Five frame numbers, three outlines
Rows are the five numbers a frame has to satisfy before anybody asks what your face is called. Columns are this site's heart row, the outline it gets confused with, and one of the two outlines its own corridor formula places lowest. Every cell is millimetres with inches in parentheses. Four of the five rows carry the same band in all three columns on purpose: those four are published as ranges of adult head and nose sizes, not as ranges of face shapes, so a shape cannot move them. Only the depth row is shape-conditioned, and it is worked at a cheekbone line of 136 mm (5.35 in) — the note under section three prints the formula and every input it uses. One caution on the round column: 44 mm is what the corridor arithmetic returns at that width, while this site's round-face glasses page publishes a tighter limit of about 40 mm for a different reason, a styling one, and defers to it there.
| Frame parameter | Heart | Diamond | Round |
|---|---|---|---|
| Total width, end piece to end piece | 130 – 145 mm (5.12 – 5.71 in) | 130 – 145 mm (5.12 – 5.71 in) | 130 – 145 mm (5.12 – 5.71 in) |
| Lens width, the first number on the arm | 40 – 60 mm (1.57 – 2.36 in) | 40 – 60 mm (1.57 – 2.36 in) | 40 – 60 mm (1.57 – 2.36 in) |
| Lens depth, not stamped | 30 – 47 mm (1.18 – 1.85 in) | 30 – 48 mm (1.18 – 1.89 in) | 30 – 44 mm (1.18 – 1.73 in) |
| Bridge width, the second number | 14 – 24 mm (0.55 – 0.94 in) across the shelf; 18 – 20 mm (0.71 – 0.79 in) is what a medium front carries | 14 – 24 mm (0.55 – 0.94 in) across the shelf; 18 – 20 mm (0.71 – 0.79 in) is what a medium front carries | 14 – 24 mm (0.55 – 0.94 in) across the shelf; 18 – 20 mm (0.71 – 0.79 in) is what a medium front carries |
| Temple length, the third number | 140 – 145 mm (5.51 – 5.71 in) as stocked; 148 – 155 mm (5.83 – 6.10 in) where a wide head needs it | 140 – 145 mm (5.51 – 5.71 in) as stocked; 148 – 155 mm (5.83 – 6.10 in) where a wide head needs it | 140 – 145 mm (5.51 – 5.71 in) as stocked; 148 – 155 mm (5.83 – 6.10 in) where a wide head needs it |
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The row that moves is not the row they disagree about
Read the depth row first, because it is the only one with three different numbers in it. Heart stops at 47 mm, diamond at 48, round at 44. Between the two labels you might be confusing, the whole published difference is one millimetre; the column next to them is three millimetres away. Round is here as the yardstick: its published face-length ratio is the joint lowest in the rule set, tied with square, so the corridor formula sets it three millimetres below heart and four below diamond. That is what makes the one millimetre legible rather than impressive.
Now read the rule set's other table, the one that decides which of the two you are. That table — five checks across all seven outlines, printed on this site's rectangle face-shape page as a published centre plus or minus one standard deviation, on the scale of a soft tape — has these four lines for our two candidates. Jaw width divided by cheekbone width: 0.60 – 0.84 for heart, 0.60 – 0.84 for diamond. Jaw angle: 112 – 128° for both. Chin taper: 0.22 – 0.38 for both. Face length divided by cheekbone width: 1.17 – 1.53 for heart against 1.22 – 1.58 for diamond, centres 1.35 and 1.40 on a shared spread of 0.18, which is a little over a quarter of a standard deviation apart.
Three of those rows are not merely close, they are identical strings. The fourth is a quarter of a standard deviation, which is nothing. And then there is the fifth row, forehead width divided by cheekbone width: 0.97 – 1.13 for heart, 0.72 – 0.88 for diamond. Those two bands do not touch. Their centres are 1.05 and 0.80, and the half-width each one carries is 0.08, so the gap between the two centres is 0.25 ÷ 0.08 = about 3.1 standard deviations. The rule set's own figure for the same separation, computed on the scale the classifier runs on, is 3.09 — which is the same number, and has to be, because the two scales are related by one straight line.
So the answer to the question this page was written to answer is awkward and worth saying plainly. The single feature on which a heart result and a diamond result disagree — the only one of the five published checks on which those two outlines do not overlap at all — contributes no millimetres at all to the frame you buy. It does not appear in the depth formula. It does not appear in the total width, the lens width, the bridge or the temple. One row moves between the two labels, one row moves by a millimetre, and that row is driven by face length, which the two labels share to within a quarter of a standard deviation.
That is not the same as saying the label is meaningless. It says the label's meaning is not in the frame. What a heart result tells you is that your forehead sits close enough to your cheekbones that the front may have to be sized above the cheekbone line — and the millimetres that costs are not on any row above. Section five works out which line they are on.
Where half a millimetre became one
The depth row is arithmetic, so it can be redone. This site's corridor ceiling is the rule set's face-length ratio multiplied by the cheekbone line, divided by three, less a 6 mm clearance; the result is rounded down to a whole millimetre. The divide-by-three turns a full face length into the brow-to-cheekbone span because the rule set's length runs from the hairline to the chin, and the lens occupies roughly the middle third of that. The 6 mm is this site's own allowance and has no external source — it is the number a fitting guide would call clearance, and it is subtracted, not added, so a smaller allowance buys you more depth, not less. The ratio itself is a classifier reading rather than a tape reading, and two paragraphs down this page works out why that distinction is worth eight millimetres.
Heart's published ratio centre on the classifier's scale is 1.182, diamond's is 1.195, round's is 1.103, and the cheekbone line all three are worked at is 136 mm. Heart: 1.182 × 136 ÷ 3 = 53.59, less 6 = 47.59, floor 47. Diamond: 1.195 × 136 ÷ 3 = 54.19, less 6 = 48.19, floor 48. Round: 1.103 × 136 ÷ 3 = 50.00, less 6 = 44.00, floor 44.
Stop on those three ratios, because they are the one place on this page where two rulers can be confused, and the wrong one returns a lens depth that does not exist. This site's rectangle face-shape page prints the same feature as a tape band — 1.17 – 1.53 for heart, 1.22 – 1.58 for diamond — and says there that the detector's raw readings sit on a different scale and are converted to the tape scale before they are ever shown to you. The corridor formula has never been converted: it is run on the classifier reading, which is what produced the 48 mm this site publishes for a diamond result. That is not an oversight you can fix by being careful, it is the definition of the formula, and the test is arithmetic. Put heart's tape-scale centre, 1.35, through the same corridor and you get 1.35 × 136 ÷ 3 = 61.2, less 6 = 55.2, floor 55 mm — eight millimetres above the 47 mm the first table prints. So a ratio inside this page's formulas is a classifier reading; a ratio you take with a soft tape belongs to the bands in section two, and swapping one for the other is the difference between a 47 mm ceiling and a 55 mm one.
Look at the two numbers the floors stepped over. The real distance between heart's 47.59 and diamond's 48.19 is 0.59 mm. The table prints 1 mm because the rounding boundary at 48 falls between them. On the cheek of a cloth tape there is no graduation finer than a millimetre, so the difference the two labels buy you is smaller than the smallest thing you can measure on your own face with the tool this site tells you to use.
The sensitivity is worth having too, because it is what makes the row usable. One millimetre of corridor costs 3 ÷ 136 = 0.022 of face-length ratio, and 0.022 is 0.46 of that feature's standard deviation. So a whole millimetre of lens depth is available for less than half a standard deviation of the one feature that can buy it — and is not available at any price from the feature that defines the label. If you want a deeper lens, changing the shape name is not a lever. Changing the cheekbone line is: same outline, same formula, and eight millimetres of travel across the published adult range, which is the next section.
- Inputs to redo every figure above: face-length ratio centres 1.182 (heart), 1.195 (diamond), 1.103 (round), all of them classifier readings; cheekbone line 136 mm; clearance 6 mm, subtracted, this site's own; round down to a whole millimetre; standard deviation of the length ratio 0.048 on the same scale the ratios are quoted on. The cross-check paragraph uses one more input, 1.35, which is the centre of heart's published tape-scale band (1.17 – 1.53) and is not a classifier reading.
Twelve millimetres that belong to neither label
The forehead bands are disjoint, and a disjoint pair of bands leaves a hole. Diamond's upper edge is 0.88 of your cheekbone line; heart's lower edge is 0.97. Anything between them is inside neither published band, and the hole is nine hundredths of your cheekbone line wide — on a 136 mm face that is 12.2 mm of forehead, which is not a rounding allowance. The bands are one standard deviation wide and they were not drawn to tile the population.
The hole has a width in millimetres, and it is not small. Take the published adult cheekbone band, 128.2 to 148.8 mm, which is one standard deviation either side of the sex means in a 2022 anthropometric dataset, and take the 136 mm line the last section used as the middle case. Multiply that line by 0.97 and by 0.88 and subtract. The result is the width of the territory where this site's own table cannot tell you which outline you have, while your tape can tell you exactly where in it you are.
Column one is your cheekbone line, taken at the published adult band's lower edge, at the 136 mm line every depth figure on this page is worked at, and at the band's upper edge. Columns two and three apply the two band edges just above to those widths: forehead = 0.97 × cheekbone puts you at the floor of the heart band, forehead = 0.88 × cheekbone puts you at the ceiling of the diamond band. Column four is the gap between those two forehead widths, which is the range in which neither label's published band covers you. Column five re-runs the corridor arithmetic of section three — floor(ratio × cheekbone ÷ 3 − 6) — at each width instead of at 136 mm, so the two labels can be compared against the one variable that moves them. Everything here is arithmetic on three published inputs: the two band edges, the adult cheekbone range, and the ratio centres 1.182 and 1.195.
| Cheekbone line | Forehead at the heart band's floor | Forehead at the diamond band's ceiling | Width of the unlabelled gap | Depth ceiling: heart / diamond |
|---|---|---|---|---|
| 128.2 mm (5.05 in) | 124.4 mm (4.90 in) | 112.8 mm (4.44 in) | 11.5 mm (0.45 in) | 44 / 45 mm |
| 136 mm (5.35 in) | 131.9 mm (5.19 in) | 119.7 mm (4.71 in) | 12.2 mm (0.48 in) | 47 / 48 mm |
| 148.8 mm (5.86 in) | 144.3 mm (5.68 in) | 130.9 mm (5.16 in) | 13.4 mm (0.53 in) | 52 / 53 mm |
Inches are given for the four width columns — the cheekbone line, the two forehead widths, and the gap between the last two, all of which a tape can show you — and left out of the fifth, which is a ceiling rather than anything you would order. Read that last column against the first: at 136 mm of cheekbone the heart ceiling is 47 mm and at 148.8 mm it is 52 mm, so your own face width moves the number by five millimetres over the twelve millimetres of cheekbone above the middle line, and by eight millimetres across the whole published adult range. The label moves it by one.
- A millimetre from the label, against eight millimetres from your cheekbone width — which is why the last column is the least useful thing on the page to argue about, and the first column is the one to measure.
- The gap column is also the honest answer to anyone who says the two shapes are easy to confuse. They are not confusable by this site's rule set: a face whose forehead sits 0.92 of its cheekbone line is not sitting between two labels, it is sitting outside both, and this site's detector is built to answer an ambiguous face with a lower confidence reading rather than a verdict.
- Diamond's ceiling of 0.88 and triangle's published forehead band share the same 0.72 – 0.88 floor-to-ceiling, so a low quotient separates heart from diamond without telling you which of diamond and triangle you have. The jaw row does: 0.60 – 0.84 against 0.96 – 1.20. The chin-taper row agrees at the chin, 0.22 – 0.38 against 0.41 – 0.58, and those are the only two of the five checks on which the two outlines do not touch — the jaw gap being four times the taper gap. Length is no help: 1.22 – 1.58 and 1.12 – 1.48 overlap across most of both bands.
Which line you put the tape on
Here is the boundary, and it is a number you compute yourself with a soft tape in about a minute. Measure your cheekbone width, apex to apex across the highest points, the tape passing just under the eyes. Then measure your forehead width across its widest part — slide the tape between the brows and the hairline and keep the largest reading you get, rather than assuming where it is. Divide the forehead by the cheekbones. Call it F.
F of 0.97 or more is the heart band. At that quotient your forehead is within three per cent of your cheekbones, or wider than them, so the two lines are close enough that the cheekbone measurement stops being the default for the width row. Measure both, and size that row against whichever of your two numbers is larger. The reason is the arms: they leave the end pieces above the rim line and travel up and back, so a front that only just clears your cheekbones still has to get past your forehead on the way, and at this quotient the higher line can be the binding one. Above F = 1.00 it is.
F of 0.88 or less is the diamond band. Your forehead is at least twelve per cent narrower than your cheekbones, the temples tuck in below the widest line, and a front that clears the cheekbones will not have to be widened for the temples at all. There, the cheekbone line binds and the total width comes off it.
Between 0.88 and 0.97 there is no label in this site's rule set, and a page that pretended otherwise would be selling you a third silhouette. The action is not to shop blind. Take the wider of your two measurements as the line the frame has to clear, and take 47 mm as your depth ceiling rather than 48 mm — the conservative side of both of the two numbers this boundary moves. That pairing is this page's convention, stated as one, and you can overrule it once you have your own two numbers.
Why the forehead binds when it is the wider of the two, mechanically: a frame's front is widest at the rim line, and the hinges sit at the end pieces a little above it. Above the hinge line the only thing that keeps spreading is the temple arms, which are narrow, stiff-to-sprung pieces of metal or plastic designed to grip, not to clear. Put a face whose widest line is above the hinges into a front that only just clears the cheekbones, and the arms arrive at the temple points already shorter than the distance between them. The frame is then held by four contacts where it should be held by three, and the extra one is on the flattest, most sensitive skin on the head.
That is also why the discomfort gets blamed on the nose pads. It is not that the pads are wrong; it is that the face has one contact point you can press on and one you can only widen. The check before you buy anything is on the frame, not on your face: with it on and level, look at four edges. The upper rim should sit at or just below the brow without covering it. The lower rim should not be touching the cheekbone when you smile, because a rim that clears the bone at rest rides it when the mid-face lifts. The temple tips should run the full length of the curve behind the ear rather than meeting it at one point. And the frame should stay put when you blink a few times and look down at the floor — if it slides, that is the nose and the weight, which is a different problem from the width, and no size on this page will fix it.
What the three stamped numbers will not tell you
The first table's rows two, four and five are the three numbers printed inside the temple arm: lens width, bridge width, temple length. They are the most convenient figures in eyewear and the least transferable, and they bite on a heart outline in a particular way: the row this page says to size first is the one this site could not find given in millimetres on any of the ten pages ranked for this keyword.
The stamped pair — the lens width and the bridge, 53□17 or 52□18 — describes a lens and a gap. It does not describe the finished front. What the front measures across is the two lenses, the bridge between them, and then the end pieces that carry the hinges, plus whatever outward set the temple arms are built with. Two frames stamped with the same 53 mm lens can read more than a centimetre apart across the temples, because the end pieces are chunkier on one and the arms spring outward on the other. This site's own total-width arithmetic spends 20 mm on end pieces across both sides of an acetate front, which is not a rounding error — it is most of the difference between the number stamped and the number that touches you.
The predictable failure is common enough to be worth naming. A frame fits badly, the stamp reads small, so a larger stamp gets ordered, and the larger stamp fits no better — or fits the rim and presses the temples — because the row that had to move is the one the stamp does not carry. The fix is a transfer instead of an upgrade: find the one pair you own that fits, read its stamp, and buy within one or two millimetres of it. If the printing has worn off, put a ruler across the finished front from end piece to end piece and keep the new frame within four millimetres of that. Both tolerances are this page's own working numbers and are printed here so you can disagree with them rather than guess at them.
Where the transfer breaks is stiffness. A spring hinge, or a temple in a material that opens under load and closes again, will forgive a front that reads a few millimetres narrow, which is part of why two frames with the same total width can fit differently. A rigid acetate arm forgives a good deal less, and bending its arms at the counter does not move the problem — heat and pliers set the temple bend behind the ear, which is a different millimetre from the one a forehead-wide face is being pressed on. So the total width row of the first table is a band and not a number, and inside that band the material decides whether you are at the top of it or the bottom.
The optics question, answered once and referred
There is one place where a wide forehead gets mistaken for something the optics care about, and it is worth closing off. Lens width and bridge width are constrained by your pupillary distance, not by your face: the finished lens has to have its optical centre moved inward from the geometric centre of the blank by roughly half the difference between the frame's centre distance and your PD, and this site publishes a ceiling of 5 mm per eye on that move. A frame stamped 52 □ 19 on a PD of 62 spends (52 + 19 − 62) ÷ 2 = 4.5 mm per eye — inside the published ceiling, and past what a strong prescription wants, because the thicker a lens is the more the wasted outer millimetres of the blank show at the edge.
Now the trap. Forehead width and pupillary distance are two different measurements of two different things, and they can run in opposite directions on the same person. A broad forehead does not licence a wide frame PD; a narrow PD inside a wide front is the combination that stops a frame being merely uncomfortable and makes it unmakeable, and buying on the widest line of your face without the refraction slip in front of you is how you arrive at a frame a lab refuses.
The two constraints are therefore on different numbers from your body — one from a tape, one from an optician's instrument — and this is the point where this page stops. The minimum-blank arithmetic, the frame-PD pegging and the seven real frames it is worked across are on this site's glasses page for a round face; the lens-blank ladder as it applies to a diamond result, including where a 136 mm cheekbone line and a 62 mm PD stop paying for depth, is on the diamond page linked below. Neither is re-derived here.
The four pages this one is not
Glasses for a diamond face shape is the sibling whose label you might actually have been given. It works the other direction: diamond is handed 48 mm of depth at the 136 mm line and handed back less than that by what the largest commonly stocked lens blank will cut and by the deepest lens height the trade actually carries. Its subject is the gap between permission and manufacturability. This page's subject is which line of your face the width has to clear, and it does not touch the blank ladder.
Glasses for an oval face reaches the flattest conclusion of the family — most of the rows do not move with an oval shape at all, so what is left of shape advice is an exclusion list of silhouettes. Read that one for the shapes to rule out rather than the sizes to buy.
Glasses for a round face is where four constraints pull against one another at once — width reaching the cheekbone, depth staying off it, decentration under its ceiling, and a blank that may refuse the combination — and it is where the arithmetic is shown rather than asserted.
Sunglasses for a round face is the same face with the prescription taken out, which switches off the row that prescription constrains and turns lens height into a question about the mid-face corridor instead.
This page is for the case none of those four is about: you have a heart result, you are not sure it is right, and you want to know what being wrong would cost you in something you can feel. The answer is a boundary you compute from two tape measurements, and a millimetre of frame you can ignore.
Two numbers, then. Take them before you look at a single frame. Across the tops of the cheekbones with the tape passing under the eyes, and across the widest part of the forehead, which you find by sliding the tape between the brows and the hairline and keeping the largest reading. Divide the second by the first.
If that quotient is 0.97 or more, your two width lines are within three per cent of each other, and the frame you buy has to be sized to clear whichever of the two is the wider one rather than the cheekbone line by default. That is what a heart result is worth at the counter: not a different set of millimetres in any row, but a different line of your face to measure the width row against. If it is 0.88 or less, the cheekbones are the widest thing a front has to get past and you can stop worrying about the temples. If it lands in between — and twelve millimetres of forehead width is a wide place to land — take the wider of the two lines and the shallower of the two ceilings, and buy on those.
What you should not do is keep re-running the photo test to settle it. The feature the test argues about is the one that appears in none of the five numbers on the first table; what it decides is which line of your face you put the tape on. That measurement takes a minute, needs no classifier, and is the one the frame will actually feel.