《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§3. Units of capacity

This section introduces Chinese units of capacity and gives the conversion rates between them. A 'short scale' is used for named powers of ten. Note that the next section (§4) uses a 'long scale'.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
量之所起、起於粟。 [Of] that which measuring capacity beginneth from: beginneth [it] from grain.
  • 量： measuring of capacity

    量、平聲、 Cantonese: lœng4, Mandarin: liáng

  • 起： beginneth from; lit. ariseth from
  • 粟： grain

    Suk (粟), a six-hundred-thousandth of the Chinese litre, shêng (升).

六粟為一圭、
十圭為一撮、
十撮為一抄、
十抄為一勺、
十勺為一合、
十合為一升、
十升為一斗、
十斗為一斛。		 Six grains make one tablet;
ten tablets make one pinch;
ten pinches make one grab;
ten grabs make one ladle;
ten ladles make one gill;
ten gills make one quart;
ten quarts make one peck;
ten pecks make one barrel.
  • 圭： (jade-)tablet

    圭、古攜切、 Cantonese: kwai1, Mandarin: guī

    Kwei (圭), a hundred-thousandth of the Chinese litre, shêng (升).

  • 撮： pinch

    Tsʻot (撮), a ten-thousandth of the Chinese litre, shêng (升).

  • 抄： grab

    Chʻao (抄), a thousandth of the Chinese litre, shêng (升). Others render this as "handful", but that sounds too big in my opinion.

  • 勺： ladle

    勺、 Cantonese: chœk8, chʻœk8, Mandarin: sháo

    Shok (勺), a hundredth of the Chinese litre, shêng (升).

  • 合： gill

    合、葛合切、 Cantonese: kap8, Mandarin: gě

    Kop (合), a tenth of the Chinese litre, shêng (升). Similar in size to the imperial gill. In English, "gill" is read [dʒɪl], i.e. with a soft 'g'.

  • 升： quart

    Shêng (升), the Chinese litre, of the same order of magnitude as the metric litre. I have avoided rendering it "litre" so as to keep SI units free, and have instead chosen "quart", after the similarly sized imperial quart.

  • 斗： peck

    Tou (斗), ten Chinese litres, of similar size to the imperial peck. A person of integrity will not 為五斗米折腰, or "for five pecks of grain bend [at the] waist" (i.e. bow down).

  • 斛： barrel

    斛、 Cantonese: huk9, Mandarin: hú

    Huk (斛), a hundred Chinese litres. James Legge instead uses "bushel", which is only about forty litres, but this is reasonable since later definitions have a huk (斛) being only fifty Chinese litres (rather than a hundred).

斛得六千萬粟。所以得知者、 [A] barrel resulteth in six thousand myriad grains. [And] that by which [one] getteth to know [this]:
六粟為一圭、
十圭六十粟為一撮、
十撮六百粟為一抄、
十抄六千粟為一勺、
十勺六萬粟為一合、
十合六十萬粟為一升、
十升六百萬粟為一斗、
十斗六千萬粟為一斛。		 six grains make one tablet;
ten tablets, [even] sixty grains, make one pinch;
ten pinches, [even] six hundred grains, make one grab;
ten grabs, [even] six thousand grains, make one ladle;
ten ladles, [even] six myriad grains, make one gill;
ten gills, [even] sixty myriad grains, make one quart;
ten quarts, [even] six hundred myriad grains, make one peck;
ten pecks, [even] six thousand myriad grains, make one barrel.
十斛六億粟、
百斛六兆粟、
千斛六京粟、
萬斛六陔粟、
十萬斛六秭粟、
百萬斛六壤粟、
千萬斛六溝粟、		 Ten barrels [be] six square-myriad grains;
[an] hundred barrels, six multitude grains;
[a] thousand barrels, six capital grains;
[a] myriad barrels, six terrace grains;
ten myriad barrels, six haystack grains;
[an] hundred myriad barrels, six soil grains;
[a] thousand myriad barrels, six ditch grains;
  • Here we first encounter named powers of ten starting from 108, which I have rendered literally.
  • 億： square-myriad
  • 兆： multitude

    Effectively a formal version of "zillion".

  • 京： capital
  • 陔： terrace

    陔、音該、 Cantonese: koi1, Mandarin: gāi

  • 秭： haystack

    秭、音姊、 Cantonese: tsee2, Mandarin: zǐ

    More accurately, "grainstack".

  • 壤： soil
  • 溝： ditch
萬萬斛為一億斛六澗粟、
十億斛六正粟、
百億斛六載粟。		 [a] myriad myriad barrels make one square-myriad barrels, six stream grains;
ten square-myriad barrels, six right grains;
[an] hundred square-myriad barrels, six carry grains.
  • 澗： (mountain-)stream
  • 正： right
  • 載： carry

    載、上聲、 Cantonese: tsoi2 (post-merger: choi2), Mandarin: zǎi

    An explanation for its use to denote a large power of ten is quoted in Kʻang‑hee's entry for 秭: 載地不能載也, "[a] carry [even the] Earth [be] unable to carry" (here the second "carry" is a verb, read in the usual 去聲, i.e. tsoi3/zài). For context, the usual phrase is 天覆地載, "Heaven covereth [and] Earth carrieth".

Extended commentary

I can't be bothered looking up a reputable source for the precise volume of a shêng (升) when Sun Tzŭ's Computational Classic was first written, but using 1 litre as an estimate, we have:

1 ⁣grain (粟)=16×10−5 ⁣quarts∼2 ⁣μL1 ⁣tablet (圭)=10−5 ⁣quarts∼10 ⁣μL1 ⁣pinch (撮)=10−4 ⁣quarts∼0.1 ⁣mL1 ⁣grab (抄)=10−3 ⁣quarts∼1 ⁣mL1 ⁣ladle (勺)=10−2 ⁣quarts∼10 ⁣mL1 ⁣gill (合)=10−1 ⁣quarts∼100 ⁣mL1 ⁣quart (升)=1 ⁣quart∼1 ⁣L1 ⁣peck (斗)=10 ⁣quarts∼10 ⁣L1 ⁣barrel (斛)=100 ⁣quarts∼100 ⁣L.\begin{alignedat}{3} 1 \unit{grain~(粟)} &={} & \tfrac{1}{6} \times 10^{-5} & \unit{quarts} && \sim 2 \unit{μL} \\ 1 \unit{tablet~(圭)} &={} & 10^{-5} & \unit{quarts} && \sim 10 \unit{μL} \\ 1 \unit{pinch~(撮)} &={} & 10^{-4} & \unit{quarts} && \sim 0.1 \unit{mL} \\ 1 \unit{grab~(抄)} &={} & 10^{-3} & \unit{quarts} && \sim 1 \unit{mL} \\ 1 \unit{ladle~(勺)} &={} & 10^{-2} & \unit{quarts} && \sim 10 \unit{mL} \\ 1 \unit{gill~(合)} &={} & 10^{-1} & \unit{quarts} && \sim 100 \unit{mL} \\ 1 \unit{quart~(升)} &={} & 1 & \unit{quart} && \sim 1 \unit{L} \\ 1 \unit{peck~(斗)} &={} & 10 & \unit{quarts} && \sim 10 \unit{L} \\ 1 \unit{barrel~(斛)} &={} & 100 & \unit{quarts} && \sim 100 \unit{L}. \end{alignedat}

In Volume II §10, the conversion between the capacity unit "barrel", huk (斛), and the volume unit "cubic rule", chʻek (尺), is given as

1 ⁣barrel (斛)=1.62 ⁣rules (尺)3.1 \unit{barrel~(斛)} = 1.62 \unit{rules~(尺)}^3.

Version C has "pinches", tsʻot (撮), and "grabs", chʻao (抄), the other way around. The order given here is that in Versions A, B, and D, and it is consistent with the order in Hong Kong's Ordinance No. 22 of 1844 (PDF), which has all of the above units as well as the "cup", yok (龠), equal to five ladles. Note however that Ordinance No. 22 has the "barrel", huk (斛), defined as five tou (斗) rather than ten tou (斗):

Image of Ordinance Number 22 of 1844, British Hong Kong. Measures of Grain. Six Suh 粟 make one 圭 Kwei. Ten Kwei 圭 make one 撮 Tsoh (or Pugil). Ten Tsoh 撮 make one 抄 Chau (or Handful). Ten Chau 抄 make one 勺 Choh (or Ladle). Five Choh 勺 make one 龠 Yoh (or Cup). Two Yoh 龠 make one 合 Koh (or Gill). Ten Koh 合 make one 升 Shing (or Pint). Ten Shing 升 make one 斗 Taw. Five Taw 斗 make one 斛 Hoh.

Unlike length and weight, the British did not standardise Chinese capacity units with respect to English units in 1885.

Here we have a 'short scale' where the named quantities go up by a factor of 10:

 ⁣square-myriad (億)=108 ⁣multitude (兆)=109 ⁣capital (京)=1010 ⁣terrace (陔)=1011 ⁣haystack (秭)=1012 ⁣soil (壤)=1013 ⁣ditch (溝)=1014 ⁣stream (澗)=1015 ⁣right (正)=1016 ⁣carry (載)=1017.\begin{aligned} \unit{square-myriad~(億)} &= 10^8 \\ \unit{multitude~(兆)} &= 10^9 \\ \unit{capital~(京)} &= 10^{10} \\ \unit{terrace~(陔)} &= 10^{11} \\ \unit{haystack~(秭)} &= 10^{12} \\ \unit{soil~(壤)} &= 10^{13} \\ \unit{ditch~(溝)} &= 10^{14} \\ \unit{stream~(澗)} &= 10^{15} \\ \unit{right~(正)} &= 10^{16} \\ \unit{carry~(載)} &= 10^{17}. \end{aligned}

However, the next section (§4) uses a 'long scale' where the named quantities go up by a factor of 108.

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §3". <https://yawnoc.github.io/sun-tzu/i/3> Accessed 2025-05-06.