https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=Sondre99vexplain xkcd - User contributions [en]2026-04-13T09:25:53ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=3065:_Square_Units&diff=3696373065: Square Units2025-03-20T21:54:38Z<p>Sondre99v: /* Explanation */ Added calculation of speed at which the insect would have to travel.</p>
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<div>{{comic<br />
| number = 3065<br />
| date = March 19, 2025<br />
| title = Square Units<br />
| image = square_units_2x.png<br />
| imagesize = 545x678px<br />
| noexpand = true<br />
| titletext = The biggest I've seen in a published source in the wild is an 80-fold error in a reported distance, which I think came from a series of at least three unit conversions and area/length misinterpretations.<br />
}}<br />
<br />
==Explanation==<br />
{{incomplete|Created by a BUG IN A SQUARE AREA DEFOLIATION BOT - Do NOT delete this tag too soon.}}<br />
<br />
In this comic, [[Megan]] is using her phone to read about an insect species that consumes (hyperbolically described as 'devours') one square inch of grass per day. As it is relayed through a chain of conversations, this measurement gets misinterpreted 11 times until [[Hairbun]] tells other people that it devours an area of grass equal to two times the land area of Australia per day, which is clearly impossible by one insect.{{citation needed}} This is similar to the premise of [[2585: Rounding]].<br />
<br />
This gross error is the result of repeatedly misinterpreting the number of square units as the side length of a square, thus increasing the described area by the power of two. The chain also involves converting between an imperial unit and a metric unit, alternating, thus introducing smaller rounding errors even while switching which measurement is "a single square with sides of a certain distance" and which is "the number of squares that are each of unit length". The upshot is that, while each statement has two roughly similar measurements of area, the chain of misunderstanding ends up claiming ever larger relative expanses. The later participants in this chain also clearly forget to sanity-check their figures, blithely informing others that an individual insect is effectively consuming impossibly huge quantities of food, and travelling enormous linear distances every day to do so. In fact, assuming the insect can eat a 1 cm strip of grass, it would need to travel at (2,500 miles)<sup>2</sup> / 1cm / 24 hours = 1.87×10<sup>7</sup> km/s, which is about 62 times the speed of light.<br />
<br />
The title text tells us that [[Randall]] once found an 80-fold error in a reported distance in a published source.<br />
<br />
===Table of conversions===<br />
{{note|Table is too wide. "Acre" starts to overlap normal page area, everything else is beyond it. Suggest perhaps three or four significant figures ''plus'' scientific exponentiation on all figures where this does not increase a cell's minimum required width?}}<br />
{| class="wikitable"<br />
! step !! percentage gain !! total percent of original area !! square inch !! square cm !! square foot !! acre !! square meters !! square kilometers !! square miles<br />
|-<br />
! 1<br />
| N/A || 100% ||style="background-color:lightgreen;"| 1||style="background-color:red;"| 6.4516 || 0.006945 || 1.594e-7 || 0.0006451 || 6.451e-10 || 2.490e-10<br />
|-<br />
! 2<br />
| -7% || 93% || 0.93 ||style="background-color:pink;"| 6 || 0.006458 || 1.482e-7 || 0.0006 || 6e-10 || 2.316e-10<br />
|-<br />
! 3<br />
| +500% || 558% || 5.580 ||style="background-color:lightgreen;"| 36 (6<sup>2</sup>)||0.03875 || 8.895e-7 || 0.0036 || 3.6e-9 || 1.39e-9<br />
|-<br />
! 4<br />
| +3,500% || 20,090% || 200.9 ||style="background-color:lightgreen;"|1,296 (36<sup>2</sup>) || style="background-color:red;"|1.395 || 3.202e-5 || 0.1296 || 1.296e-7 || 5.004e-8<br />
|-<br />
! 5<br />
| -28.3% || 14,400% || 144 || style="background-color:red;"|929.03 || style="background-color:pink;"|1 || 2.296e-5 || 0.09290 || 9.290e-8 || 3.587e-8<br />
|-<br />
! 6<br />
| -3.12% || 13,950% || 139.5 || style="background-color:pink;"|900|| 0.9688 || 2.224e-5 || 0.09 ||9e-8 || 3.475e-8<br />
|-<br />
! 7<br />
| +89,900% || 12,555,025.1% || 125,550.251 || style="background-color:lightgreen;"|810,000 (900<sup>2</sup>)|| style="background-color:green;"|871.9||0.02002 || 81||8.1e-5 || 3.127e-5<br />
|-<br />
! 8<br />
| +3.22% || 12,960,000% || 129,600 || 836,127||style="background-color:lightgreen;"| 900 (30<sup>2</sup>) ||0.02066|| 83.61||8.361e-5 || 3.228e-5<br />
|-<br />
! 9<br />
| +89,900% || 11,664,000,000% || 1.166e+8 || 7.525e+8 ||style="background-color:lightgreen;"| 810,000 (900<sup>2</sup>) || style="background-color:green;"|18.59|| 7.525e+4 || 0.07525 || 0.02905<br />
|-<br />
! 10<br />
| +7.55% || 12,545,275,491% || 1.255e+8 || 8.094e+8|| 871,200||style="background-color:lightgreen;"| 20|| style="background-color:green;"|8.093e+5 || 0.08093 || 0.03125<br />
|-<br />
! 11<br />
| +7,907,375% || 992,001,984,003,868% || 9.920e+12 || 6.4e+13|| 6.889e+13 || 1.581e+6 || style="background-color:lightgreen;"| 6.4e+9 (80,000<sup>2</sup>) || 6,400 ||2,471<br />
|-<br />
! 12<br />
| +0% || 992,001,984,003,868% || 9.920e+12 || 6.4e+13|| 6.889e+13 || 1.581e+6 || 6.4e+9 || style="background-color:lightgreen;"|6,400 (80<sup>2</sup>) ||style="background-color:green;"|2,471<br />
|-<br />
! 13<br />
| +252,928% || 2,509,056,048,112,096,000% || 2.509e+16|| 1.618e+17 || 1.7424e+14|| 4.000e12 || 1.619e+13 || 1.618e+7 || style="background-color:lightgreen;"|6.250e+6 (2,500<sup>2</sup>)<br />
|-<br />
|}<br />
The total area of Australia is 7,688,287 square km or 2,968,464 sq mi, making it the 6th largest country on Earth by area. A 2,500-mile square would actually be about 2.1 times greater than the land area of Australia, once again having a rounding error.<br />
<br />
==Transcript==<br />
{{incomplete transcript|Do NOT delete this tag too soon.}}<br />
:[Arrows point to each consecutive panel.]<br />
<br />
:[Megan is looking at her phone, with Cueball standing next to her.]<br />
:Megan: This newly-described insect can devour up to a square inch of grass per day.<br />
:Cueball: Oh, neat.<br />
<br />
:[Cueball is speaking to Ponytail.]<br />
:Cueball: ...it eats a square inch, or 6 cm², of grass per day...<br />
<br />
:[Ponytail is speaking to Hairy.]<br />
:Ponytail: ...a 6-centimeter (2½ inch) square of grass, or 36 cm²...<br />
<br />
:[Arrows now point to each consecutive conversion.]<br />
:Written out of panel: ...a 36 centimeter square, or over a square foot...<br />
:Written out of panel: ...a square foot, or 900 cm²...<br />
:Written out of panel: ...a 900 cm (30 foot) square...<br />
:Written out of panel: ...a 30 foot square of grass (900 square feet)...<br />
:Written out of panel: ...a 900 foot square, or almost 20 acres...<br />
:Written out of panel: ...20 acres (8 hectares, or 80,000 square meters)...<br />
:Written out of panel: ...an 80,000 meter (80 km) square...<br />
:Written out of panel: ...a square 80 km wide, or roughly 2,500 square miles...<br />
:Written out of panel: ...a 2,500-mile square, or twice the land area of Australia, per day...<br />
<br />
:[An arrow points from the last conversion to the last panel.]<br />
:[Hairbun is looking at her phone, with White Hat, Danish and Blondie standing next to her.]<br />
:Hairbun: Did you hear about this insect that defoliates the entire land area of Australia twice a day?<br />
:White Hat: Gosh!<br />
:Danish: Wow.<br />
:Blondie: I hope at least it's contained there...<br />
<br />
{{comic discussion}}<br />
[[Category:Animals]]<br />
[[Category:Math]]<br />
[[Category:Comics featuring Megan]]<br />
[[Category:Comics featuring Cueball]]<br />
[[Category:Comics featuring Ponytail]]<br />
[[Category:Comics featuring Hairy]]<br />
[[Category:Comics featuring Hairbun]]<br />
[[Category:Comics featuring White Hat]]<br />
[[Category:Comics featuring Danish]]<br />
[[Category:Comics featuring Blondie]]</div>Sondre99v