The strip is longer than the stone
Wrapping a strip round a stone is the same bending problem as a ring shank. The inside of the strip compresses, the outside stretches, and the line that keeps its length runs through the middle of the metal. So the length to cut is:
strip = perimeter of the inside line + pi x bezel thickness
On 0.3 mm bezel that adds 0.94 mm. On 0.5 mm it adds 1.57 mm. Those are not large numbers, but they are the same size as the gap that makes a joint look bad, which is why the allowance is worth having rather than filing away at a strip that was cut to the wrong number in the first place.
The clearance goes in before the thickness allowance, because it enlarges the inside line. With the defaults on this page — a 10 mm round stone, 0.1 mm clearance all round, 0.3 mm bezel — the inside line is a 10.2 mm circle at 32.04 mm, the thickness adds 0.94 mm, and the strip is 32.99 mm.
Perimeters that are not circles
Round stones are a single multiplication. Ovals are not, because an ellipse has no closed-form perimeter. This page uses the Ramanujan approximation, which for the axis ratios ordinary cabochons come in is accurate to far better than the thickness of a saw blade:
p = pi x [ 3(a+b) - sqrt((3a+b)(a+3b)) ], with a and b the two semi-axes.
An 18 by 13 oval has semi-axes of 9 and 6.5, and that formula gives 49.01 mm. The lazy version, pi times the sum of the semi-axes, gives 48.69 — a third of a millimetre short, which is exactly the kind of error that shows at the joint.
Rectangles with rounded corners are four straight runs plus four quarter circles, which add up to one whole circle of the corner radius:
p = 2(L - 2r) + 2(W - 2r) + 2 pi r
And for anything irregular — a freeform slab, a piece of agate with a personality — a strip of paper wrapped round the seat line and measured flat beats every formula on this page. That is what the fourth shape option is for.
Height is two decisions, not one
A bezel has to do two things: clear the straight part of the stone before it starts to curve away, and then come over the top far enough to hold. Those are separate numbers and this page keeps them separate.
The first is measurable. Sit the stone on a flat surface and see where it stops being vertical. The second is a judgement about the dome, about how much of the stone you want visible, and about how much metal you fancy pushing over. A high dome takes more bezel to reach the same grip than a low one because it curves away faster, and a bezel that is too tall for the stone folds into pleats instead of laying down.
There is no formula for the second number that is worth trusting more than cutting a scrap and offering it up. What the page does instead is add whatever you enter to the measured part and tell you the total, so the strip gets cut once.
The backplate
The plate has to be at least the outside of the bezel, which is the stone plus two clearances plus two thicknesses. Whether it stands proud beyond that is a design decision — a visible margin reads as a frame, a flush one disappears. The page sizes it from whatever margin you enter and works out the area, which matters mostly because backplate is usually heavier stock than bezel and ends up being most of the weight of the setting.
With the defaults, the bezel strip is 33 mm by 3.6 mm of 0.3 mm stock, which is 0.37 g in sterling. The backplate is a 12.8 mm disc of 0.5 mm — the stone plus two clearances, two bezel thicknesses and two margins — which is 0.67 g. So the plate is nearly two thirds of the metal in the setting, and its share climbs as the stone gets bigger, because plate area goes with the square of the stone while the strip is only a perimeter times a height.
That does not mean the plate is always the thing to thin, which is the assumption worth checking rather than repeating. Taking 0.05 mm off each in turn, on the defaults here:
| Setting | Total | 0.05 mm off the plate | 0.05 mm off the bezel |
|---|---|---|---|
| 10 mm stone, 3.6 mm bezel | 1.036 g | saves 0.067 g | saves 0.074 g |
| 5 mm stone, 6.6 mm bezel | 0.602 g | saves 0.025 g | saves 0.068 g |
| 20 mm stone, 3.6 mm bezel | 2.836 g | saves 0.212 g | saves 0.141 g |
The plate holds most of the weight but the bezel wraps a long way round and is often the better place to take metal off, because the strip length is large next to the plate area on anything but a big stone. On a small stone with a tall bezel it is not close. Change the two numbers on the form and read both rows rather than working from a rule of thumb.
What this page cannot tell you
Whether a given clearance is right, whether a bezel of that height will lay down over that particular dome, and whether the metal is soft enough to push are all bench questions and they depend on the stone in front of you. Heat-sensitive stones, stones with cleavage, and anything that has been dyed or stabilised bring their own constraints that have nothing to do with the arithmetic here. The numbers get the strip cut once instead of three times; the rest is looking at the work.
Questions people ask
How long should a bezel strip be for a 10 mm round stone?
About 33 mm, using 0.3 mm bezel with 0.1 mm of clearance. That is a 10.2 mm inside circle at 32.04 mm, plus 0.94 mm for the thickness because the strip bends round its own middle rather than its inside face. Cut it to the bare 31.42 mm circumference of the stone and it comes up 1.57 mm short.
How do I work out the bezel length for an oval stone?
The Ramanujan ellipse approximation, then add pi times the bezel thickness. For an 18 by 13 oval the bare perimeter is 49.01 mm; add 0.1 mm of clearance all round and it is 49.64 mm, and with 0.3 mm bezel the strip is 50.58 mm. The rough version some people use, pi times the sum of the semi-axes, comes out a third of a millimetre short, which is visible at the joint.
How tall should a bezel be?
Tall enough to clear the straight part of the stone plus however much you intend to push over the top, and the second half is a judgement rather than a formula. A high dome needs more to reach the same grip because it curves away faster; a bezel that is too tall pleats instead of laying down. Measure the straight part, decide the rest by cutting a scrap and offering it up.
Do I add clearance before or after the thickness allowance?
Before. The clearance enlarges the inside line of the bezel, and the thickness allowance is then calculated from that enlarged line. With a 10 mm stone and 0.1 mm clearance all round, the inside line is a 10.2 mm circle, and pi times the bezel thickness is added to its circumference. Doing it the other way round gets a slightly different and slightly wrong answer.
How much does a bezel setting weigh?
Less than people expect for the bezel and more than they expect for the backplate. A 10 mm round setting in sterling with 0.3 mm bezel 3.6 mm tall and a 0.5 mm backplate comes to about 1.0 g, of which nearly two thirds is the plate. Which of the two is worth thinning is not fixed: on this 10 mm setting, 0.05 mm off the bezel saves slightly more than 0.05 mm off the plate, and the two cross over at about 12 mm and past that the plate is the bigger saving. Tall bezels push the crossover further out.