Before you delve into this document, which is an extensive discussion of a layperson's guide to assesing the round brilliant diamond cut, you should read the excellent diamond FAQ's written by Jim Kokernak and Peter Mlynek. It will also help to know how the various diamond terms and measurements are defined.
In my opinion, the optical properties of a round brilliant cut diamond are its most important characteristic. Unfortunately however, unlike clarity, color and carat weight, there are no commonly used simple gradings of cut. This doesn't mean that you can't tell how well cut a particular stone is; this document is an effort to help others who are concerned about the cut of their stones to know what to look for.
There are two mutually complementary ways in which the quality of the cut can be evaluated.
I will first describe the mathematical model of an ideally cut round brilliant diamond and then how to judge the quality of the cut by looking at the stone. I strongly recommend the later method for purposes of diamond selection. While it is helpful to know about the ideal angles and sizes so that they can be discussed and used as potential benchmarks, diamond cutting is as much an art as it is a science. I am now of the opinion (I didn't used to be of this opinion) that attempting to buy a diamond solely on the basis of its numbers without either you personally or a qualified gemologist actually looking at the stone to see how it "faces up" is a foolish enterprise. It will be helpful to keep that in mind.
One other issue with diamonds is whether the stone has a "certificate" (a 'certed' stone) or not. The "cert" is a piece of paper issued by a (hopefully) major gemological laboratory such as the GIA, EGL etc. The cert will list the stone's weight in carats, its color and clarity grades, and some physical measurements of the stone. There will also be a map of the nature and location of the various inclusions that the stone might have. Don't get all wrapped up in the stats listed on the cert in an effort to judge cut. To my mind, by far the most useful feature of the cert is the physical map of the inclusions of the stone. Since these are unique to each stone (with the exception of flawless stones which don't have inclusions) the cert can be used to positively identify your particular stone. Having a cert thus means that you will always be able to verify that the stone you have is the same one you initially bought. For this reason only, I recommend getting certed stones. Some words of caution: the color and clarity grades listed on a cert are not absolutes. They are the composite opinions of the humans at the lab that looked at the stone. It is normal and reasonable to expect that a stone could be re-evaluated to plus or minus one grade. Thus, unless your stone is evaluated as radically different from the cert grading (such as SI2 clarity when it was certed VS1) you have no cause for concern should there be a minor difference of opinion.
The first consideration is the degree of symmetry of the cut. If the diamond is not cut with reasonably good symmetry, then the mathematical dimensions lose their meaning and you have to judge by eye. The easy way to tell how symmetrical the cut is, is to read the symmetry grade right off the stone's certificate. The rest of this discussion will assume at least good symmetry.
The main optical purpose to the round brilliant cut is to reflect as much light as possible. There is one, and only one, dimension which affects this characteristic, although there are two measurements which can describe it: pavilion angle and/or pavilion depth. The pavilion angle is the angle made by the girdle and the pavilion facets. Its ideal measure is 40.75 degrees. Note that this could also be specified as pavilion depth, since tan(pavilion angle)=2x(pavilion depth). From this we can see that a pavilion depth of 43.1% will give you the optimal pavilion angle. A well-done pavilion will take the light that enters the top of the stone, and reflect it twice so that it exits the top of the stone with a slightly altered path. This altered path means that light which entered through crown facets will be reflected out through the table. It will also take some of the light which entered through the outer part of the table and reflect it back out the crown facets. Both of these will contribute to the "fire" or "dispersion" of the stone, that is, the refracted spectral colors you see coming off a diamond. The light that enters through the inner part of the table will be reflected back out the table. This light will be refracted only to a small degree and will thus be approximately the color it was when it entered the stone. This light gives the stone its "brilliance".
So you can see just how important pavilion angle/depth is. If the pavilion angle is too large (which would give a larger pavilion depth as well), light will make the first reflection, but will then leave the stone instead of making the second reflection. These stones will appear dark. If the pavilion angle is too small (which would give a smaller pavilion depth as well), light will not make even the first reflection and will simply pass directly through the stone. These stones will appear "watery". In the extreme, a deeply cut pavilion will make the table look black: a nailhead stone. An extremely shallow pavilion will reflect the girdle back out the table. Since the girdle is typically frosted in appearance, you will see a whitish donut figure through the table. Such stones are called "fisheyes".
Next in importance is the crown angle. The crown angle is the angle between the girdle and the bezel (also called kite) facets of the crown. Ideally it will be 34.5 degrees. Note that the crown angle can also be derived from the table and crown height of the stone. The formula for this is: tan(crown angle)=2x(crown height)/(1-table). The crown facets are what create the "fire" or "dispersion" of the stone, since light will enter/exit the stone through the crown facets at an oblique angle and thus be refracted. If the crown angle is too shallow, the light will not be refracted as much, and although the total amount of light will be the same, the dispersion will be less. Shallow crown angles thus trade dispersion for brilliance. A shallow crown angle can also potentially mean that the girdle becomes sharper. This sharper girdle can increase the fragility of the stone. The other consideration is the physical size of the crown facets. A diamond with a 53% table and crown angles of 34.5 degrees will have 50% dispersion and 50% brilliance. If the table is cut larger than 53%, it is possible to maintain the ideal crown angle by shortening the crown facets. This would occur for example if you took an "ideal" cut diamond and then made another cut, parallel to the table, slightly under the table, while maintaining the relative proportions of the crown facets. The crown angles would be the same, the new table would be larger and the crown facets would be shorter. Doing this will make the stone appear larger (since people mainly notice the table size) and will trade dispersion for brilliance. Total light reflected will be the same. The last possibility is that the crown angles are too steep. Making the crown angles too steep, like making the pavilion too deep, is a way to keep the weight of the finished cut stone up. Although increasing the crown angle will lead to greater dispersion of the light that is refracted through it, if the crown angle is too steep, light will tend to reflect off the external surface of the stone rather than entering the stone. This effective light loss will reduce the fire of the stone. Since brilliance comes from light which both enters and exits through the table, brilliance will not be affected by steep crown angles.
The final consideration is table size. The larger the table, the larger the stone will appear to look. For this reason, tables are commonly cut larger than 53%. Note that increasing the size of the table must either steepen the crown angles or make the crown facets shorter. In either case, fire is traded for brilliance. Be aware however that having a larger table, so long as the crown angle is maintained, is not necessarily a negative thing; the stone will be just as bright, however it will be more "white" with less flashes of color. Some people like this. Many people also like the larger appearance of the stone. Making the table larger, while maintaining crown angles, will also make the stone weigh less. Since stones are sold by weight, you can potentially save a lot of money this way. If you get a stone with a larger table and want to maximize dispersion, simply make sure that the crown angles are still near 34.5 degrees. A stone with a 65% table, which has crown angles of 34.5 degrees and pavilion angles of 40.75 degrees will look bright, white, and larger than its weight would suggest: a very nice stone.
The main problem with assessing the cut of a stone by its measurements is that you don't have critical information you need. A GIA certificate will tell you the table% and the total depth% and that's all. It's not enough information. You will hear that the ideal depth% is 59.3%. This is true, but what is really important is how that 59.3% is broken down into pavilion and crown heights. Also, this 59.3% figure does not include the thickness of the girdle. Note that the total depth of the stone = (crown height)+(girdle thickness)+(pavilion depth). For the measurements to describe the stone, you need to know pavilion depth (absolutely crucial), and crown height (less crucial). The certificate will supply neither of these measurements. Also, the 59.3% is the optimal overall depth only for stones with tables of 53%. Let's use our 65% table, ideal angle stone from the above example. Pavilion depth should be 43.1% (not a function of table size). The crown height should be 12% in order to have 34.5 degree crown angles. The overall depth of this stone should thus be 43.1+12+(girdle thickness). Say the girdle is 1%, then this stone's overall depth should be 56.1%, considerably less than the 59.3% you would want with a 53% table stone. Again note that even if you got a certificate which said "table: 65%, depth 56.1%", you still have no idea how this stone is cut. A real possibility would be that this stone is cut too deep in the pavilion, and too shallow in the crown, maintaining "ideal total depth", but dark, and dull nonetheless. Unless you can get the measurements you need:
the mathematical model of an ideal stone is not going to help you. You certainly will not get these measurements from a GIA certificate, although a competent gemologist should be able to measure these parameters for you.
This leads us to assessment method #2: How to judge the stone's optical properties by physical inspection. The disadvantage of this method is two-fold:
The overwhelming advantage of this method is that you get the bottom line. You care about how the stone looks, and you judge it by actually looking at it.
You will need a gemological microscope at 10x power. If your jeweler doesn't have one, find another jeweler. You will not be able to tell anything with a loupe. Mount the stone in the microscope. A loose stone is better, but you can still do this evaluation if the stone is set in a ring. Look straight down at the stone through the table. First, just look at the stone for a little while so your eyes get used to the microscope and you get comfortable with this stone. Now, inside the table you will see a smaller image of the table, which is the table reflected in the pavilion. This table reflection is absolutely crucial and will let you judge both the depth of the pavilion, and the symmetry of the pavilion cut. In a stone with an absolutely perfectly cut pavilion, you will see the reflection of the table, an octagon, one third the diameter of the actual table, centered in the stone. Note that no stone is cut perfectly, but this is what you are looking to see. If the pavilion is cut too deep, the table reflection will be larger than one third the size of the table. The perimeter of the table reflection will also appear dark, due to light lost through the pavilion. The larger the pavilion angles are out from the ideal 40.75 degrees, the larger and darker this table reflection will be. Ultimately, the table reflection would be completely dark and fill the table, yielding a black-looking stone. If the pavilion is cut too shallow, the table reflection will be smaller than one third of the table. The reflection will also appear dimmer (less well defined). This too is due to light losses through the pavilion. Ultimately, the table reflection will be so small and so dim as to disappear, and you might start to see the reflection of the girdle in really extreme cases: a fisheye stone. The size and darkness of the table reflection thus let you judge pavilion depth. How symmetrical the cut of the stone is will be shown by how regular the perimeter of the table reflection will be. In a stone with good symmetry, the table reflection will be octagonal or circular, with a smooth perimeter. Deviations from symmetry will show up as knifelike stabs through the perimeter of the table reflection into the center of the stone. A stone with bad pavilion symmetry will have a very disrupted and discontinuous perimeter to its table reflection. Note that the symmetry and depth can be evaluated independently. The size and darkness of the perimeter of the reflection will still indicate the pavilion depth, even in a cut with poor symmetry. Learn to look for, and to assess, the table reflection in the stone; a stone which has a table reflection with the desirable characteristics above (one third table size, regular perimeter, well defined, neither dark nor dim) is a well cut stone. As long as the rest of the stone is anywhere near reasonable, your stone is optically fine and will look great.
The second thing you can judge is table size and crown symmetry. Again, looking straight down at the stone through a microscope, look at the octagonal table. The star facets (also called upper crown facets) are triangular facets which have as one of their edges one of the octagonal edges of the table. The combination of the eight star facets and the table will appear to form two interlocked squares, each displaced from the other by a rotation of 45 degrees. In a stone with a good table size, these squares will appear to have edges that are either straight, or bow inwards (towards the center of the stone) slightly. Stones with tables that are larger than optimal will have the edges of these squares appear to bow outwards slightly. You can judge the symmetry of the crown by how regular these squares appear to be. Ignoring the curvature of the edges, are they really squares, or are they more like rectangles, or skewed squares? Judging the size of the table and the symmetry of the crown is much easier than judging the table reflection as described above, however, it is also less important.
In contrast to the pavilion depth, pavilion symmetry, table size and crown symmetry, each of which are fairly easy for the layperson who knows what to look for to judge, judging the crown angle by eye is considerably more subtle and difficult. It is also likely that if the cutter has taken sufficient care with the stone to make the pavilion, table and overall stone symmetry good, that he or she will also have taken care with the crown angles, so that you probably don't need to worry about the crown angle. For the sake of completeness though, here is what to look for to judge crown angle: The crown of the stone has 8 four-sided bezel facets. These correspond to the 8 four-sided pavilion main facets, and are aligned such that each bezel facet has a pavilion main facet which lies directly below it. You can, if you look closely, see a pavilion main facet if you look straight down through a crown bezel facet, "looking straight down" meaning perpendicular to the table, not the bezel facet. Since you are looking through a bezel facet at an angle, the appearance of the pavilion main facet will appear altered by refraction, in a way that it will not appear altered when looking at it through the table. It is this alteration due to refraction which reveals the crown angle. If the crown angle was 0 degrees, the pavilion main facets would appear the same when seen though the bezel facets and the table. As the crown angle increases in steepness, the appearance of these main pavilion facets seen through the bezel facets gets both shorter and wider. In a stone with crown angles near 34.5 degrees, the narrow angle subtended by the pavilion main facets as they approach the girdle will appear thickened enough to subtend twice the angle that they do when viewed through the table. A shallow crown will make this pavilion main facet angle look less than twice as large and more similar as seen through the bezel facets and the table. As the crown angle increases past 34.5 degrees, the appearance of the pavilion main facets through the bezel facets continues to get shorter and thicker; wider than twice the angle as when seen through the table. Eventually, the pavilion main facet will actually appear to become squarish and in really extreme cases, the pavilion facets will shorten up so much that you will be able to see the culet itself through the bezel facets -- 8 culet images. Again though, judging crown height is quite subtle as it is difficult to judge the size of the small angles involved by eye. For this reason, I recommend skipping this aspect of the evaluation and going directly to the ultimate visual test described below.
Really well cut stones are a rarity, a few percent of all cut stones at best, and probably less. Have your jeweler put a tray of cut stones before you, under any reasonable lighting conditions (best is white, bright, incandescent point-source lights at a distance -- the best I've ever seen was in a basketball stadium!). It doesn't really matter what the sizes of the stones are, although if they are all approximately the same size, it would be better. A really well cut stone will appear to jump right off the tray at you. You should have no trouble whatsoever in picking out the well-cut stone, so crucial is the cut to the appearance of the stone. If your stone passes this final test, buy it; you've found a winner. An anecdote: recently my fiancee and I went out, just for grins, to look at diamonds in a local mall jewelry chain store. We saw a tray of about 8 diamonds ranging in size from 0.25 carat up to and including two 0.50 carat stones. One of the 0.25 carat stones seemed to leap off the tray; there was no real contest. The half carat stones looked dull and boring compared to this quarter carat gem. Sure enough, when we looked at the stones under the microscope, this quarter carat, even though it showed significant inclusions and a large surface scratch on its table, had a table reflection and table/crown facet geometry characteristic of a well-cut stone. By contrast, all of the other stones showed problems: large, dark, choppy table reflections, skewed crown angles, poor symmetry in the pavilion and/or the crown. Your eyes really can judge! Educate yourself, educate your eyes, and you are fully equipped to judge the cut of a diamond.
The quality of the cut of a diamond is limited by both the skill and patience of the cutter. For this reason, most diamonds are more or less suboptimally cut. Cutters are paid for each stone cut. Since cut quality isn't currently strongly correlated to stone price, cutters are better off doing a poorer job on more stones. As mentioned before, diamond cutting has a considerable degree of artistry involved as well. Each stone is different, and each requires a different approach in order to maximize its beauty. Some cutters simply lack this artistic touch. The way diamonds are sold is also responsible for lowering the quality of the cut. Since stones are sold by weight, a cutter who makes the pavilion too deep, or the crown too high, or the girdle too thick, can keep more of the weight of the rough diamond in the finished product. There is also a temptation to cut stones that are too shallow in both the pavilion and crown. These so called "stretched" stones are an effort to make the stone look larger than it really is. If you hear of a stone that has a "one carat spread", that means that for the diameter of this stone, it should weigh one carat, and some people will try to sell it as if it weighed one carat, even though it doesn't and has sacrificed optical beauty to that effect. One last consideration is that the price of diamonds on a per carat basis takes large jumps at the one, two and three carat marks, and to a lesser extent at the 0.5 carat mark. This means that the stone will sell for significantly more if the cutter can just push the weight of the finished stone over one of these marks. For this reason, I would avoid stones with weights like 0.51 ct, 1.02 ct, 2.01 ct etc. Maybe the stone should have these weights, but it is more likely that rough that should have been taken off was left on solely to get these finished weights.
Your jeweler will probably have the (mainly black) brochure from DeBeers called "Quality and value. It's as important in diamonds as in anything else you own." On the inside is the heading "There's more to diamonds than meets the eye." and two pictures of diamonds shown at 10x power. Study these diamonds carefully. The one on the left is a very well cut diamond, and exhibits the diagnostic visual characteristics of a well cut diamond described above. The diamond on the right, by contrast, is a much poorer cut stone, and shows a large, dark rimmed, disrupted perimeter table reflection, and a table that is too large (although the crown symmetry is fine). Once you know what to look for, it will only take seconds for you to tell these otherwise outwardly similar stones apart.