Buddhist Measurements and Units

Numbers

Eka (一): 1 or $10^0$
Daśa (十): 10 or $10^1$
Śata (百): 100 or $10^2$
Sahasra (千): 1,000 or $10^3$
Daśasahasra (萬): 10,000 or $10^{4}$
Śatasahasra (億): 100,000 or $10^5$
Koṭi (百億): 10,000,000 or $10^7$
Ayuta (萬億, 阿由多): 100 Koṭi or $10^9$
Sahasrakoṭi(千百億): 1,000 Koṭi or $10^{10}$
Nayuta (尼由多): 100 Ayuta or $10^{11}$

Kañkara (更割羅): 100 Nayuta or $10^{13}$
Vivara (頻婆羅): 100 Kañkara or $10^{15}$
Akṣobhya (阿芻婆): 100 Vivara or $10^{17}$
Vivāha (毘婆訶): 100 Akṣobhya or $10^{19}$
Utsaṅga (欝僧迦): 100 Vivāha or $10^{21}$
Bāhula (婆呼羅): 100 Utsaṅga or $10^{23}$
Nāgabala (那迦婆羅): 100 Bāhula or $10^{25}$
Tiṭilambha (底致婆羅): 100 Nāgabala or $10^{27}$
Vyavasthānaprajñapti (卑波婆他般若帝): 100 Tiṭilambha or $10^{29}$
Hetuhila (醯兜奚羅): 100 Vyavasthānaprajñapti or $10^{31}$
Karahu (迦羅頗): 100 Hetuhila or $10^{33}$
Hetvindriya (醯都因陀利): 100 Karahu or $10^{35}$
Samāptalambha (僧合怛覽婆): 100 Hetvindriya or $10^{37}$
Gaṇanāgati (伽那那伽致): 100 Samāptalambha or $10^{39}$
Niravadya (尼羅闍): 100 Gaṇanāgati or $10^{41}$
Mudrābala (目陀羅婆羅): 100 Niravadya or $10^{43}$
Sarvabala (薩婆婆羅): 100 Mudrābala or $10^{45}$
Visaṃjñāgati (毘僧以若跋致): 100 Sarvabala or $10^{47}$
Sarvasaṃjña (薩婆僧以若): 100 Visaṃjñāgati or $10^{49}$
Vibhūtaṃgamā (毘浮登伽摩): 100 Sarvasaṃjña or $10^{51}$
Tallakṣaṇa (怛羅絡叉): 100 Vibhūtaṃgamā or $10^{53}$
Dhvajāgramaṇī (度闍阿伽羅摩尼): 100 Tallakṣaṇa or $10^{55}$
Dhvajāgra­­maṇīśāni (度闍阿伽摩尼舍梨): 100 Dhvajāgravatī or $10^{57}$
Vāhanaprajñapti (婆訶那婆若爾炎致): 100 Dhvajāgra­niśā­maṇī or $10^{59}$
Iṅgā (伊吒): 100 Vāhanaprajñapti or $10^{61}$
Kurutu (古盧鼻): 100 Iṅgā or $10^{63}$
Kuruṭāvi (古吒鼻那): 100 Kuruṭu or $10^{65}$
Sarvanikṣepā (娑婆尼叉): 100 Kuruṭāvi or $10^{67}$
Agrasārā (阿伽羅娑羅): 100 Sarvanikṣepā or $10^{69}$

Lengths

Small Particle: 7 Smallest Particles
Water Particle: 7 Small Particles
Dust Particle: 7 Water Particles
Hare-Dust Particle: 7 Dust Particles
Sheep-Dust Particle: 7 Hare-Dust Particles
Cow-Dust Particle: 7 Sheep-Dust Particles
Lice Egg: 7 Cow-Dust Particles
Mustard Seed: 7 Lice Eggs
Barley Grain: 7 Mustard Seeds
Finger Joint (指節): 7 Barley Grains
Handspan (搩手): 12 Finger Joints
Cubit (肘): 2 Finger Spreads
Bow (弓): 4 Cubits
Krośa (Shouting-Distance, 里, 拘盧舍): 1,000 Bows
Yojana (由旬): 4 Shouting-Distances;

1 Yojana is equal to 1 Hetuhila, 3 Vivara, 70 Koṭi, 32 Śatasahasra, and 512 Sahasra of the Smallest Particles. Mathematically this is:

$1\cdot10^{29}+3\cdot10^{15}+70\cdot10^7+320\cdot10^5+512\cdot10^3$

Which is 100,000,000,000,003,000,000,732,512,000 Smallest Particles!

Jambudvipa: 7,000 Yojanas
Godaniya: 8,000 Yojanas
Purvavideha: 9,000 Yojanas
Uttakuru: 10,000 Yojanas

Great Trichiliocosm (Buddhakṣetra): 1 Ayuta of Four Continents, 1 Ayuta of Great Oceans, 1 Ayuta of the Circular Mountains, 1 Ayuta of the Outer Mountains, 1 Ayuta of Mt. Meru the King of Mountains, 1 Ayuta of the Heavenly Kings Realm, 1 Ayuta of the Trāyastriṃśa Realm, 1 Ayuta of the Yāma Realm, 1 Ayuta of the Tuṣita Realm, 1 Ayuta of the Nirmāṇarati Realm, 1 Ayuta of the Parinimirtavaśavartin Realm, 1 Ayuta of the Brahma Realm, 1 Ayuta of the Brahmakāyika Realm, 1 Ayuta of the Mahābrahma Realm, 1 Ayuta of the Parīttābha Realm, 1 Ayuta of the Apramāṇābha Realm, 1 Ayuta of the Ābhāsvara Realm, 1 Ayuta of the Parīttaśubha Realm, 1 Ayuta of the Apramāṇaśubha Realm, 1 Ayuta of the Śubhakṛtsna Realm, 1 Ayuta of the Anabhraka Realm, 1 Ayuta of the Puṇyaprasava Realm, 1 Ayuta of the Bṛhatphala Realm, 1 Ayuta of the Asaṃjñisattva Realm, 1 Ayuta of the Avṛha Realm, 1 Ayuta of the Atapa Realm, 1 Ayuta of the Sudṛśa Realm, 1 Ayuta of the Sudarśana Realm, 1 Ayuta of the Akaniṣṭhā Realm.

Lokadhātu: Can be in Length and Width, 100 Yojanas, 1,000 Yojanas, 1 Lakṣa Yojanas, 1 Koṭi Yojanas, 1 Nayuta Yojanas, up to 1 Agrasārā Yojanas. Also in Length and Width they are all Asaṃkhyeya Smallest Particles.

Notes

The Chinese measurement of Li can be matched one-to-one with the Indian Buddhist Measurement of Krośa by comparison of the Chinese and Sanskrit Manuscripts of the Longer Sukhāvatīvyūha Sūtra:

「又無量壽佛其道場樹，高四百萬里，其本周圍五千由旬，枝葉四布二十萬里。

Furthermore, Amitāyus Buddha has a Bodhimaṇḍa Tree four-hundred daśasahara krośas in height, its roots are five-thousand yojanas in circumference, and its twigs and leaves spread out twenty daśasahasra krośas in radius.

Tasya khalu punarānanda amitāyuṣastathāgatasyārhataḥ samyaksaṃbuddhasya bodhivṛkṣaḥ| sa daśa yojanaśatānyuccaistvena, aṣṭau yojanaśatānyabhipralambitaśākhāpatrapalāśaḥ pañcayojanaśatamūlārohapariṇāhaḥ

Furthermore, Ānanda, Amitāyus, the Tathāgata, Arhat, Samyaksambuddha’s Bodhi Tree is ten yojanas of a hundredfold in height, the branches and leaves spread out by eight yojanas of a hundredfold, and have roots which spread out five yojanas of a hundredfold.

We can look at each one that mentions a li and a krośa. The Chinese manuscript says that the height is four-hundred daśasahasras in krośas, while the Sanskrit says it is ten by a hundred yojanas in height. The Chinese manuscript says that the branches and leaves spread out by twenty daśasahasras in krośas, while the Sanskrit says it is eight by a hundred yojanas.

If we do a one-to-one correspondence:

4,000,000 krośas = 1,000 yojanas

And since 1 yojanas = 4 krośas, then all we have to do is divide the numbers in the Chinese by 4 to obtain this correspondence:

1,000,000 yojanas = 1,000 yojanas

The other measurements are a little off but we may also note this section from the Second Avalokita Sūtra in the Mahāvastu, which describes the height of the Bodhi Tree of Śākyamuni:

tatrakeciddevāyojanaṃuccatvenabodhivṛkṣaṃsaṃjānanti / anyedevāḥpaṃcayojanamuccatvena // anyedaśayojanamuccatvena //

Those devas saw beheld the Bodhi Tree to be a yojana tall; other devas saw it has five yojanas tall; other devas saw it as ten yojanas tall;

anyeviṃśayojanamuccatvena / anyetriṃśayojanamuccatvena / anyecatvāriṃśayojanamuccatvena / anyedevāpaṃcāśadyojanamuccatvenabodhivṛkṣaṃsaṃjānanti / 

Others, twenty yojanas tall; others thirty yojanas tall; others forty yojanas tall; other devas saw it as fifty yojanas tall;

anyeyojanaśatamuccatvenabodhivṛkṣaṃsaṃjānanti / yathāsvakasvakenajñānenabodhivṛkṣamuccatvenasaṃjānanti // 

Others beheld the Bodhi Tree to be a hundred yojanas tall;

The height of the Bodhi Tree was seen by them in proportion with their knowledge.

santidevāyojanasahasramuccatvenabodhivṛkṣaṃsaṃjānanti / santidevādīrghāyuṣkāpurimajinakṛtādhikārāyojanaśatasahasramuccatvenabodhivṛkṣaṃsaṃjānanti / santidevaputrāabhisaṃjātakuśalamūlaniryātāyāvadbhavāgramuccatvenabodhivṛkṣaṃsaṃjānanti //

Some devas beheld the Bodhi Tree to be a thousand yojanas tall; some devas who had served the Jinas during the long lives of their past, beheld the Bodhi Tree had a śatasahasra in height; while some devaputras who had achieved escape by means of their wholesome roots of virtue, beheld the Bodhi Tree as tall as the highest of highest existences.

The rest of the text follows the same fashion for the roots, branches, and leaves. We may find this section interesting as it lists yojanas, krośas, tāla trees, and humans, as measurements in descending order:

anyedevāyojanamuccatvenasiṃhāsanamaddaśensuḥ / 

Other devas saw the Siṃhāsana of the Bodhi Tree to be a yojana tall;

anyedevādvikrośamuccatvenasiṃhāsanamaddaśensuḥ / anyedevākrośamuccatvenasiṃhāsanamaddaśensuḥ / 

Other devas saw the Siṃhāsana to be two krośas in height; other devas saw the Siṃhāsana to be one krośa in height;

anyedevāsaptatālamuccatvenasiṃhāsanamaddaśensuḥ / anyedevāṣaṭṭālamuccatvenānyedevāpaṃcatālaṃanyedevācatutālaṃanyedevātritālaṃanyedevādvitālaṃanyedevātālamātraṃbodhivṛkṣasyamūlesiṃhāsanamaddaśensuḥ / 

Other devas saw the Siṃhāsana to be seven tāla trees in height; other devas six tāla trees in height and other devas five tāla trees and other devas four tāla trees and other devas three tāla trees and other devas two tāla trees and other devas one tāla tree;

anyedevāsaptapauruṣeyamuccatvenasiṃhāsanamaddaśensuḥ

Other devas saw the Siṃhāsana as seven people tall;

Now, unless we wish to do a disservice to all of the Indian and Chinese translations during the history of Buddhism, it is obvious here that a Li would be a Krośa.

However, here we can see directly that a Li is exactly a fourth of a yojana:

[0278c10]  今據三千大千世界之中。諸佛世尊皆垂化  現。現生現滅導聖導凡。約一四天下。即以  一日月所照臨處。以蘇迷廬山為中(唐云。妙高山。舊名須彌山。又曰迷留。亦云彌婁山。此皆訛略耳)  高三百三十六萬里。四  寶所成。東面黃金。南面琉璃。西面白銀。北面  玻 [王*(黍-禾+利)]。

Now…. within Mt. Meru, its height is three-hundred and thirty six daśasahasra li….

Now we all know Mt. Meru is 84,000 yojanas tall and we can see 336,000 divided by 4 is exactly 84,000! Thus, 4 li is exactly 1 yojana!