Feb 29, 2024
Feb 29, 2024
by Rajat K Pal
Indus people have used exceptionally developed units of measurement. They have even used binary and decimal methods of counting.
In the Magnum Opus on Indus Civilization published by John Marshal [1931] A. S. Hemmy wrote an extensive essay by the name ‘System of weight in Mohenjo Daro’. There Hemmy has shown that the weight items were not abrupt, rather interlinked [ .87 gm, 1.76 gm, 3.41 gm, 6.82 gm etc]. The same pattern was found at other excavated sites like Chanhudaro etc. From the evidences we can reach to the decision of the use of Binary [ 1, 2, 4, 8, 16…] and Decimal [10, 20, 50, 100 etc.] practices at Indus valley civilization.
According to Hemmy the smallest unit of weight measure was .87 gm and others were its multiples. A. R. Hall and J. M. Mackey opined that the basic unit was 13.65 gm. We can arrange them by three tables …
Table  1
Multiple of the Smallest Unit 
1  2  4  8  16  32  64 
Multiple of the 13.65 gm Unit 
1/16  1/8  1/4  1/2  1  2  4 
Idealized Weight 
.87 gm 
1.75 gm 
3.45 gm 
6.85 gm 
13.65 gm 
27.35 gm 
54.65 gm 
Table  2
13.65 gm and larger weights found by factor of 10
X 10  X 20  X 40  X 12.5 
136.5 gm  273.5 gm  546.5 gm  170.6 gm 
Table  3
13.65 gm larger by factors of 100
X 100  X 200  X 400  X 500  X 800 
1.365 kg  2.73 kg  5.46 kg  6.83 kg  10.920kg 
Clearly the weights were properly calculated. Though slight differences are found, that should have been the effect of natural decaying and/or natural addition of dust etc for more than 3000 years. The same weight items are found in Ur, Dilmun [ Bahrain] and Magan [Oman].
Vedic Veight System
Going through the Vedic system of weight and measurements we can get the following information.
1. Smallest unit = Ratti. It is actually opium seed [Abrus Precatorius] .
The seed is reddish. Actual name is Raktika.
Raktika > Ratti. Another name of it was Krishnal.
2. Another unit is Maasha or Maashaka.
Smallest unit of length was Angula.
Maashaka or maasha = mass of 1 cubic angula of water.
3. Other units are saana, pala, mushthi, karsha, suvarna, nishka etc
From Rigveda, Mahabharata, Charaka Sanhita, Astadhyayi and other Smriti texts we get chart of weight units and their relations –
To mesure GOLD  To measure other than GOLD 
10 ratti = 1 maasha  10 ratti = 1 maasha 
4 maasha = 1 saana  3 maasha = 1 saana 
4 saana = 16 maasha = 1 suvarna 
4 saana = 1 karsha 
16 saana = 64 maasha = 4 suvarna = 1 nishka 
4 karsha = 16 saana = 1 pala/mushthi 
In Manu Sanhita 5 ratti = 1 maasha for measuring gold is taken, thereby 80 ratti = 1 suvarna and 320 ratti comes to 1 nishka.
4. From Bhagabata Purana (for measuring the volumes of dry items) we get
I. Vreehi = dhaan or rice with husk
II. 4 vreehi = 1 gunja
III. 5 gunja = 1 pana [= 20 vreehi]
IV. 8 pana = 1 dharana [ = 160 vreehi or dhaan]
V. 8 dharana = 1 karsha [ = 1440 vreehi]
VI. 4 karsha = 1 pala [ = 5760 vreehi]
VII. 100 pala = 1 tula
VIII. 20 tula = 1 bhaar
To calculate the volume of dry materials Narada Purana has mentions
Dongre [1] has valuated, 1 andaka = .2825 gm
To him 10 krishnala = 4 andaka = 1 maasha
He even has found a similar andaka unit in Heavy Assyrian System with the same value. There 60 andaka = 1 shekel = 16.8 gm. According to him in Light Babylinian System, 1 shekel = 30 andaka = 8.4 gm
To be precise, Arthashastra of Kautilya has referred silver coins by the name of pana, ardhapana, pada etc and copper coins by maashaka, ardha maashaka, kakini etc.
Panini referred karshapana or pana of 32 rattis. According to him 16 maasha = 1 karshapana; vimastika = 40 rattis, trimastika = 60 rattis, satamaana = 100 rattis, and saana = 12.5 rattis. Silver coin is of karshapana = 32 rattis, though several other weights were found. Weight of krishnala varies from 1.7 to 2.25 grains.
To the ancient Indians, a coin was not a piece of inanimate metal with an official stamp, but a form pulsating with symbols, names of kings, gods and goddesses portraying wealth and prosperity.
For a much probable study we will here mention some of the units used in India at least since Mauryan era. They are
In comparing Vedic weight and measure system with Indus system we can have a comparative table.
Hazra [1] and Dongre[2] separately had studied comparatively the weights found in Indus sites with Vedic measurements and compared the weights thereof with the weights found from Taxaila [Buddhist period] and Nevasa [postHarappan] [5].
Purana is actually equivalent to karshapana, the name used in later Buddhist period. From his study we can find that the weight units of Chanhudaro, Nevasa and Taxila (three different periods and cultures) have striking similarities.
Table 4
Weight in gm 
Canhudaro (gm) 
Nevasa (gm) 
Taxila (gm) 

1 purana = 32 rattis **  3.616  3.6, 3.8  
1 shatamana = 10 purana  32.16  36.89  35.96  
2 shatamana = 1 nishka  72.3  60.93, 69.93  69.1  69.6 
1 maasha = 5 ratti (for Gold)  .56  .56 .59 
** 1 purana = 1 saana = karshapana = 3.6 gm
Table – 5 [from Hazra [1], N.G.Dongre (2) and Mackey (3)]
Vedic Unit 
Vedic Weight [gm] [2] 
Indus Weight [gm] [2] after Marshall ** 
Indus Weight [gm][3]*** 
Weights from Nevasa (N) and Taxila (T) [gm] [1] 
paadasaana  .8475  .87  .88  
saanaardha  1.695  1.76  1.63  
1 maashaka or maasha 
1.13 
1.14 (1.255) 

2 maashaka  2.26  2.28  
1 saana  3.3  3.41  3.40  
1 drakshana  6.78  6.82  6.78 
6.78 [N] 7.06 [T] 
1 karsha = 4 saana = 16 maasha 
13.56  13.65  13.51  
Palardha = 2 karsha = 8 saana 
27.12  27.38  27.14  27.10 [T] 
1 pala/mushthi = saana 
54.24  54.23  54.13 
54.82 [N] 53.45 [T] 
40 saana = 10 karsha 
135.6  135.15  136.04  
50 saana  169.5  170.6  
5 mushthi = 80 saana 
271.2  272.9  273.59  284.3 [N] 
10 mushthi = 160 saana 
542.4  546.5  544.77  
25 mushthi = 400 saana = 100 karsha 
1356  1365  1330.68  
1 B.L. saana **** 
3.03  2.95  
1/3 B.L. saana  .985  .980  
2/3 B.L. saana  2.07  1.97  
4/3 B.L. saana  3.94  3.92  
8 B.L. saana  23.65  24.50  
16 B.L. saana = 1 B. mushthi 
47.30  47.30 
** weights taken by Dongre from Marshall (1931).
*** weights from Mackey (1943).
**** B L Saana = Bhaajani Lauha Saana [2]. This ancient measuring units and table are also found in Mohenjodaro.
From this table we can take that the basic unit of Indus weight as identified by Hall and Mackey i.e. 13.65 gm is equivalent to Vedic Karsha [one unit].
From Table 4 and 5, it is obvious that the same continuous weight system was practiced by the Indian merchants from Indus to Vedic period through the postHarappan and Buddhist periods. The intermittent use of weights and measures was started in Indus civilization and carried by others without any break. From this study we can put the unit names, as found in Vedic and Buddhist literatures, to the Indus inscriptions to decipher them.
Probably this was identified with [Image] sign when precious items are to be weighted. This sign was used as letter ‘ka’ when used in a word and that very sign was used as unit ‘kumbha’, when volumes of items were to be mentioned.
Other weight units can also be identified by the valuations of letters identified in earlier articles. Saana, karsha, shatamana etc for weight measures and kumbha, bhaar etc for volumetric measures and 5, 10, 100 etc for counting are very much written in Indus inscriptions along with proper names and other information.
Notes:
References:
01Apr2018
More by : Rajat K Pal
to Mr. J King, Sir, Thank you for reading this article. the marginal differences occurred owing to decaying naturally for hundreds of years. 
I may have misread, but there is a small query on the data shown. For Table 1 &2 &3 weights are built from a base of 13.65grams at 1/2; 1/4; 1/8; 1/16 & 2; 10; 20; 40; 12.5; 100; 200; 400; 500 & 800. From these there are ‘idealized weights’ which are fractionally adrift at the smaller values – perhaps by only showing 2 decimal places as 6.85; 3.45; 1.75; 0.87 rather than the more precisely calculated 6.825; 3.41; 1.70; 0.85 which give a 1 to 2.5% discrepancy. Can you assist. Thanks 