Nothing published puts a figure on that last instruction. Of the eight positions whose text could be read, every one names where the tape goes and five call the fit snug, tight or loose — and a tolerance with a number on it appears in none of the eight, on a band whose entire 80 mm width is only 12.73 mm of radius.
A hat is sold on a ring. How tall the crown stands and how wide the brim runs are argued at length on this site's other hat page, and neither argument decides what a shelf can offer you: crown and brim are both cut to sit on a skull of a given distance round, and the figure stamped inside a band is taken over the hair, not off a face. The measurement comes before the styling, and it is one distance.
How to measure head for hat size is asked as though the answer were a number to look up, and the pages that rank for it do supply ladders — four of the eight positions whose text could be read print a table, three more give steps in running text, and one gives no head measurement at all. What none of them supplies is the part that decides whether a ladder is yours. A ring needs four things: where it rides, whether it stays level, where the number is read, and one allowance for what the reading can be wrong by, which is the pull on the tape and the hair under it. That fourth thing has not been written with a figure beside it anywhere in the record read on 7 October 2026.
Where the Tape Rides, and What the Reading Is
One reading, one band, and the tool places your number against the published ends. The procedure is below; the arithmetic that decides whether the result means anything is in the two tables after it. hat size calculator ↓
How to measure your head for a hat is four decisions before it is one reading. Which ridge the tape rides on fixes the height of the ring at the sides and at the front. Whether it stays level fixes whether you have one ring or a spiral that climbs to the back of the head. Where you take the number — at the point the tape crosses itself, with its zero end under that crossing — fixes whether you read a distance or a distance plus a tail. And how hard you pull decides how much air stays between tape and skull, which is the only one of the four a hat cares about, because a band has to pass over the widest part and then sit still. Hair sits under that same tape, and the record read here treats the two as one unnamed quantity: five of the eight positions say a word about the pull, one says hair is there, and none says what either of them is worth in millimetres.
A search for hat size chart cm is a request for this ladder at the tape's own resolution. The printed figures on a sewing tape are centimetres and the small marks between them are millimetres, so the reading you take is a centimetre number with millimetres lying under it, and the table below keeps both. It adds a third figure that is pure arithmetic: divide any ring by π and you have the distance straight across a round opening that ring would make, which is what a hat block is turned to, and the only way to see how narrow the common band really is.
Average adult head circumference is a phrase for a quantity nobody in the record prints. One position names a common adult band and attaches no bounds to the name; another sells youth and extra-large labels and never says where the adult range stops. The bounds published here are 540 to 620 mm, with both ends counted as inside. They are a band rather than an average, and they are global: nothing on this page pairs a circumference with the shape of a face, and nothing in this site's rule set pairs them either, because the five readings that rule set takes — a length, three widths and an angle, all of them across a face — describe an outline, and a ring round a skull enters none of them.
Read the last column as the size of a mistake budget. Readings 10 mm apart on the tape are 1.59 mm apart in radius, so a head measured at 530 mm sits one printed division and a third below the floor of the band, while a head at 580 mm has 40 mm of ring — 6.37 mm of radius — of slack in either direction. Which of those two numbers is the one to worry about is what the next two tables are for.
The ring as a tape gives it, against the common adult band of 540 to 620 mm: inches and the across-head figure both come from the unrounded millimetres
| Ring round the head | In inches | On a centimetre tape | Straight across, C ÷ π | Against the band, and the radius behind it |
|---|---|---|---|---|
| 510 mm | 20.08 in | 51.0 cm | 162.34 mm (6.39 in) | Below by 30 mm — 4.77 mm of radius |
| 520 mm | 20.47 in | 52.0 cm | 165.52 mm (6.52 in) | Below by 20 mm — 3.18 mm of radius |
| 530 mm | 20.87 in | 53.0 cm | 168.70 mm (6.64 in) | Below by 10 mm — 1.59 mm of radius |
| 540 mm | 21.26 in | 54.0 cm | 171.89 mm (6.77 in) | On the floor of the band |
| 550 mm | 21.65 in | 55.0 cm | 175.07 mm (6.89 in) | Inside by 10 mm — 1.59 mm of radius |
| 560 mm | 22.05 in | 56.0 cm | 178.25 mm (7.02 in) | Inside by 20 mm — 3.18 mm of radius |
| 570 mm | 22.44 in | 57.0 cm | 181.44 mm (7.14 in) | Inside by 30 mm — 4.77 mm of radius |
| 580 mm | 22.83 in | 58.0 cm | 184.62 mm (7.27 in) | Inside by 40 mm — 6.37 mm of radius |
| 590 mm | 23.23 in | 59.0 cm | 187.80 mm (7.39 in) | Inside by 30 mm — 4.77 mm of radius |
| 600 mm | 23.62 in | 60.0 cm | 190.99 mm (7.52 in) | Inside by 20 mm — 3.18 mm of radius |
| 610 mm | 24.02 in | 61.0 cm | 194.17 mm (7.64 in) | Inside by 10 mm — 1.59 mm of radius |
| 620 mm | 24.41 in | 62.0 cm | 197.35 mm (7.77 in) | On the ceiling of the band |
| 630 mm | 24.80 in | 63.0 cm | 200.54 mm (7.90 in) | Above by 10 mm — 1.59 mm of radius |
| 640 mm | 25.20 in | 64.0 cm | 203.72 mm (8.02 in) | Above by 20 mm — 3.18 mm of radius |
| 650 mm | 25.59 in | 65.0 cm | 206.90 mm (8.15 in) | Above by 30 mm — 4.77 mm of radius |
Column one is the ring as read. Column two is column one divided by 25.4 and rounded separately, which is why 630 mm prints 24.80 in and 640 mm prints 25.20 in rather than landing on tidy steps. The two ends of the band appear twice on this site in two forms, on purpose: the tool writes 21.3 to 24.4 in, one decimal, and this table writes 21.26 and 24.41, two — the same two numbers under the site's two live rounding conventions, and neither one is a correction of the other. Column four is the ring divided by π: the diameter of a circle whose distance round equals that ring, which is why the whole published band is 25.46 mm of width across, barely more than one inch. Column five measures to the nearer edge of 540 to 620 mm in millimetres of ring and then divides that by 2π, converting an error on the tape into an error on the head; the conversion is exact for a gap uniform all the way round, because pushing a closed curve outward by δ lengthens it by 2πδ whatever the curve's shape — a head is not a circle and does not have to be one for this column to hold. Both ends count as inside the band, which is this site's published convention and not a rounding habit of this page. The ladder runs at whole centimetres because that is the resolution a tape prints; a reading between two rows is read by dividing, not by looking up.
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What Air Under the Tape Costs, to the Millimetre
Head circumference for hat purposes is measured over the hair, and the oldest printed instruction read for this page says so outright. A millinery course manual printed in 1915 defines the head measure as the distance round the head taken over the hair, states that it varies with the size of the head and with the style of dressing it, and gives no figure for either of those two things. In its wiring instructions the same manual warns that the measure must not be drawn tight and names the allowance after a finger pushed between wire and head all the way round, and adds what that gap is there for: letting facing and lining go into a frame once it is finished. Print has nothing more to offer on that term: an error is named, located on a body part, and left unnumbered.
The size of the error does not need anybody's head measured, because it is a property of closed curves. Take any ring — circular, oval, the shape a head actually presents — and push it uniformly outward by δ. Its length grows by 2πδ. Nothing else enters that result, so air under a tape converts into millimetres on a reading by one multiplication: half a millimetre is 3.14 mm of ring, one is 6.28, two is 12.57, three is 18.85. Read the same row in the other direction and a tape pulled one millimetre into the hair reports a ring 6.28 mm smaller than the head is.
Now set that against the band's own width. The entire published adult range is 80 mm of ring, which is 12.73 mm of radius: that is all the room between the smallest and the largest head a standard hat is built for. Two millimetres of air spends a sixth of it. One spends a thirteenth. The arithmetic that turns air into room is one multiplication by 2π, and the arithmetic that turns a reading back into a head is one division by it.
The face of a tape hides this. Its printed figures step by centimetres, and one millimetre of air moves the reading 0.63 cm — two thirds of a printed division — which is how two readings of the same head can land two centimetres apart while both were taken by somebody who believed they had read it correctly. Five of the eight positions whose text could be read use the words snug, tight or loose, sixteen times between them, and not one of those sixteen is attached to a number.
Uniform air left between tape and head, priced on the ring: every row is 2π times the gap, with the share of the band's whole 80 mm width beside it
| Air kept under the tape | In inches | Added to the ring | On the tape's printed figures | Share of the band's width |
|---|---|---|---|---|
| 0.5 mm | 0.02 in | +3.14 mm (0.12 in) | +0.31 cm | 3.9% |
| 1 mm | 0.04 in | +6.28 mm (0.25 in) | +0.63 cm | 7.9% |
| 2 mm | 0.08 in | +12.57 mm (0.49 in) | +1.26 cm | 15.7% |
| 3 mm | 0.12 in | +18.85 mm (0.74 in) | +1.88 cm | 23.6% |
| 4 mm | 0.16 in | +25.13 mm (0.99 in) | +2.51 cm | 31.4% |
Columns three and four are 2π multiplied by the row's millimetres, taken from the unrounded product; column five divides that by 80 mm, which is 620 minus 540, the width of the published band. The gap has to be uniform all the way round for the multiplication to hold — a tape that rides high over one ear and sits low over the other is the case the next table prices instead. This ladder is this page's worksheet: the rungs from half a millimetre to four were chosen so they could be read against a finger and a hairstyle, and the record supplies no number for either of those two things. Sensitivity, both directions: 6.28 mm of ring is a twelfth of the whole band, so any reading that sits less than 6.28 mm inside an edge is one millimetre of air away from being outside it; and read backwards, a ring figure that comes back one centimetre high is not a centimetre of head but 1.59 mm of it, because the inverse of 2π is 0.159. The rows of the first table at 550 and 610 mm sit 10 mm of ring from an edge, which is 1.59 mm of air — the distance a comb and a parting cover without anyone thinking about it.
What a Tilted Tape Costs, Which Is Less Than It Feels Like
The landmarks in the section above are not four names for one ridge, and the difference between them is mostly a tilt. A tape whose front end rides on the brow while its back end stays level with the ear line is a ring taken on a slant, and a slant can be priced without knowing anybody's head. Model the head as a cylinder whose level ring equals the reading, tip that ring about the ear-to-ear axis until its front edge sits Δh below its back edge, and the ring becomes an ellipse: stretched along the slope by exactly as much as the cylinder allows, and longer by an amount that grows with the square of the angle, not with the angle itself.
At the middle of the band the arithmetic gives this: a front end 10 mm low costs 0.43 mm of ring, 20 mm low costs 1.70 mm, and 30 mm low — a tape hanging more than an inch below the ear line at the front, a tilt of 9.2 degrees — costs 3.81 mm. It takes 39 mm of front-to-back difference to move a reading as far as one millimetre of air does. The landmark argument is second-order and the pulling of the tape is first-order, and that ranking is the finding worth carrying out of this page.
What that table cannot price is the larger half of the same mistake. A head is not a cylinder. The ring over the brow and the ring at the widest part of the skull are cross-sections of different shapes at different heights, and how far apart those two rings are is a measurement of heads, which this site publishes none of. One position anchors its ring on the widest point and another on the line above the ears, and this page can say by how much a tape tilted between them changes length while it cannot say by how much the head changes underneath. The row a reader would actually want is the row the record does not contain.
A front-to-back tilt priced on a cylinder whose level ring equals the reading, by Ramanujan's second approximation for an ellipse: the tilt component of a landmark error, and only that component
| Front edge below the back edge by | Tilt at a 580 mm head | Ring added at 540 mm | Ring added at 580 mm | Ring added at 620 mm |
|---|---|---|---|---|
| 5 mm (0.20 in) | 1.6° | +0.11 mm | +0.11 mm | +0.10 mm |
| 10 mm (0.39 in) | 3.1° | +0.46 mm | +0.43 mm | +0.40 mm |
| 15 mm (0.59 in) | 4.6° | +1.03 mm | +0.96 mm | +0.89 mm |
| 20 mm (0.79 in) | 6.2° | +1.82 mm | +1.70 mm | +1.59 mm |
| 25 mm (0.98 in) | 7.7° | +2.84 mm | +2.65 mm | +2.48 mm |
| 30 mm (1.18 in) | 9.2° | +4.09 mm | +3.81 mm | +3.57 mm |
The model, stated so it can be redone: a cylinder of diameter D = C ÷ π, a ring tipped about a horizontal diameter so its two edges differ vertically by Δh, therefore θ = atan(Δh ÷ D) and ellipse semi-axes D ÷ 2 and D ÷ (2 cos θ), with the perimeter from Ramanujan's second approximation. Three columns price the same tilt at the floor, the middle and the ceiling of the published band, and the spread is the point: at 30 mm the ring grows 4.09 mm on a 540 mm head and 3.57 mm on a 620 mm one, so this component barely depends on whose head it is. For small tilts the whole result is close to C θ² ÷ 4 — checked against the exact form at 0.42 versus 0.43 mm and at 3.76 versus 3.81 mm — which is why doubling the tilt quadruples the cost and why the first row of this table is invisible on any tape made. Clearance and tilt are added rather than traded: the 1915 instruction not to draw a measure tight is a clearance instruction, so a tape worn low at the front and pulled tight carries 3.81 mm of tilt error and 6.28 mm per millimetre of air at the same time. In the eight positions read here the words for a slant, an angle or a degree appear twice between two pages and carry no number on either. Not priced, because nothing published here could price it: the change of cross-section when the ring moves to a different height on the skull.
Six Ways to Fix One Ring, and the Element Nobody Writes Down
Sort the eight readable positions by the four things a ring needs — an anchor, a level, a point to read at, and one statement about what the reading can be wrong by, whether that is written as how hard the tape is pulled or as the hair lying under it — and no page in the set carries all four. Three of them carry three, five carry two, and the count of pages carrying all four is zero. That is the exact shape of the gap, and it needs stating precisely because the opposite claim would be false: these positions are not silent about the procedure. Every one of the eight names where the tape goes, five say something about how hard to pull it, three say keep the ring level, two tell you to read the number where the tape crosses itself, and one says there is hair under it.
They do not name the same place. Read as anchors rather than as sentences, the eight use four landmarks between them: six invoke the line above the ears, four the middle of the forehead, three the brow, and one — a single position, and the only one that uses it — the widest part of the head. Grouped into the anchor sets those words actually describe, the eight reduce to six: two pages pair the ear line with the forehead and so agree with each other, two more name the ear line and nothing else, and the remaining four are each their own combination. One page names the ear line and the widest part in the same instruction, and does not say whether it means one ridge or two, and nothing else in the eight says either.
This site's own page is one of the positions with the hole in it. Its three lines name the ear line and the middle of the forehead, tell the reader to keep the tape level and snug, and print no tolerance of any kind — the same zero that the arithmetic above exists to fill, and it is worth saying plainly that a band published with both ends and a procedure published without an error budget are two halves of one job rather than two finished jobs. Put the counts beside each other and the pattern is not a matter of taste: a landmark appears in every procedure read here, and a quantified uncertainty appears in none of them, in a subject whose whole purpose is a number that has to be right to within about one centimetre.
The anchors used for one ring, counted as word-boundary hits in the body text of the eight positions whose text could be read; times mentioned and pages agreeing are printed apart on purpose
| How the ring is anchored | Positions that use it | Times the words appear | What that wording fixes | What it leaves to the reader |
|---|---|---|---|---|
| The line above the ears | 6 of 8 | 9 | The height of the ring at the sides | Whether the front rides on the forehead or on the brow |
| The middle of the forehead | 4 of 8 | 11 | A front edge set high | Which side landmark holds the ring level to it |
| Just above the brow | 3 of 8 | 5 | A front edge set low | Whether the ring still clears the skull behind it |
| The widest part of the head | 1 of 8 | 1 | An anchor set by prominence alone | Everything else — no other position uses this anchor at all |
The counts are occurrences of the words in text left after markup was stripped, so a page that repeats one instruction three times reports three; three pages naming the ear line nine times is not three definitions that disagree. Grouping those occurrences into anchors, levels and reading points is this page's reading of the recorded counts, not a field any source publishes, and the four-element ledger it is read against is in the paragraph above. A ring is fixed by two landmarks and a level, which is why one page can name two anchors and still describe a single ring, and why six pages invoking the ear line does not mean six pages agreeing. Positions are described by what kind of page they are and not by who publishes them, and no link to any of them is given anywhere on this page.
What the Printed Manual and the Screened Charts Left Blank, Both
Order what can be dated by the date each source carries, and let the undated ones sit below with their word counts so the gap in the record stays visible instead of smoothed over. The printed manual carries an imprint year and nothing else. The oldest dated position in the web set was published on 17 July 2017 and last marked itself modified on 5 June 2025; the newest date any readable position carries is 7 August 2026. From the two possible days of that 1915 imprint to that last date is 40,397 to 40,761 days, which is 110.60 to 111.60 years, and across the whole of it the instruction is still the one this page is written against: a ring round the head, a place to hold that ring, and a statement about how hard to pull it. Every one of the eight names the first two, five of the eight name the third, and the count of positions that puts a figure on any of the three is zero.
Inside the web record alone the finding repeats at shorter range. Between the oldest and the newest publication dates in the eight are 1,872 days, 5.13 years. The position that prints the finest ladder in the set — two decimal places in centimetres, where the printed manual worked in inches and quarters, and where its 1915 contemporary worked in wire — has been revised across 3,209 days, 8.79 years, and every revision moved the decimals rather than the error. Five of the eight carry no date in either their text or their machine-readable fields, which is why the table below has nine rows and its footnote accounts for the two positions that get no row at all.
The last column of the table below is where those ladders run out. Every row leaves the reader holding a number to compare against and nothing to compare it with. 1915 leaves a finger and a worked example head of 24 inches. The two 2017 positions leave rungs at one and two decimal places of precision with no accuracy claimed under either. The 2022 page leaves the word snug four times in 250 words of text, the shortest in the eight against a longest of 3,133. Precision moved repeatedly across the span; the size of a wrong reading was never written down at all.
Dates as each source carries them, read against the ten positions on 7 October 2026 — eight have a row, the other two are accounted for in the note — and the printed row is described in this page's words rather than quoted, because it was read through a transcription and a transcription is not clean
| Published | What kind of source | What it says the ring is | What its instruction leaves you holding |
|---|---|---|---|
| 1915, imprint year and nothing else | A printed millinery course manual in two parts; the author's name is garbled in the transcription and is not printed here | The head measure defined as the distance round the head taken over the hair, said to vary with the head and with the style of dressing it; the wire not to be drawn tight, with an allowance named after a finger; one worked example at 24 in | A definition and an allowance, neither of them numbered, and an example head that lands 10.4 mm inside the ceiling of a band published 111 years later |
| July 17, 2017, marked modified June 5, 2025 | A shop's care-blog sizing guide, 1,605 words, no table | A ladder from 51 to 61 cm in two-centimetre steps; the forehead and the brow named, the tape kept level, the fit called snug once | A rung to land on and three of the four elements of a procedure; the fourth element is not in the document |
| October 24, 2017, marked modified August 7, 2026 — the newest date any readable position carries | An instructional site's article, 2,313 words, no table | Centimetres written to two decimals from 54.61 to 64.45 against inches from 20 to 25.375; the ear line and the forehead, the reading taken where the tape overlaps, and the presence of hair under it | A finer ladder than anything in print, and never a word on how hard to pull; the one mention of hair is that hair is there, not how much it is worth |
| September 1, 2022, marked modified November 12, 2024 | A maker's own size guide, 250 words, no table | Six scattered numbers, none of them a head measure; the ring anchored on the ear line and the brow, kept level, and called snug four times | The word snug more often than any other position and nothing to hold it against; 250 words, the shortest text in the eight against a longest of 3,133 |
| Undated; 2,027 words, no table | The only position of the eight to name a common adult band as such | Names the band and attaches no bounds to the name; anchors the ring on the ear line alone and reads it where the tape overlaps | The phrase everyone is looking for, with no lower end and no upper end under it |
| Undated; 3,133 words, one table | A hat maker's sizing page — the longest text in the eight | Centimetres at 55, 57, 59 and 64 inside one table, with the surrounding text running from 53 to 65; the word for a tilt appears once, without a number, and an outline of a face is matched to a hat number 27 times | The most face-shape sentences in the record and no figure for the fit; the one word that admits the ring can sit at an angle carries no measurement |
| Undated; 406 words, one table | A university's graduation-cap conversion page, written for a ceremony rather than for a shop | A centimetre ladder 53 to 58 beside inches from 20 7/8 to 23 3/8; the ear line and the widest part named together, and the fit called tight twice | The only use of the widest-part anchor in the eight, given without saying whether it is the same ridge as the ear line |
| Undated; 1,326 words, four tables | An athletic-goods maker's fit page — the most tables in the eight | Sizes as US 6 1/2 to 7 7/8 and 20 1/2 to 25 inches across four tables, with youth and extra-large labels but no statement of where the adult range ends; the brow anchors the ring and the tape is kept level | Four tables and no bounds: labels at both ends of a range whose ends are never given, which is the one thing a fit page is for |
| Undated; 2,013 words, one table | A makers' association chart — the only position that tells you to take the measure again | A centimetre ladder 52 to 65 in one table, fourteen numbers printed as ranges; the ear line, the forehead and the brow all named, the fit called snug seven times, and the instruction to measure again twice | Every element except the one with a figure on it: the re-measure is commanded and what it is meant to catch is not stated |
Two positions get no row and are accounted for rather than dropped. Both refused the plain fetch and were then opened in a real browser — the first landed on a shop's own error page, the second stopped at a verification screen — so neither body was read, and neither is counted among the eight anywhere on this page. The single line carried about the second is a search-result summary telling readers to divide the inch figure by 3.14 and round; a summary is not a read body, and no sentence on this page rests on it. Word counts are counts of text after markup was stripped, so a page with four tables and a product grid reports a large number for reasons that have nothing to do with how much it teaches. Five positions carry neither a printed date nor a machine-readable one; those rows say so and keep their word counts, because a table sorted by date that quietly omitted the undated rows would present the record as tidier than it is.
What These Tables Do Not Settle
Whether the ring you read becomes the number a seller prints is a different question, and this page does not answer it. One position's line in the result list says to divide the inch figure by 3.14 and round; that page refused the plain fetch, was opened in a real browser, and gave up its body to neither, so the sentence exists here only as a summary. Among the eight positions whose text was read, not one prints the division — one uses the word diameter, and one sets an inch ladder of 20 7/8 to 23 3/8 beside a centimetre one, which is the shape of a relation without the relation written out. Dividing a ring by π returns a diameter, which is why the fourth column of the first table exists. Whether a trade then uses that number as a size label is not settled by anything read here, and this site publishes no conversion from a ring to a size.
The band is also not quite what it looks like. 540 to 620 mm is a common range published here as a starting point, with both ends inside it, its ends checked against the ends other charts used at the time it was set — and it is not a measurement this rule set has ever taken. The five readings this site publishes are face length, forehead width, jaw width, chin width and the jaw angle; a ring round a skull is not among them, and no head inside a hat has ever been measured here. So the 1915 example can be placed at 609.6 mm, 87.0% of the way up a band printed in the century after that manual, and it cannot be checked against anything on this site.
What survives all of that is a procedure and a price list. Take the ring over the hair, level, snug rather than tight, and read it where the tape meets itself; that number is yours before a chart is opened. Then know what it costs: a millimetre of air is 6.28 mm of ring, a millimetre of ring is 0.159 mm of head, and the whole published adult band is 12.73 mm of radius, which is smaller than most of what goes under a tape.
- Four decisions, one of them numbered only here: anchor, level, reading point, tightness. The first three are in the published record; the fourth exists as a word — snug, tight, loose, sixteen times in five pages — and never as a figure.
- Multiply the air by 6.283 and it is a ring error; divide a ring error by 6.283 and it is a head. That one multiplication is the whole tolerance arithmetic, and it holds whatever shape the head turns out to be.
- Tilt is the small one. A tape worn 30 mm low at the front — a visible, arguable mistake — moves the reading 3.81 mm at the middle of the band, while 1 mm of air moves it 6.28 mm, and it takes 39 mm of tilt to catch up.
- The band is global and it has ends. 540 to 620 mm with both inside, and no correspondence between a ring and the shape of a face on this page or anywhere in this site's rule set.
A hat size is a distance round a head, so the honest summary is four sentences and one multiplication: ride the tape on the ridge your hat rides on, keep it level, read it where the tape meets itself, pull it snug and not tight — and know that every millimetre of air you leave under it is 6.28 mm on the ring. Ask it as hat size inches head and you are asking for one distance stated twice: 580 mm is 58.0 cm is 22.83 in, and none of the three is a size until somebody prints one.
What the published record supplies instead is ladders and vocabulary: 13,073 words of text across the eight positions whose body could be read on 7 October 2026, seven tables sitting in four of those eight, centimetre rungs from 51 to 65, decimals to two places, the words snug, tight and loose sixteen times, and a tolerance with a number on it zero times. One of those pages matches a hat number to the outline of a face twenty-seven times without once saying how far round the head that number was taken.
What is still missing is a measured head. The clearance ladder, the tilt table and the radius column in the first table are arithmetic on a published band and on the geometry of closed curves, and they are this page's worksheet rather than findings about anybody: the operand no table here can reach is a population of heads measured with a tape held to a stated tolerance, and that exists nowhere on this site. Measure the ring, price your own air against 6.28 mm per millimetre, and redo that multiplication with the number on your tape. Every column above is one division or one multiplication apiece, so none of them has to be taken on trust.
Questions this page answers
Should the tape go over the hair or against the scalp?
The instruction in the printed record is over the hair, and the same sentence adds that the measure varies with how the hair is dressed without giving a figure. What the geometry gives is the size of it: every millimetre left under the tape is 6.28 mm on the ring. So measure the way you intend to wear the hat, and treat the difference as a tolerance you can name rather than as a mistake you hope nobody notices.
Is a hat size the same thing as a measurement round the head?
They are one distance and two uses. The ring is the measurement; a size is whatever a seller decides to print beside it. This site publishes the common range of the ring — 540 to 620 mm, both ends inside it — and publishes no conversion from a ring to a size number, because none of the eight positions whose text could be read stated that conversion with both of its operands written out.
What if my reading lands between two steps on a chart?
One position in the eight steps its ladder by two centimetres and five of them address what to do between sizes, so the rounding advice exists. On the arithmetic here there is nothing to round: 540 to 620 mm is one continuous range with both ends inside it, and 575 mm differs from 585 mm by 10 mm of ring, which is 1.59 mm of radius. Round only when you are near an edge — a reading within 6.28 mm of one can be carried across it by a single millimetre of air.
Does the shape of my face change the ring a hat needs?
No pairing is published on this site, and none appears in the record read here. The ring is taken on the skull while the five readings this site measures are taken on a face, and the common band does not move with the shape of either. One position matches hat numbers to a facial outline twenty-seven times in a single page; that is a claim about which style a shop points you at, and it changes no millimetre of the distance round your head.