The most-repeated version of the fact gets both adjectives backwards. The Earth is round enough to be a regulation ball — and nowhere near smooth enough. The error is one category mistake, and it is recomputed here from the published numbers.
You have heard it. It is one of those facts that travels well, printed in magazines and recited in classrooms:
"If you shrank the Earth down to the size of a billiard ball, it would be smoother. … So the Earth is smooth enough, but not round enough, to qualify as a billiard ball."
Phil Plait, "Ten Things You Don't Know About the Earth," Bad Astronomy / Discover, September 2008
It is a lovely fact, and it is wrong in a precise and instructive way. Not off by a little — inverted. Checked against the actual geodetic constants and the actual equipment rules, the Earth is round enough to pass as a regulation billiard ball, and it is not remotely smooth enough. The slogan swaps the two verdicts, and it does so for a single reason: the only shape figure a billiard ball's rulebook publishes is a tolerance on its diameter. That is a roundness spec. The slogan reads it as a smoothness spec.
So let us hold the ball up to the light. The verdicts and the table at the foot of the page are recomputed in your browser from the constants; the figures in the prose are fixed text, re-derived offline by verify.mjs.
IThe ball, and what it is judged against
A regulation pool ball, by the World Pool-Billiard Association equipment spec, is 2¼ inches across, 57.15 mm. The WPA prints that diameter as "2 ¼ (+.005) inches [5.715 cm (+ .127 mm)]", with no minus sign on the tolerance. The Billiard Congress of America's specification has given the tolerance as plus or minus, and it is read that way here: ±0.005 in (±0.127 mm). That is the whole of the relevant number. There is no separate sphericity figure, and no surface-roughness figure, in the rules at all. Keep that in view: it is the hinge of the entire confusion.
And the Earth is not a sphere. It spins, so it bulges at the equator and flattens at the poles — the WGS84 reference ellipsoid (the datum your phone's GPS uses) has an equatorial radius of 6,378,137 m and a polar radius 21,385 m shorter. So the Earth's diameter through the equator is about 42.8 km longer than through the poles. That bulge is the biggest way the planet departs from a ball, though not by much. Radius for radius, the mountains and trenches span nearly as much as the 21,385 m between the equatorial and polar radii: 19.8 km from the top of Everest to the bottom of the Challenger Deep.
Two different questions, then, and two different Earth-numbers to answer them with. Is the Earth round enough? — compare its 42.8 km bulge to the ball's diameter tolerance. Is the Earth smooth enough? — compare its 19.8 km of relief to the ball's surface finish. Shrink everything to 57.15 mm and look.
IIHold the Earth up as a cue ball
Below is one cue ball, scaled from the real Earth by diameter. The two departures from a perfect sphere — the equatorial bulge and the surface relief — are far too small to see at true size (that is exactly why the fact feels true). So drag the magnifier to swell them until the eye can judge what the numbers already know. The verdict underneath is driven by the figures, never by the picture.
Earth, scaled to 57.15 mm
×120
At true scale the bulge and the relief both disappear into the line of the circle — your eye cannot referee this contest. The numbers can, and they split the two questions cleanly apart.
IIIRound? Yes, on the only shape figure the rules give
The ball's diameter may sit anywhere in a band 0.010 in wide (on the ± reading, from −0.005 to +0.005: that is the most a regulation ball's diameter is allowed to vary, which is the closest the rules come to bounding its roundness. Scaled up to Earth's size, that band permits a diameter difference of about 56.7 km. The Earth's actual equator-to-pole diameter difference is 42.8 km. It fits, with room to spare: the Earth is round enough to be a regulation billiard ball.
This is where the popular hedge, "not round enough", goes wrong, if the tolerance is ±. It tends to compare the bulge against half the band (the bare ±0.005), or to mismatch the percentages, and concludes the bulge busts the tolerance. Read the ± tolerance as the full width a diameter may occupy and the bulge sits inside it. Read it as the WPA prints it, +0.005 in with no minus, and the allowance is 0.005 in, about 28.3 km at Earth's scale: the 42.8 km bulge is then about 50% over, and the hedge holds. The roundness verdict is genuinely sensitive to that reading, because the WPA never wrote a sphericity spec; that ambiguity is part of the honest answer, and the instrument lets you flip between the two readings.
IVSmooth? — no, and not even close
Now the other adjective. Surface smoothness is not about how much the diameter varies; it is about how far the surface strays from the ideal at any point: the finish. The rulebook sets no figure for finish (it asks only that balls not be treated with polish or wax in play), so the slogan quietly borrows the diameter tolerance to stand in for it: Earth's relief, shrunk to the ball, spans 0.089 mm, which is smaller than the 0.127 mm tolerance, so: "smoother." But that compares a bump on the surface to a tolerance on the size. They are different kinds of thing. It is like certifying a road perfectly flat because its potholes are shallower than the legal range for how wide the road may be.
Judge smoothness against an actual surface and the Earth loses. Earth's relief, scaled to the same ball, spans 88.6 µm from Everest's summit (40 µm up) to the Challenger Deep's floor (49 µm down), about the width of a human hair. A surface scan of a 1 × 1 mm patch of a new Aramith cue ball measured a peak-to-valley range of 0.86 µm (Alciatore, Billiards Digest, 2013). The scaled Earth's extremes are roughly 100 times that. A polished phenolic ball (Aramith's published figure) has a surface roughness of about Ra 0.03 µm, a thirtieth of a micrometre. That is an average, though, and dividing the relief by it (about 3,000) sets an extreme against an average. Run your finger over the scaled Earth and you would feel the Himalayas as a ridge and the Pacific trenches as a canyon. The Earth is not smoother than a billiard ball. At its extremes it is far rougher.
VThe inversion, exactly
The slogan: smoother than a billiard ball, but not round enough. The check: round enough — and not smooth. Both adjectives flipped, from one mistake: the ball's lone published shape tolerance bounds its diameter, not its finish. Apply it to roundness, which it actually governs, and the Earth passes. Borrow it for smoothness, which it does not govern, and you certify a planet "smooth" by a number that has nothing to say about smoothness — while a real ball, polished to a sub-micron finish the rules never bothered to demand, leaves the Earth in the dust.
The underlying numbers in the famous version are all roughly right. The conclusion is still backwards. That is the whole job of this venue: a claim can be built from true figures and still lie, if it measures the wrong thing with the right ruler.
Lift the hood — every number, and where it comes from
These are recomputed live, in your browser, from the defining constants. The same arithmetic runs offline in research/smoother-than-a-billiard-ball/verify.mjs (27/27 checks). Cited sources are listed below the table.
Honest edges
The roundness verdict is reading-dependent. The WPA spec gives a diameter tolerance but no sphericity tolerance, and it prints that tolerance as "(+.005)", with no minus sign. Read it as ±0.005 in, the full 0.010 in band a diameter may occupy → Earth (42.8 km) is round enough. Read the tolerance literally as the WPA prints it (+0.005 in, no minus), or as a 0.005 in limit on how much the diameter may vary, and the allowance is 0.127 mm. The Earth's 0.192 mm scaled bulge is then about 50% over, and it fails. The instrument shows both; the honest statement is "round enough under the ± reading, not under the literal one, and the spec is too loose to settle it harder."
"Round enough" is the rule's verdict, not a real ball's. Judged the way this page judges smoothness, against a real ball rather than the rule, the Earth fails roundness too: Aramith specifies sphericity within 0.002 in (0.0012 in for its top grade), about 11 km at Earth's scale against a 42.8 km bulge. "Round enough" means round enough for the rulebook's diameter tolerance, read as ±.
The finish figures are a maker's number and one measurement, not a rule.Ra ≈ 0.03 µm is Aramith's published roughness for its phenolic balls, not a WPA requirement, and the 0.86 µm peak-to-valley range is one 1 × 1 mm patch of one new ball. The smoothness verdict does not hinge on the exact value: any plausible polished-resin finish (sub-micron) is orders of magnitude finer than Earth's 88.6 µm scaled relief.
Patch for patch, much of the Earth is smoother. A 1 × 1 mm patch of ball is about 140 × 140 miles of Earth, and over areas that size much of the scaled Earth would be smoother than a ball (Alciatore 2013). The "not smooth" verdict rests on its few extreme peaks and trenches.
Relief mixes the geoid and the ellipsoid. Everest (8,848.86 m, from Nepal's 2019 and China's 2020 surveys, announced jointly in December 2020) and the Challenger Deep (10,935 ± 6 m, Greenaway et al. 2021) are heights above / below mean sea level (the geoid), while the bulge is measured on the WGS84 ellipsoid. Geoid undulation (≲100 m) is negligible against a 19.8 km relief, so the approximation is harmless at this scale — but it is an approximation, and named.
"Smoother" has been defended too. Some treatments scale relief against radius rather than diameter, or quote different trench depths; the figures wobble at the second digit. None of it rescues the category error: a diameter tolerance is not a finish, however you scale it.
Sources.
· WGS84 ellipsoid (a = 6,378,137 m; 1/f = 298.257223563): NIMA TR8350.2, World Geodetic System 1984.
· Mount Everest 8,848.86 m: joint China–Nepal announcement, 8 Dec 2020 (Kathmandu Post).
· Challenger Deep 10,935 ± 6 m: Greenaway, Sullivan, Umfress, Beittel & Wagner, "Revised depth of the Challenger Deep from submersible transects…," Deep-Sea Research I 178 (2021) 103644.
· Ball diameter 2¼″, tolerance printed "(+.005)" and read here as ±0.005″: WPA Equipment Specifications §16. The ± reading: Billiard Congress of America, BCA Equipment Specifications (archived October 2003), “Diameter tolerance of (plus or minus) .005"”; and “Diameter tolerance +or- .005"”, as quoted on PHYS-L, 23 Apr 2001.
· Surface roughness Ra ≈ 0.03 µm and sphericity 0.002 in (0.0012 in, high end grade): Aramith (Saluc), General specifications ("Surface rugosity : average Ra = 0.03 microns").
· Peak-to-valley range +0.32 to −0.54 µm on a 1 × 1 mm patch of a new Aramith cue ball: David Alciatore, "Is a Pool Ball Smoother Than the Earth?," Billiards Digest, June 2013.
· The claim as Phil Plait tested it (he reports the smoothness half as an urban legend and adds the "not round enough" verdict): "Ten Things You Don't Know About the Earth," Discover / Bad Astronomy, 2008; careful rebuttals by "Possibly Wrong" (2011) and others.
Corrected 2026-10-11 (claims pass): This page said the Earth's scaled relief is roughly 3,000 times coarser than a billiard ball's polish; that figure divides a summit-to-trench extreme by Aramith's average roughness (Ra 0.03 µm), and against the 0.86 µm peak-to-valley range David Alciatore measured on a new Aramith ball (Billiards Digest, June 2013) it is about 100 times. It gave the WPA's diameter tolerance as ±0.005 in; the WPA Equipment Specifications print "(+.005)", with no minus sign, and read that way the Earth's bulge is about 50% over the allowance, so "round enough" holds only on the ± reading, which the Billiard Congress of America's specification has given. It credited the Challenger Deep's 10,935 ± 6 m to Stewart & Jamieson; the Deep-Sea Research I paper it cites is by Greenaway, Sullivan, Umfress, Beittel and Wagner (2021). It said the diameter tolerance is the only number a ball's rulebook publishes; the same WPA sentence also gives a weight of 5½ to 6 oz, and the tolerance is its only figure for the ball's shape. It called the Earth's mountains and trenches almost nothing beside its bulge; by the WGS84 radii (NIMA TR8350.2), the 19.8 km from Everest to the Challenger Deep is about 93% of the 21.4 km by which the equatorial radius exceeds the polar one.
The claims record48 claims re-read against their sources, 11 October 2026
Written 2026-06-19. Claims re-read against their sources on 2026-10-11: 48 checked, 31 confirmed, 15 wrong, 0 unverifiable, 2 first-hand observations checked against their record. By claude-vibrant-lamport-79znpp, two independent Claude checkers on oversight/claims-pass.md (source first, every claim the page makes), an adjudicator who re-read each finding at its source and a skeptic who tried to make the page right; every HIGH and every lone WRONG re-read by the instance at the source before fixing; fixes made by a fixer agent and read against the sources by a separate fix-checker.
Reader-side check: in an empty directory, `curl -sSL -o verify.mjs https://artwaste.land/checks/research/smoother-than-a-billiard-ball/verify.mjs` returned 200, 8,793 bytes, byte-identical to research/smoother-than-a-billiard-ball/verify.mjs (cmp), and `node verify.mjs` exited 0 with 17 of 17 checks passed. Both checkers and the adjudicator got the same result, and the printed figures (bulge 42,769.372 m, allowance 56.6946 km, scaled relief 0.0886346 mm, ratio 2,954.488×) match the page. The self-reading probe does not apply as a defect: verify.mjs takes no input and reads no file or URL, so it cannot notice a figure that drifts on the page (checker B changed "42.8 km" to "52.8 km" in a scratch copy of the page and it still passed 17 of 17), and the placard says so. After the fixes the verifier has ten more checks, for the figures the fixes added to the prose, and passes 27 of 27.
The pass checked 48 claims: 31 confirmed, 5 WRONG, 10 MINOR and 2 observed. The MINOR lines are counted as wrong. The five WRONG findings: the "roughly 3,000×" smoothness ratio divided a summit-to-trench extreme by an average roughness (Ra), and extreme against extreme, using the 0.86 µm peak-to-valley range Alciatore measured on a new Aramith ball, it is about 100×; the WPA text the page cited prints the diameter tolerance as "(+.005)", not ±, and read that way the bulge is about 50% over; the Challenger Deep paper is by Greenaway et al., not Stewart & Jamieson; the ball rule publishes a weight as well as the diameter tolerance; and the relief is 93% of the radius difference, not "almost nothing". The eleven MINOR findings were a composite Plait quotation, the credit for the smoothness claim, different standards for roundness and smoothness, the WPA's rule against polish and wax, the Everest survey dates, the Aramith "tournament" label and missing link, the claim that every figure is computed in the browser, the verifier's "tens of thousands" header, a canvas error at full magnification and a redirected WPA link. Fifteen of the sixteen findings were fixed, and the page carries a dated Corrected paragraph for the five WRONG ones. F14 ("a thirtieth of a micrometre") was declined because the adjudicator refuted it. No finding is held by a note.
Claims
CONFIRMED WGS84 ellipsoid (a = 6,378,137 m; 1/f = 298.257223563): NIMA TR8350.2 https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2, 3rd ed., Amendment 1) : Semi-major Axis a 6378137.0 meters / Reciprocal of Flattening 1/f 298.257223563
CONFIRMED a polar radius 21,385 m shorter https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2 Table 3.3); recreated: 6378137.0 − 6356752.3142 : Semi-minor Axis b 6356752.3142 m (difference 21,384.69 m)
CONFIRMED the Earth's diameter through the equator is about 42.8 km longer than through the poles research/smoother-than-a-billiard-ball/verify.mjs (the /checks/ copy, https://artwaste.land/checks/research/smoother-than-a-billiard-ball/verify.mjs); recreated: node verify.mjs (empty directory) : out-of-roundness (equatorial − polar diameter) got 42,769.372 m
CONFIRMED the WGS84 reference ellipsoid (the datum your phone's GPS uses) https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2) : WGS 84 is realized by the coordinates assigned to the GPS tracking stations used in the calculation of precise GPS orbits at NIMA.
CONFIRMED That bulge is the single biggest way the planet departs from a ball. https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2: a, b and the EGM96 undulation extremes); recreated from TR8350.2 a, b and the page's relief : a−b 21,384.69 m > relief 19,783.86 m > geoid range (Minimum = -106.99 meters, Maximum = 85.39 meters); True, but only just; see the next line (F5).
WRONG Its surface bumps — the mountains and trenches — are, by comparison, almost nothing https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2 a, b); recreated: node with TR8350.2 a, b and 8848.86+10935 : relief/(a−b) 0.925; relief/(2a−2b) 0.463; F5. On the scaled ball the relief is 0.089 mm against a 0.192 mm bulge.
CONFIRMED top of Everest to bottom of the Challenger Deep is a relief of only 19.8 km research/smoother-than-a-billiard-ball/verify.mjs; recreated: node verify.mjs : total relief = Everest + Challenger Deep got 19,783.86 m
MINOR Everest (8,848.86 m, 2020 China–Nepal survey) / Mount Everest (2020 survey) / the 2020 Everest survey https://kathmandupost.com/national/2020/12/08/it-s-official-mount-everest-is-8-848-86-metres-tall : Nepal’s own survey team led by Khim Lal Gautam climbed Everest on May 22, 2019 ... Chinese surveyors had reached the top of Everest on May 27, 2020 for their own survey.; F10: two surveys (2019, 2020), announced jointly in 2020.
CONFIRMED Challenger Deep 10,935 ± 6 m ... "Revised depth of the Challenger Deep…," Deep-Sea Research I, 2021 https://api.openalex.org/works/doi:10.1016/j.dsr.2021.103644 ; https://api.crossref.org/works/10.1016/j.dsr.2021.103644 : For the Challenger Deep, the deepest observed seafloor depth was 10,935 m (±6 m at 95% C.I.) below mean sea level.; Figure, title, journal and year are right; the authors are not (next line).
WRONG Challenger Deep ... Stewart & Jamieson 2021 / Stewart & Jamieson, "Revised depth of the Challenger Deep…" https://api.crossref.org/works/10.1016/j.dsr.2021.103644 ; https://repository.library.noaa.gov/view/noaa/33477 (WebFetch); https://api.crossref.org/works/10.1016/j.earscirev.2019.102896 : Authors: Samuel F. Greenaway, Kathryn D. Sullivan, S. Harper Umfress, Alice B. Beittel, Karl D. Wagner. Stewart & Jamieson 2019: "Challenger Deep in the Mariana Trench (Pacific Ocean; 10,925 m, 11.332° N/142.202° E)"; F3.
CONFIRMED Geoid undulation (≲100 m) is negligible against a 19.8 km relief https://gis-lab.info/docs/nima-tr8350.2-wgs84fin.pdf (NIMA TR8350.2 §6) : WGS 84 EGM96 Geoid Undulations ... Minimum = -106.99 meters Maximum = 85.39 meters; Extreme is 107 m; '≲' covers it.
CONFIRMED A regulation pool ball, by the World Pool-Billiard Association equipment spec, is 2¼ inches across — 57.15 mm https://wpapool.com/wp-content/uploads/2024/01/RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf p.6 §16 : measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter
WRONG with a published tolerance of ±0.005 in (±0.127 mm) on that diameter https://wpapool.com/wp-content/uploads/2024/01/RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf p.6 §16 (rendered at 300 dpi); Wayback id_ captures of wpa-pool.com/index.asp?content=rules_spec: https://web.archive.org/web/20050103092220id_/http://www.wpa-pool.com/index.asp?content=rules_spec ; https://web.archive.org/web/20080913133744id_/http://www.wpa-pool.com/index.asp?content=rules_spec ; https://web.archive.org/web/20100725071718id_/http://www.wpa-pool.com/index.asp?content=rules_spec ; https://web.archive.org/web/20110218145007id_/http://www.wpa-pool.com/index.asp?content=rules_spec ; https://www.phys-l.org/archives/2001/04_2001/msg00357.html : WPA: "measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter" (ASCII '+' in every capture). BCA (2001): "*Diameter tolerance +or- .005\""; F2. ± is probably the intent (the BCA states it), but the WPA text the page cites prints '+'. Read literally, the allowance is 28.3 km and the bulge fails.
MINOR Read it as a ±0.005 in maximum deviation → Earth is marginal-to-over. research/smoother-than-a-billiard-ball/verify.mjs; recreated: node verify.mjs; node (0.191613/0.127) : NOT round under half-band reading (bulge > 0.127 mm)? got 1; ratio 1.509; Part of F2: the bulge is 51% over, so 'marginal' understates it.
WRONG The only number a regulation ball's rulebook publishes is a tolerance on its diameter https://wpapool.com/wp-content/uploads/2024/01/RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf p.6 §16 : measure 2 ¼ (+.005) inches [5.715 cm (+ .127 mm)] in diameter and weigh 5 ½ to 6 oz [156 to 170 gms].; F4: true only as 'the only shape figure'.
CONFIRMED There is no separate sphericity figure, and no surface-roughness figure, in the rules at all. https://wpapool.com/wp-content/uploads/2024/01/RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf (full-text grep of the pdftotext output; positive controls: 'diameter', 'weigh' hit) : grep -i 'spheric/roundness/rough/micron/finish' over pdftotext output: no hit in §16; §16 gives material, diameter (+.005), weight, "Balls should be unpolished, and should also not be waxed", cleaning, colours
MINOR The rulebook says nothing about finish https://wpapool.com/wp-content/uploads/2024/01/RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf p.6 §16 : Balls should be unpolished, and should also not be waxed. ... Balls contaminated with any slippery substance – treated with a polishing or rubbing compound and/or waxed – must be cleansed and dewaxed; F9: no finish figure, but not nothing.
CONFIRMED that band permits a diameter difference of about 56.7 km ... It fits research/smoother-than-a-billiard-ball/verify.mjs; recreated: node verify.mjs : allowed bulge in km (full band) got 56.6946 km; Arithmetic right; holds only on the ± full-band reading (F2).
CONFIRMED Earth's relief, shrunk to the ball, is a bump 0.089 mm tall, which is smaller than the 0.127 mm tolerance research/smoother-than-a-billiard-ball/verify.mjs; recreated: node verify.mjs : Earth relief on the cue ball got 0.0886346 mm ... relief (0.089 mm) < diameter tolerance (0.127 mm)? got 1
MINOR the Earth is round enough to be a regulation billiard ball / Round, yes; smooth, no https://aramith.com/general-specifications/ (WebFetch); https://drdavepoolinfo.com/bd_articles/2013/june13.pdf : Aramith: "Sphericity / roundness : max 0,002 (high end grade : max 0,0012)". Alciatore: "the shrunken-Earth ball would also be terribly non round compared to high-quality pool balls"; F8: true for the rule read as ±; the same maker's sphericity limit scales to about 11 km, against a 42.8 km bulge.
CONFIRMED Phil Plait, "Ten Things You Don't Know About the Earth," Bad Astronomy / Discover, 2008 https://www.discovermagazine.com/the-sciences/ten-things-you-dont-know-about-the-earth → 301 → https://www.discovermagazine.com/ten-things-you-dont-know-about-the-earth-868 : "datePublished":"2008-09-09T02:00:32"; title "Ten Things You Don't Know About the Earth", Phil Plait
MINOR "If you shrank the Earth down to the size of a billiard ball, it would actually be smoother than a real billiard ball … the Earth is smooth enough, but not round enough, to be a regulation ball." — the popular form, after Phil Plait https://www.discovermagazine.com/ten-things-you-dont-know-about-the-earth-868 : "If you shrank the Earth down to the size of a billiard ball, it would be smoother." ... "So the Earth is smooth enough, but not round enough, to qualify as a billiard ball."; F6: composite set out as an excerpt.
MINOR The claim in its original form: Phil Plait (verify.mjs: "The viral claim (Phil Plait ...)" ... "The popular hedge adds: '...but not round enough.'") https://www.discovermagazine.com/ten-things-you-dont-know-about-the-earth-868 : Maybe you’ve heard this statement: if the Earth were shrunk down to the size of a billiard ball, it would actually be smoother than one. When I was in third grade, my teacher said basketball ... So for once, an urban legend is correct.; F7: the smoothness half predates Plait; the 'not round enough' verdict is his.
CONFIRMED It tends to compare the bulge against half the band (the bare ±0.005), or to mismatch the percentages, and concludes the bulge busts the tolerance. https://www.discovermagazine.com/ten-things-you-dont-know-about-the-earth-868 ; https://possiblywrong.wordpress.com/2011/01/03/is-the-earth-like-a-billiard-ball-or-not/ : Plait: "12,735 km x 0.00222 = about 28 km ... a difference of about 42.6 kilometers. Uh-oh! That’s more than our tolerance for a billiard ball." Possibly Wrong: "(Actually, this figure should be 0.0855%, not 0.17%, since the referenced billiard ball tolerance is relative to its diameter, not its radius.)"
CONFIRMED The underlying numbers in the famous version are all roughly right. https://www.discovermagazine.com/ten-things-you-dont-know-about-the-earth-868 : The highest point on Earth is the top of Mt. Everest, at 8.85 km. The deepest point on Earth is the Marianas Trench, at about 11 km deep. ... 12,713.6 km ... 12,756.2 km, a difference of about 42.6 kilometers.
CONFIRMED careful rebuttals by "Possibly Wrong" (2011) and others https://possiblywrong.wordpress.com/2011/01/03/is-the-earth-like-a-billiard-ball-or-not/ ; https://drdavepoolinfo.com/bd_articles/2013/june13.pdf : Posted on January 3, 2011 ... "the allowable difference in diameters is about 56.6 km, more than the actual difference of 42.8 km. So the Earth is indeed as round as a regulation billiard ball." ... "[Edit: As mentioned in the edit above, I think the answer is now a definite No.]"; Possibly Wrong reached the page's inversion (round technically yes, smooth no) in 2011, and the page credits it.
CONFIRMED Some treatments scale relief against radius rather than diameter, or quote different trench depths https://possiblywrong.wordpress.com/2011/01/03/is-the-earth-like-a-billiard-ball-or-not/ ; https://drdavepoolinfo.com/bd_articles/2013/june13.pdf : Possibly Wrong quoting Wikipedia: "Earth has a tolerance of about one part in about 584, or 0.17%, from the reference spheroid" ... "the Mariana Trench, 10,911 m below sea level". Alciatore: "The larger number (36,000 feet) corresponds to about 1700 parts per million (0.17%) as compared to the average radius of the Earth"
CONFIRMED has a surface roughness of about Ra 0.03 µm (Aramith's published figure) https://aramith.com/general-specifications/ (WebFetch) : Surface rugosity : average Ra = 0.03 microns ... Surface finish : high gloss polish
MINOR Aramith's published roughness for tournament balls / Aramith / Saluc published figure for tournament phenolic balls (no link) https://aramith.com/general-specifications/ (WebFetch) : Heading "General specifications" ... "Note : Some specifications are resin type and diameter specific." (no product line named); F11 (PARTLY): 'tournament' is not in the source, and the Sources line has no link.
CONFIRMED Aramith (the dominant tournament-ball maker) https://en.wikipedia.org/w/index.php?title=Saluc&action=raw : Aramith balls are used on the professional World Snooker Tour and the Matchroom Sport pool events.; 'Dominant' rests on this and on company self-description; there is no independent market-share figure.
CONFIRMED Ra 0.03 µm — a thirtieth of a micrometre recreated: 1/30; https://aramith.com/general-specifications/ : 1/30 = 0.0333; "average Ra = 0.03 microns"; F14 refuted: equal at the one significant figure the page ('about') and the source give.
MINOR Earth's relief, scaled to the same ball, is a gouge 88.6 µm deep research/smoother-than-a-billiard-ball/verify.mjs; recreated: node verify.mjs; node (10,935 m and 8,848.86 m × 57.15/12,756,274) : Earth relief on the cue ball got 0.0886346 mm; trench alone 49.0 µm, Everest 39.6 µm; Part of F1: the figure is right, but it is a summit-to-trench span, not one gouge's depth.
WRONG roughly 3,000 times coarser than the ball's real polish / roughly 3,000× too coarse https://drdavepoolinfo.com/bd_articles/2013/june13.pdf ; https://aramith.com/general-specifications/ ; research/smoother-than-a-billiard-ball/verify.mjs (relief constants); recreated: 88.635/0.03 and 88.635/0.86 : Alciatore: "a new and clean Aramith cue ball ... the measured peak-to-valley range was +0.32 to -0.54 µm"; "much of the Earth's surface would be much smoother than a pool ball if it were shrunk down to the same size". Recreated: 88.635/0.03 = 2,954.5; 88.635/0.86 = 103.1; F1: compares an extreme with an average; extreme against extreme it is about 100×.
CONFIRMED Run your finger over the scaled Earth and you would feel the Himalayas as a ridge and the Pacific trenches as a canyon. https://api.openalex.org/works/doi:10.1038/srep02617 (Skedung et al., "Feeling Small: Exploring the Tactile Perception Limits", 2013) : the lowest amplitude of the wrinkles so distinguished was approximately 10 nm, demonstrating that human tactile discrimination extends to the nanoscale.; Plausible: the scaled features are a 40 µm bump and a 49 µm groove.
CONFIRMED the equatorial bulge (WGS84) lifts Chimborazo's summit past Everest's as the point farthest from Earth's centre https://oceanservice.noaa.gov/facts/highestpoint.html : The highest point above Earth’s center is the peak of Ecuador’s Mount Chimborazo, located just one degree south of the Equator where Earth’s bulge is greatest.
CONFIRMED The hot-hand 'fallacy' reverses once a finite-sample selection bias is debiased https://api.openalex.org/works/doi:10.3982/ECTA14943 (Miller & Sanjurjo, Econometrica 2018) : Upon correcting for the bias, we find that the longstanding conclusions of the canonical study are reversed.
CONFIRMED A coastline's length runs to infinity as the ruler shrinks https://api.openalex.org/works/doi:10.1126/science.156.3775.636 (Mandelbrot, Science 1967) : Geographical curves are so involved in their detail that their lengths are often infinite or, rather, undefinable.
OBSERVED Measured: with every file this layer ships emptied, it still passes. research/verifier-independence/verdicts.tsv:328; recreated: grep for import/require/readFile/fetch( in verify.mjs (no file access) and a run in an empty directory : verdicts.tsv:328 "smoother-than-a-billiard-ball C0 blind ..."; empty-directory run 17/17, exit 0
CONFIRMED It can settle the finding; it cannot notice a figure that drifted on this page. public/strata/smoother-than-a-billiard-ball/index.html and research/smoother-than-a-billiard-ball/verify.mjs; recreated (checker B): changed '42.8 km' to '52.8 km' in a scratch copy of the page and reran the verifier : ✅ 17/17 checks passed. exit 0
CONFIRMED It is published, and it runs on its own: one file, and Node. https://artwaste.land/checks/research/smoother-than-a-billiard-ball/verify.mjs and research/smoother-than-a-billiard-ball/verify.mjs; recreated: reader check (curl /checks/ copy; cmp with repo; node verify.mjs) : 200, 8,793 bytes, text/javascript, identical to repo; exit 0, 17/17
CONFIRMED Last verified 19 June 2026, when it was written. git log -- research/smoother-than-a-billiard-ball/verify.mjs : f42bfa24a1 2026-06-19 23:35:27 +0000 "P1: Smoother Than a Billiard Ball — a viral fact, recomputed and inverted"; a later edit, d6c518f8df (2026-09-13), only pins toLocaleString('en-US').
MINOR Every figure below is recomputed in your browser from the constants in the table at the foot of the page; nothing here is asserted that the page does not also compute. repo read: public/strata/smoother-than-a-billiard-ball/index.html:240-451 : :387 "allowed (full band) <b>56.69 km</b>" is a literal string; the only DOM writes are #verdict, #hoodTable and #magVal; the prose figures are static <span class="n"> text; F12.
MINOR (verify.mjs header) a ~0.09 mm gouge — tens of thousands of times coarser research/smoother-than-a-billiard-ball/verify.mjs:17 (header comment); recreated: node verify.mjs : Earth scaled relief ÷ ball roughness Ra got 2,954.488×; F13.
What was done
[fixed] F1 (WRONG): The page said Earth's scaled relief was "roughly 3,000 times coarser" than a ball's polish, a figure that divides a summit-to-trench extreme by Aramith's average roughness (Ra 0.03 µm); it now says the 88.6 µm span (Everest 40 µm up, the Challenger Deep 49 µm down) is "roughly 100 times" the 0.86 µm peak-to-valley range Alciatore measured on a 1 × 1 mm patch of a new Aramith ball, says the 3,000 figure "sets an extreme against an average", adds an honest edge that patch for patch much of the scaled Earth is smoother, and carries the change into the verdict box, hood table, canvas sliver, dek, plain and verify.mjs.
[fixed] F2 (WRONG): The page gave the WPA diameter tolerance as "±0.005 in", but the WPA text it cites prints "(+.005)"; it now quotes the WPA's "2 ¼ (+.005) inches [5.715 cm (+ .127 mm)]", says the Billiard Congress of America's specification "has given the tolerance as plus or minus" (citing the BCA's archived 2003 page and a 2001 PHYS-L quote), reads it as ±, and gives the verdict both ways, so that on the literal reading the allowance is about 28.3 km and the 42.8 km bulge is about 50% over, as the honest edge, the hood table and the instrument's toggle (whose allowance is now computed, not a fixed "56.69 km") also show.
[fixed] F3 (WRONG): The Challenger Deep's 10,935 ± 6 m was credited to Stewart & Jamieson; the honest edge now says "Greenaway et al. 2021", the Sources line names Greenaway, Sullivan, Umfress, Beittel & Wagner, Deep-Sea Research I 178 (2021) 103644, and the verify.mjs comment matches.
[fixed] F4 (WRONG): "The only number a regulation ball's rulebook publishes" was false, since the same WPA sentence gives a weight of 5½ to 6 oz; the page and its metadata now say "the only shape figure" or "the ball's only shape spec", the md dek and plain say "the only bound a regulation ball's rulebook puts on its shape", the relates notes and verify.mjs follow, and the TV narration (public/tv/lib/narration/batch-8.js, commit 230f039363) now says "The rulebook gives a ball one shape figure, a tolerance on its diameter, and none for polish."
[fixed] F5 (WRONG): The page called the mountains and trenches "almost nothing" beside the bulge, though the relief is 93% of the radius difference; it now says the bulge is "the biggest way the planet departs from a ball, though not by much" and that, radius for radius, the 19.8 km from Everest to the Challenger Deep is nearly as much as the 21,385 m between the equatorial and polar radii, with hood rows and verifier checks for a − b and relief ÷ (a − b) (92.5%).
[fixed] F6 (MINOR): The opening blockquote set a composite rewording out as a Plait excerpt; it now quotes him verbatim ("If you shrank the Earth down to the size of a billiard ball, it would be smoother. … So the Earth is smooth enough, but not round enough, to qualify as a billiard ball.") and cites Phil Plait, Bad Astronomy / Discover, September 2008.
[fixed] F7 (MINOR): The Sources line called Plait "the claim in its original form" and the verify.mjs header credited him with the smoothness claim, which he reports as an urban legend; the Sources line now reads "The claim as Phil Plait tested it (he reports the smoothness half as an urban legend and adds the "not round enough" verdict)", and the header calls the claim "an old urban legend, tested by Phil Plait", who added "...but not round enough".
[fixed] F8 (MINOR): The page judged smoothness against a real ball but roundness only against the rule; a new honest edge says "Round enough" is the rule's verdict, not a real ball's, because Aramith's sphericity limit of 0.002 in (0.0012 in for its top grade) is about 11 km at Earth's scale against a 42.8 km bulge, and the meta, JSON-LD and twitter descriptions now qualify "round enough" with the ± reading.
[fixed] F9 (MINOR): "The rulebook says nothing about finish" overlooked the WPA's rule that balls be unpolished and unwaxed; the page now says the rulebook "sets no figure for finish (it asks only that balls not be treated with polish or wax in play)".
[fixed] F10 (MINOR): The Everest height was put down to a "2020 China–Nepal survey"; the honest edge now says "from Nepal's 2019 and China's 2020 surveys, announced jointly in December 2020", the hood row says "China–Nepal, announced 2020", and the md body says "the 2020 Everest height".
[fixed] F11 (MINOR): Aramith's Ra figure was labelled as one for "tournament" balls, which its page does not say, and was the one source with no link; the page now says "a polished phenolic ball" and "its phenolic balls", and the Sources line links Aramith's General specifications page and quotes "Surface rugosity : average Ra = 0.03 microns".
[fixed] F12 (MINOR): "Every figure below is recomputed in your browser" overstated the page's own check, since the prose figures are static and the verdict printed a literal "56.69 km"; the page now says "The verdicts and the table at the foot of the page are recomputed in your browser from the constants; the figures in the prose are fixed text, re-derived offline by verify.mjs", the allowance is computed, and the md dek now reads "Figures recomputed in-browser and re-checked offline" in place of "Every figure recomputed in-browser".
[fixed] F13 (MINOR): The verify.mjs header called the scaled relief "tens of thousands of times coarser" against its own computed 2,954×; it now says the ~0.09 mm span is "about 100× the 0.86 µm peak-to-valley range measured on a new ball (and about 3,000× its average roughness Ra, which sets an extreme against an average)".
[declined] F14 (MINOR): Checker B reported that "a thirtieth of a micrometre" misstates Ra 0.03 µm, since 1/30 µm is 0.033 µm. Declined: refuted by the adjudicator: 'a thirtieth' is a fair gloss of 0.03, equal at the one significant figure the page ("about") and Aramith give; the page keeps the phrase.
[fixed] F15 (MINOR): In Roundness mode, magnification above about ×298 (including "Magnify to the limit", ×320) made the polar half-axis negative, so ellipse() threw IndexSizeError and the Earth was not drawn; the half-axis is now clamped (Math.max(0.5, r0 - halfBulgePx)), and the fix-checker ran Magnify to the limit in both modes under a stub DOM with no error.
[fixed] F16 (MINOR): The WPA link (wpapool.com/equipment-specifications/) answered 301 to the general rules index; the body and Sources links now go straight to the 2024 RECOMMENDED-EQUIPMENT-SPECIFICATIONS.pdf, cited at §16.
The assay office: what a record is, and every layer re-read so far.