average diameter as in the example provided above for determining table size and then divide the measurement from the top to the bottom of the stone by that number. Although the AGS Proportions Scale does not indicate a range for total depth, we prefer a total depth between 59 – 61.8% and will consider diamonds with a total depth up to 62% if the critical Crown and Pavilion angles are tight.

Crown Angle:

The Crown Angle is determined by viewing the diamond from a side profile and visually estimating the angle of the top portion of the diamond. We realize that visual estimation seems rather unscientific, but that’s how the majority of our industry does it. Remarkably with practice, most experienced graders evolve to a level where they are accurate within one or two percent.

Gently set the diamond in a pair of locking tweezers so that it is held by the table facet and culet so that you can view the diamond from its side. Place a flat object against the tweezers tips and estimate the angle of the crown (top half of diamond) as it relates to the edge of the pointer (see arrow – left). In this case, the diamond has a crown angle of 32 degrees (actual Sarin measurement) which would result in an overall proportions rating of no higher than AGS-3 Good on the AGS Proportions Scale. By the way, this is not the diamond that we used to create the charts used in the previous examples. Be very careful when setting the diamond in the tweezers because it is possible to chip the culet if the diamond is handled improperly!

Estimating crown angle from the profile view is similar to looking at various drafting triangles. Remember that a right angle is 90 degrees, half is 45 degrees, and one-third is 30 degrees. You can compare other angles to these convenient references. A 25 degree crown angle, for example, is slightly shallower than one-third of a right angle, and a 34 degree crown angle is slightly steeper. If this doesn’t make you appreciate our Sarin machine, we don’t know what will.

Most diamonds have crown angles between 30 and 35 degrees; if they are shallower than 30 degrees they will look flat and there may be a noticeable loss of fire even though the stone may appear to be quite brilliant. The crown angle measurement for an ideal cut diamond [AGS-0] must be between 33.7 and 35.8 degrees with our preference falling between 34.3 and 34.8 degrees. And yes, 34.5 degrees is right on the money but is difficult to find. But we’d like to mention that a steeper crown angle of 35.3 degrees is perfectly acceptable if the pavilion angle of the diamond is on the shallower side of 40.4 – 40.6 degrees.

Now if the little engineer side of your brain is screaming “That’s the stupidest, most antiquated system of measurement that I’ve ever heard of there should be a machine to do that!” then we’re right there with you. And that’s why when we had our jewelry store, we purchased a $45,000.00 Sarin DiaMension computerized proportions analysis system. Both the GIA and AGS use this type of technology to measure the diamonds that they evaluate and we figured if it’s good enough for them, then it’s good enough for us. The Sarin spins the diamond around in a computerized chamber and spits out a full page report and 3D computerized model indicating the measurements, angles and degrees of the primary diamond facets in facet-by-facet format.

The Sarin machine is so accurate that if there is dust or lint on the stone it will stop its analysis and say something rude like “dirt on facet seven”… Like we’re really going to be able to figure out which friggin’ facet that is. So back to the cleaner we go and yes, something as subtle as a fingerprint is enough to tilt our favorite toy into a refusal to perform due to unsanitary conditions. Many times throughout the day you could hear little voices from our diamond grading room singing the Sarin Song “blip! blip! blip! dirt on facet four my @ss!!! I’ll give you dirt on facet four!!!” followed by the stomp of little footsteps wandering off to the cleaning unit. Ah, the brilliant sound of perfection! You’ll be happy to know that most of the vendors we work with today also have a Sarin or equivalent in their diamond grading room and will be happy to answer all of your questions.

Assuming that you’re not chomping at the bit to plunk down a wad of cash on a computerized chamber that you can’t use to surf the internet, here’s how you can visually estimate a diamonds’ crown angle the prehistoric way, but we recommend that you obtain a Sarin or OGI computerized proportions analysis on the diamond you are buying from the seller because the results are a lot more accurate than what we described previously.

Girdle Thickness:

Remember, the girdle is the edge of the stone located in the middle of the diamond between the crown (top half) and the pavilion (lower half). It is the edge of the stone that the prongs hold; it needs to be just thick enough to let the stone be set securely. If it is extremely thin (less than 0.6%), it may be easily chipped or damaged. If it is extremely thick, it can be unattractive and difficult to set. The girdle edge of a diamond can be faceted or unfaceted, it may be polished or unpolished which will formally be referred to as a bruted girdle. The girdle edge should appear to be a thin to medium straight line with symmetrical peaks and valleys (like ocean waves). On poorly cut diamonds the girdle edge will not be straight, might appear to be wavy, or have areas that range from extremely thin to extremely thick. An extremely thick girdle often creates large, fuzzy, gray reflections in the diamond, and has a greater tendency to accumulate dirt and grime. An extremely thick girdle also has a tendency to make grandma appear lumpy in all the wrong places, while clearly separating the upper and lower halves, enjoy the correlation.

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Pavilion Depth Percentage:

A diamonds’ brilliance is largely determined by its’ pavilion angle which is expressed by most of the trade as the pavilion depth percentage, which is the distance from the girdle plane to the culet expressed as a percentage of girdle diameter. Diamond cutters judge the pavilion angle, the angle between the pavilion mains and the girdle plane, the steeper the angle the greater the depth percentage.

The difference between Pavilion Angle and Pavilion Depth Percentage is an important point to understand. The Sarin and OGI computerized proportions analysis machines actually measure the Crown and Pavilion Angle measurements, but they estimate the Depth Percentage measurements based on the angle measurements and the other factors of the diamond. Since the depth measurements are estimates based upon the actual angle measurements, you should focus on the angle measurements when selecting a diamond and pay no attention to the depth measurements for Crown Height and Pavilion Depth.

Most “experts” agree that for round brilliant cut diamonds a pavilion depth between 43 – 44% is optimum, although the percentage can vary slightly because the crown angle and table size also affect a diamonds’ brilliance. The accepted range for pavilion depth of a round brilliant ideal cut diamond is between 42.2% and 43.8%. In terms of Pavilion Angle (the accurate measurement) we prefer that the measurement be between 40.6 – 40.9 degrees – remember to think in terms of degrees and not percentage! It is important to note that other pavilion angles are acceptable, as stated previously on this page, a shallower pavilion angle of say 40.4 – 40.5 degrees may go well with a steeper crown angle and a steeper pavilion angle of say 41.2 degrees may go well with a shallower crown angle. A round brilliant cut diamond that displays an unattractive white ring along the girdle edge would probably have a pavilion depth of 35 – 38%. The white ring is called a “fish eye” and is a good indication that a diamond has been poorly cut and is too shallow. A pavilion depth of 49 – 51% might cause the table area and star facets to be dark and lifeless, this is referred to as a “nail head” and is also an indication that a diamond has been poorly cut and is too deep.

Although pavilion depth percentages can be measured and calculated, it is usually done visually, or by placing a pointer on the culet and judging the distance of the reflection between the culet and table corner as viewed from the top of the stone. This one takes a lot of practice, and is usually best left for the experts. Once again, this is where a Sarin or OGI machine comes to the rescue and takes the guess work out of the puppy on the pedestal.

Culet Size:

The culet is the bottom point of a round brilliant cut diamond, it is the last facet put on a stone. Culet size is another factor that has traditionally been visually estimated, but which is more accurately determined by Sarin Analysis. Doing it visually…. When you look down through the diamonds’ table (top flat facet) you will see that all of the facets travel down to a center point, this is the culet. Ideally, the culet will come to a fine or medium point. A large culet can often be seen through the table without magnification and is not considered to be attractive. Our preference for culet size is “pointed” or “very small” if you are considering a diamond graded by the AGS Laboratory and “none” or “very small” if you are considering a diamond graded by the GIA Laboratory. The terms “pointed” and “none” are synonymous and the difference is merely a matter of semantics as used by the two laboratories. The AGS Laboratory used the term “none” until a few years ago when the Board of Directors determined that the term “pointed” was more accurate because there is always technically a culet facet and therefore they consider the term “none” to be inaccurate. By the way, culet is pronounced Q-Let, it is not a steak cutlet and it’s a dead giveaway to the clerk at the jewelry store that you have no clue what you’re talking about if you refer to it as one.

Symmetry:

For round diamonds symmetry is the difference between one that looks round like a properly formed circle, and one that looks like a flat tire. With a fancy shape diamond, symmetry is about making sure that opposite sides of a diamond complement each other in shape. In technical terms, it’s the equality between corresponding parts of the diamond. Basically, does the left cleft of a heart shape diamond match the right, or is one side nicely rounded while the other is straight and sharp?

Understand that there are no perfectly round diamonds. However a round brilliant cut diamond with an outside diameter (measurements) of 6.10 – 6.15 millimeters would appear to be round while one that measured 5.80 – 6.20 mm would look more like an oval or out-of-round like a flat tire. With round brilliant cut diamonds our preference is that the outside diameter of the diamond be within 10/100th’s of a millimeter, so an outside diameter of 6.55 – 6.65 would be on the edge of being acceptable but 6.55 – 6.66 would not be acceptable. Obviously a smaller difference between the minimum and maximum measurements is preferable, but don’t expect to find a diamond that is perfectly round because they simply don’t exist in the real world.

Other factors of symmetry are not as easy to detect, but include characteristics such as facets which are misaligned; facets which fail to point properly; misshapen facets; table facets which are noticeably misaligned off of the culet (they are always a little off center but should not be extremely off center); table facets which are not parallel to the girdle planes; wavy girdles (where the girdle edge resembles the edge of a warped record). In addition to these, a fancy shape diamond might also have uneven corners and sides; on emerald cuts, sides that are not parallel; uneven wings on pears, marquises, and hearts; uneven lobes on hearts; uneven shoulders on pears and ovals; off-center keel lines; culets which are too high or too low in pears and hearts.

So what is symmetry? It’s a matter of semantics, a desperate female might try to convince her mate that symmetry is having a one carat diamond on her hand, a one carat diamond on her other hand, a one carat diamond in each ear, and a one carat diamond on her neck… Thus she’s perfectly symmetrical, i.e. perfectly “balanced” and if this scenario happens to describe the woman that you’re about to marry, then we’re about to become your new best friend. Look no further, you’ve found the perfect woman! With regards to the symmetry of a diamond, we recommend that you leave the evaluation of symmetry up to the labs and shoot for either AGS Ideal or GIA Excellent.

Girdle Outline (fancy shapes only):

Round brilliant cut diamonds are supposed to be round, so it should not be necessary to judge the relative attractiveness of their shape or girdle outline. However, not all fancy shape diamonds are equally attractive. Some outlines of fancy shape diamonds are simply not attractive. This is not to say that some fancy shapes are not attractive, but that the outline variations of a particular shape might not be. For instance, some oval shape diamonds look like ovals and others look like a rectangular shape diamond with blocky rounded corners. Obviously this portion of diamond grading is judged visually and is subjective to what your personal preferences are.

However, it is generally agreed upon that the heads of pears and the ends of ovals should be pleasingly rounded and not blocky or flat topped. Likewise, shoulders on pears, ovals, and heart shapes should be gently but distinctly and evenly rounded, they should not appear to be blocky, squashed, or flat-topped. The sides, or wings, of marquises, pears, ovals, and hearts, should curve in attractive arches. If they are too flat, they tend to make the diamond look top-heavy or wide bellied.

The Length-To-Width Ratio (fancy shape diamonds only):

The appeal of a fancy shape diamond is also affected by its length-to-width ratio. Some length-to-width ratios are more pleasing visually and psychologically than others. These vary depending on a diamonds’ shape, but if standard head sizes are any indication, the most popular length-to-width ratio’s are as follows:

* Marquises between 1.75 and 2.25 to 1.00
* Ovals between 1.33 and 1.66 to 1.00
* Emerald cuts, rectangular cushions, and pears falling somewhere between 1.50 and 1.75 to 1.00
* Hearts seem to look best as close to 1.00:1.00 as you can get.

Calculating the length-to-width ratio of a fancy shape diamond is relatively easy, simply divide the length by the width. Example: if a diamonds’ length = 7.53 mm and its’ width = 5.43 mm, then divide 7.53 by 5.43 = 1.39 to 1.00 or 1.39:1.00

Now Kids, Be Nice…

Remember that not everybody cares about the degrees and angles of your diamond quest as much as you engineer types and ourselves do. Don’t expect your local jeweler to be a walking, talking, diamond dictionary, with the ability to spout mathematical prose at your every whim. Some will… Some won’t… You may find this amazing, but even we have to look up stuff from time to time! It’s true. No seriously, it’s true. Whatever you do, don’t let this newly acquired information swell your head to dangerous proportions that will spark another fight on the playground. Not every jeweler is geared up for the challenge and you don’t want to get thrown out of the jewelry store again do you? There’s nothing worse than an over-excited, newly-educated, analytical (or was that anal?) incredibly zealous diamond buyer, who doesn’t know better than to try to teach their jeweler how to calculate a diamonds’ proportions! Of course, a few of you naughty pranksters have told us that it makes an entertaining field trip and that you delighted in going from store to store and collecting the heads of jewelers for your trophy wall. We however suggest you exercise (a little, very little) restraint when on Safari because a lot of jewelers happen to be armed.

Some jewelers sell diamonds based on beauty alone, others sell diamonds based on their properties. Whether you’re a flower child or an analytical, we strongly suggest you find a jeweler you can identify with. You know, one that speaks your language. God help us, we speak Netite.

We’ve shared this “top secret” industry insider information with you so that you might better understand how a diamonds’ proportions and cut rating are determined. Now you can determine for yourself whether a diamond is exceptionally cut or has the refractive properties of frozen spit which is the technical term for a diamond with a clarity grade of I-3 and below… Seriously.

On a final note, keep in mind that a lot of this is a matter of personal taste, unless of course, you’re an engineer, software specialist, architect, accountant, genius, or proctologist. In which case, you won’t be able to function or sleep at night until we’ve found you a diamond with precise proportions with a Three Dimensional Sarin Report to prove our assessment of perfection. Lucky for you, we specialize in locating hard to find ideal cut puppies and work closely with a select group of vendors who hand select their diamonds for maximum visual performance. Want us to give the diamond details page a once over for you using a professional set of eyes? Just ask.

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