The price list has one surprising line in it. At the centre of that band, one millimetre added at each side of the face buys 3.30 times what one millimetre taken off the visible length buys. A centimetre of wave at cheekbone height is worth the same as 33 mm of forehead buried under a fringe. That is why the volume advice comes first on this page and the fringe advice comes second — not because fringes are worse, but because at equal millimetres they are the more expensive direction, and because width is something a style puts on and takes off while the length a fringe covers has to be grown back.
Two pages here already carry the styling half. The rectangle face shape guide holds the cuts — the blunt chin-length bob, the collarbone cut, the four men's lengths in centimetres, the crown-volume rule — and the oblong hairstyle guide holds the sentences to say in a salon. This page holds the arithmetic under all of it, so that the next time a cut is offered to you as a number, you know what that number buys.
The first table: what width at the sides is worth
Read the row for your own ratio down the page. The columns are how much wider the silhouette gets at the sides, counted on each side of the head, at cheekbone height. Every cell is the outline ratio the face then reads at — the number a stranger's eye works with, not the number your bone carries.
Outline ratio after adding width at the sides, at the 136 mm working width — millimetres in, read out as a ratio
| Your face-length ratio | Face length at 136 mm (5.35 in) | No width added | +5 mm (0.20 in) each side | +10 mm (0.39 in) each side | +15 mm (0.59 in) each side | +20 mm (0.79 in) each side |
|---|---|---|---|---|---|---|
| 1.47 | 199.9 mm / 7.87 in | 1.47 | 1.37 | 1.28 | 1.20 | 1.14 |
| 1.65 | 224.4 mm / 8.83 in | 1.65 | 1.54 | 1.44 | 1.35 | 1.27 |
| 1.83 | 248.9 mm / 9.80 in | 1.83 | 1.70 | 1.60 | 1.50 | 1.41 |
Each cell is face length ÷ (cheekbone width + twice the width added), carried out at the 136 mm cheekbone line this site uses on its eyewear pages and rounded to two decimals, so the arithmetic can be redone on a phone: at 1.65 the length is 1.65 × 136 = 224.4 mm, and 224.4 ÷ (136 + 20) = 1.44. Inches in the headers are the millimetres divided by 25.4. The three rows are not invented: 1.65 is the centre this site's rule set puts on this family and 1.47 and 1.83 are one published standard deviation either side of it (0.18 on this scale). The four stops are chosen rather than measured and are marked as such — nobody's perm is specified in millimetres, and nothing stands behind the five-millimetre spacing except that it is the finest division a hand can judge in a mirror and a tape reads without squinting. The rate falls as you buy more: on the 1.65 row the first 5 mm of the 10 mm each side takes 0.113 off the ratio and the second takes 0.099, so the price paid in each column is slightly less than the column before it. Twenty millimetres per side comes to 0.375 of the ratio, which is 2.06 of those published standard deviations — a long face wearing that much width does not read as a slightly shorter long face, it reads as another shape altogether, which is why the two columns in the middle of the table are the working ones and the last is a ceiling.
- How to get your own number: measure cheekbone width over bare skin, then measure the same line again through the finished style — tape passed over the widest point of the hair silhouette, not around the head. Subtract, divide by two, and that is the figure to read across the columns. If the second number is smaller than the first, the style is sitting inside the face and the columns do not apply to it.
- Where the same row lands at the two ends of the published adult cheekbone band, 128.2 mm and 148.8 mm, is in the fourth section, because the width changes the price and the ratio does not.
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The model, and the three things it does not claim
Two levers move the outline ratio and nothing else on this page does. The first is width: it enters the calculation twice, once on each side of the head, which is the whole reason it is the cheaper direction. The second is length: a fringe covers part of the forehead and a stacked crown adds height above the hairline, and each millimetre of either moves the numerator by one millimetre exactly.
It does not claim your face shape changes. The bone measurements on the rectangle face shape guide are what they are, and this table prices the read, not the skeleton — the same distinction this site makes about weight and age on that page.
It does not claim width can go anywhere. The model puts the added width on the cheekbone line because that is where the denominator is measured, and it is where this site's other guides put volume for the same reason. Width added at the jaw does not divide the same number; it changes a different feature, the one the jaw-width ratio carries.
It does not claim symmetry is free. A wave on one side and a flat fall on the other buys roughly the same ratio at half the effort, which is exactly why the asymmetry advice on the other guides works — and why a single number here is a budget, not a prescription.
The exchange rate between the two directions
Divide what a millimetre of width buys by what a millimetre of length buys and the cheekbone width cancels out of the quotient. What is left is twice your own ratio. That is the whole result of this page, and it is the sentence no page in the comparison below prints.
What one millimetre of each lever is worth at the 136 mm line, and what the same job costs in the other currency
| Lever | Ratio moved per millimetre | In published deviations (0.18) | The same job in the other currency | Does the rate depend on your ratio? |
|---|---|---|---|---|
| Width added at each side, at cheekbone height | 0.0216 at 1.47 · 0.0243 at 1.65 · 0.0269 at 1.83 | 0.119 · 0.133 · 0.148 | 3.3 mm / 0.13 in hidden at the hairline does the same as 1 mm per side at 1.65 | Yes — it rises with it |
| Forehead covered by a fringe | 0.00735 at every ratio | 0.040 | 0.30 mm / 0.012 in per side does the same as 1 mm of fringe | No — it is one over your width |
| Height stacked at the crown | 0.00735, added rather than removed | 0.040, against you | 5 mm / 0.20 in of height is repaid by 1.5 mm per side at 1.65 | No |
| A beard line or shading dropped below the chin | 0.00735, added | 0.040, against you | Same repayment: 1.5 mm per side for 5 mm below the chin | No |
The width rate is twice the face length over the square of the cheekbone width, evaluated at zero added width; the length rate is one over the cheekbone width. Both are the first millimetre's price — the width rate is about 40% lower by the time twenty millimetres per side have been added, which is why the fourth section is built by solving the exact fraction rather than by multiplying this rate. The equality in the last two columns is the neat part of the whole page: the number of millimetres at the hairline needed to equal one millimetre per side is exactly twice your ratio, 2.94 at the bottom of the band, 3.30 at its centre and 3.66 at the long end. The repayment figures quoted for the crown and the chin are that quotient run backwards, at 1.65.
- The practical reading of the last column: the long end of the band is the one that gets paid best at the sides. A face at 1.83 gains 0.0269 of ratio per millimetre per side while a face at 1.47 gains 0.0216 — 24% more for the same perm. The advice to wear width is therefore not equally valuable across the family, and the faces who should take it most seriously are the ones the other guides call extreme.
- And the same quotient explains the crown rule on the rectangle guide in one line: height above the hairline is charged at the cheapest rate on this page, 0.00735 per millimetre, but it is charged in the wrong direction. Everything stacked upward is cheap to undo at the sides — a millimetre of crown height costs 0.30 mm per side at 1.65 to pay back — while a millimetre per side takes 3.30 mm of height to do the same job the other way. That asymmetry is why the crown warning on the other guides is worth reading as arithmetic rather than as a rule.
How much width to stop reading as long
The question a reader actually arrives with is the reverse one: not what a millimetre buys, but how many millimetres the job needs. The table below solves the fraction exactly for three landmarks taken from this site's own published bands rather than from a styling convention — the top of the zone the family shares with oval at 1.63, the floor of the family's own band at 1.47, and the centre the rule set puts on an oval at 1.45.
Those three targets are chosen, and choosing them is this page's editorial act, so they are labelled here rather than presented as findings. They are useful because they are the two borders this site publishes and the one centre between them; anything else you would want to reach is arithmetic on the same line.
Millimetres needed at each side of the face to bring the outline read down to three published landmarks
| Your ratio | Cheekbone width | To read 1.63 | To read 1.47 | To read 1.45 |
|---|---|---|---|---|
| 1.65 | 128.2 mm / 5.05 in | 0.8 mm / 0.03 in | 7.8 mm / 0.31 in | 8.8 mm / 0.35 in |
| 1.65 | 136 mm / 5.35 in | 0.8 mm / 0.03 in | 8.3 mm / 0.33 in | 9.4 mm / 0.37 in |
| 1.65 | 148.8 mm / 5.86 in | 0.9 mm / 0.04 in | 9.1 mm / 0.36 in | 10.3 mm / 0.40 in |
| 1.83 | 128.2 mm / 5.05 in | 7.9 mm / 0.31 in | 15.7 mm / 0.62 in | 16.8 mm / 0.66 in |
| 1.83 | 136 mm / 5.35 in | 8.3 mm / 0.33 in | 16.7 mm / 0.66 in | 17.8 mm / 0.70 in |
| 1.83 | 148.8 mm / 5.86 in | 9.1 mm / 0.36 in | 18.2 mm / 0.72 in | 19.5 mm / 0.77 in |
Each cell is cheekbone width × (your ratio ÷ target − 1) ÷ 2, so it is a division and a multiplication and can be redone for a face outside the published adult band — 128.2 and 148.8 mm are the ends of that band, one standard deviation either side of the measured sex means this site published, and 136 mm is its working line. Cross-check with the first table rather than trusting this one: the 1.65 row at 136 mm says 8.3 mm per side reaches 1.47, and the first table's 1.65 row shows +10 mm per side landing at 1.44, which is on the right side of the same border. The equivalence worth carrying out of the shop: 8.3 mm per side is the same move as 27.5 mm (1.08 in) of forehead under a fringe, because the quotient is twice the ratio. At the long end the same border costs 16.7 mm per side, or 61.0 mm (2.40 in) of forehead — more forehead than most faces have above the brows, which is the arithmetic reason the long rectangle wears length in waves rather than in a fringe alone.
The 1.5 that two of the ten print
Two positions in the comparison below state a number for this shape: a style consultancy's entry from 2014 says the face is more than 1.5 times its width, and a men's grooming page from August 2026 says a ratio greater than 1.5 points to it, and repeats the threshold in its own checklist. Those two uses of 1.5 are the only figures in the twelve that state the shape's own proportions rather than a length to cut — the nose-length parenthetical inside the 2014 sentence is the only other proportion any of them gives. Neither page says how its number was arrived at, which is the difference between a threshold and a measurement, and is why it deserves to be checked rather than copied.
Against this site's floor it is not a contradiction. 1.5 sits 0.03 above the published band floor of 1.47, which is 0.17 of one standard deviation and 8% of the width of the band. On a 136 mm face those two readings are 4.1 mm (0.16 in) of face length apart; on the published band's two width extremes the pair sits at 188.5 and 192.3 mm, or 218.7 and 223.2 mm. So a face measuring 1.49 is a rectangle here and is not one there, and the disagreement between the two rules is a strip about four millimetres of tape long at working width.
Two things the external figure does not carry are worth naming, because they are the difference between a threshold and a band. It has no stated source and no stated uncertainty — the 2014 page says it once, inside the sentence that defines the shape, and never uses it again; the 2026 page gives it twice and prints no tolerance. And it has no upper end, so nothing can be disqualified by being too long, which is the half of a band that tells a very long face to stop taking advice from a rule built to catch the short end.
One trap to avoid while comparing the two. 1.5 and 1.47 are both on the tape scale, so they can be argued about side by side. A face-length ratio read out of a photo detector in this browser is on a different scale and sits near 1.26 for this family, because the landmarks differ — the conversion is documented on the about page, and mixing the two scales in one comparison is the one arithmetic error on this subject that is genuinely fatal.
Cornered or soft-cornered: what the difference is worth
Twelve natural positions were read for this page; the ones that take a position on the word oblong split four ways, and the split is the interesting part. A salon's service page writes that the shape is often called oblong and does not distinguish. A men's grooming page puts both names in one heading. A how-to page says the terms are used interchangeably and then, in the next sentence, gives the oblong a more rounded and narrow chin. A picks site carries the two as separate rows of its one table: a square jaw for one, softer corners for the other. Nobody says what the difference is measured in.
This site's rule set does not split them either: one row, labelled oblong, covers the whole family, and it is the same row's bands that the first table above is built from. Within that row the cornered reading and the softer reading are carried by two features rather than one — the jaw angle, banded at 110 to 126°, and the chin taper, banded at 0.41 to 0.58 — and the site has published its own limits on both. The angle is the weakest reading in the calibration: on those fifty photographs the angle did not tell a round face from a square one, the two groups landing within a degree of each other. So the honest statement is not that an angle decides which word applies to you. It is that five readings are scored together and what comes back is a margin rather than a verdict, and that no sentence on this page asks you to settle the corner by angle on its own.
Here is the part the numbers on this page add. The price list contains exactly two inputs: your ratio and your cheekbone width. Neither is the jaw angle and neither is the chin taper. So the cornered end and the softer end of this family pay the same millimetre prices — 0.0243 of ratio for a millimetre per side at the band's centre for both of them — and the difference between the two adjectives is not a difference in how much the fix costs. It is a difference in what you are fixing the illusion of.
Which is also why the styling rows for the two names come out nearly identical. On that one table in the comparison, the rectangle row and the oblong row open with the same instruction, add width, and differ only in what follows it. On the arithmetic, they could not differ in the first instruction: both faces are long, both need the denominator, and the denominator is bought at the same price. What the corner changes is the second half of the sentence — a hard corner reads as a line to be crossed by a blunt ending at the chin, a soft corner as a curve to be interrupted — and that half is the styling pages' work, not this one's.
What each of the ten said, in the order they said it
Ten of the twelve positions read for this page are in this table: nine that carry a date and one that carries none, sorted oldest first with the undated entry last. The two that are not here are named in the note underneath, and neither has been replaced with a row it cannot support. The third column is what each position had to say about this shape at that date, in its own words where they are short enough to quote.
Nine dated positions and one undated one, in the order they were published, and what each left out
| Date, and how it is carried | What the source is | What it said | What follows from putting it on a date axis |
|---|---|---|---|
| 11 December 2012, in the page's own metadata; nothing printed where a reader can see it | A 503-word styling page credited to a named hairstylist | “go for a little more horizontal volume and steer clear of too much height” | Both halves of this page's argument, fourteen years and four months before the newest entry here, with no number attached to either half |
| 13 May 2014 in its metadata and structured data, revised 22 November 2024; six dates print where a reader can see it, and none of the six is that date | An image-and-style consultancy's entry | “more than 1.5 times it’s width (and more than 3 noses long)” | The first 1.5 in the set, and the only time that page uses it: it sits in the sentence that defines the shape and is never applied to a cut |
| 9 November 2020 in its structured data, revised 11 April 2026; the only date printed where a reader can see it reads 28 September 2026, which is neither of those two | A scissors retailer's cutting guide, 4,634 words in this reading | “Measure The Width Of Your Jaw … Multiply the resulting numbers by two” | A full measuring procedure with no quotient at the end of it: the millimetres are collected and never divided by anything. Its fourteen inch figures are scissor sizes |
| 17 July 2023 printed on the page and in its structured data, revised 21 July 2026 | A salon's service page | “The forehead, cheeks, and jaw share the same width”, and “Often called an oblong face shape” | The parallel widths and the merged name in one place, and zero millimetre, centimetre or inch figures anywhere on it |
| 18 February 2025 as its structured publication date, while the same block carries 13 January 2025 as its modification date, which is earlier; the article cards on it print 7 February 2018 | A hair-content publisher's category page | “a face longer than it is wide, often accompanied by a strong, angular jawline” | The one entry here whose machine-readable dates disagree with each other, and whose printed year disagrees with both |
| 26 February 2025 printed on the page; its structured data carries 25 February 2025 as the publication date | A hairstyle directory entry, 1,335 words | “The textured layers create extra movement and reduce the heavy feel of the jawline” | A named cut with an anatomical reason given, and no measurement of any unit in the whole reading |
| 11 August 2025 as its structured creation date; the page prints 7 August 2026 | A how-to site's collaboratively written page, 4,256 words | “choose hairstyles that add width to the sides of the face”, and separately a beard kept to “no more than 1 inch (2.5 cm)” | The measuring method is on the page — tape, length and width, half a jaw doubled — and the only unit figures it prints are a beard kept to no more than 1 inch (2.5 cm) |
| 18 June 2026 printed on the page and in its metadata, revised 1 August 2026 | A picks page — the only one of the ten carrying a table | Its table's two rows: “Long, with a square jaw” and “Long, with softer corners”, both under a Styling Goal column beginning “Add width” | The only table in the set puts the cornered-and-soft distinction in a column of adjectives, and the first instruction is identical in both rows — which is what the arithmetic says must happen |
| 12 August 2026 printed on the page, the newest dated entry here | A men's grooming editorial page, read through a browser because the plain fetch was blocked | “A ratio greater than 1.5 points to a rectangular face”, and in its checklist “Face length exceeds width by 1.5x or more” | The only page in the set that uses the word ratio. It also prices hair in centimetres — a parting moved 1 inch, a 1 inch barrel, a 1–2 inch nape-to-front difference — and the two never meet: no cut length on it is chosen by the ratio it defines |
| No date on the page, in its metadata or in its structured data; the address carries the year 2025, which is not a date | A men's grooming page organised by hair length | “long layers that start around cheekbone level”, and a short cut “keeping about 2–3 cm of length on top” | The closest the set comes to anchoring a cut to a landmark: a level is named without millimetres to place it. The centimetres on the page are on top of the head, the axis this page prices as the direction that has to be paid back |
Column one records each date the way the source itself carries it rather than smoothing it over: printed where a reader can see it, present only in metadata or structured data, or absent. Two of the twelve positions are not in this table and neither is replaced with a row it cannot support. One returned a block to both reading paths, so its headline — which names oblong while ranking for this phrase — is the only fact available about it. The other carries a single structured date belonging to a video record on the page, an upload timestamp rather than a publication date, so it cannot sit on an axis sorted by publication. Between the oldest and the newest dated entry here the span runs from 11 December 2012 to 12 August 2026: 4,992 days, thirteen years eight months and one day. Where a quotation begins or ends mid-sentence, the break is inside the quotation marks.
Questions about the numbers
How many millimetres is a wave actually worth? Measure once over bare skin and once over the finished silhouette at the same height, subtract and halve. On a face that has never been measured this way, five millimetres per side is a reasonable expectation for loose waves at cheekbone height and ten for a perm built for volume; the first table carries both. Anyone who measures their own two numbers will find that the answer differs by head, which is the reason the table is a matrix and not a rule.
Is a fringe or width the better buy? Per millimetre, width, by 3.30 times at the centre of the band. Per hour of maintenance and per month of growing-out, that ranking is not so stable: a fringe is a fixed amount of length removed every day it is worn, while volume has to be rebuilt each morning. The arithmetic prices the millimetres, not the routine.
Will these numbers change my face shape? No. They change the ratio your outline reads at, which is a different quantity and is the one a stranger uses. The bone measurements on this site's rectangle guide stay whatever they are whether or not you wear width.
I measured 1.49 and a guide told me the line is 1.5. You are inside this site's published band and outside the single threshold that guide prints, in a strip 0.03 wide — about 4 mm of face length at a 136 mm cheekbone width. Nothing here resolves that by measurement, because the two rules are not the same kind of object: one is a band with a published centre and tolerance, the other is a cut-off with neither.
Does this arithmetic work for a square or oval face? The two formulas work at any ratio and any width; plug your own numbers. Only the rows change. On a square outline the quotient between the directions is nearer two than three, which is one reason the volume advice reads differently there.
Why does this page not name the cuts? Because they are already published here twice and repeating them would make a fourth copy. The rectangle guide carries the cuts for this shape and the oblong hairstyle guide carries the sentences for the chair; this page carries the only thing neither of them has, which is what each millimetre costs.
Where these numbers are weakest
The volume figure is an assumption about hair, not a measurement of it. The model treats width added at the sides as though the silhouette simply widened at the cheekbone line. Real hair also moves the widest point, and a style whose widest band sits above or below the cheekbones is being described by a number that assumes it does not. A photograph of the finished style, measured at two heights, would settle which band the eye uses; this site has not taken that photograph.
There is no perception calibration behind the ratio cells, and the site says so where it has one. The beard guide published the only measured millimetre-to-ratio transfer this site owns, from beards worn against the skin. Nothing hanging or voluminous has been put through the same test — and a 10 mm shell of hair beside a face is not the same visual event as 10 mm of bone, so the cells should be read as a budget in the right order of magnitude rather than as a prediction of what a face looks like.
The width band is borrowed, and it is soft where you are not. 128.2 to 148.8 mm is the adult range this site publishes from one anthropometric data set; a face outside it should redo the tables with its own number, which is one multiplication and one division.
The stops and the three targets are chosen. Five-millimetre spacing is a convenience; the landmarks at 1.63, 1.47 and 1.45 are this site's own borders rather than a styling convention. Neither is presented as a finding.
Two ears, hair between a drop and a cheek, and a collar are not in the model, and neither is the fact that a haircut is chosen at a chair in inches and centimetres rather than at a mirror in millimetres of silhouette. The point of the exchange rate is that it lets you convert between the two conversations.
Sources, and how we know what we know
The band, the centre, the tolerance and the working width are this site's own published rule set: the seven prototypes, their standard deviations and the calibration's two stated limits — three shapes interpolated, and the square and round jaw angles not separable in the data — are printed on the about page. Every cell above was computed from those constants at writing time, and the table can be regenerated from them.
The measurement definitions follow craniofacial anthropometry: Farkas, L.G. (1994), Anthropometry of the Head and Face; Farkas, Katic and Forrest (2005), Journal of Craniofacial Surgery. The site's one disclosed deviation — face length taken from the top of the forehead rather than the hairline in the photo path — is documented on the about page.
The detector runs on MediaPipe: Lugaresi et al. (2019), MediaPipe: A Framework for Building Perception Pipelines; Kartynnik et al. (2019), Real-time Facial Surface Geometry from Monocular Video on Mobile GPUs.
The ten-entry comparison is a read of the natural results for this phrase on 28 September 2026, taken page by page; each quotation is the source's own wording and no sentence of theirs is used as this page's own. Styling conclusions are an editorial synthesis grounded in the trade literature (Milady Standard Cosmetology, 14th ed.) and in the geometry of the rule set. They are not yet reviewed by a licensed cosmetologist — we are looking for one, and we say so rather than invent a credential.
What we do not do: no search volumes, no difficulty scores, no clamped confidence figures, no attractiveness scores, no golden-ratio claims, no prevalence percentages for any shape. We do not sell hair products or glasses, and your photo never leaves your device.
Two moves do all the work on this outline, and they are not equally priced. A millimetre added at the side of the face is worth between three and four millimetres at the hairline — 2.94 times as much at the bottom of the published band, 3.30 at its centre and 3.66 at the long end — and it is worth it at every width, for every face in the family. Take that as the order to do things in: width first, length second, and nothing stacked upward, because height above the hairline is charged at the cheapest rate on this page and charged against you.
The single figure worth carrying into a shop is the one that fits on a card: eight millimetres to each side, at cheekbone height, is what it takes to move a face at 1.65 down to the floor of its own band, and the same move costs 27.5 mm of forehead under a fringe. Ask for the first one. Say the second one out loud when somebody offers it as an easier fix.