Harappan units of weight

Series of cubical chert weights

Weights found in excavating the settlement at Allahdino.

© J. M. Kenoyer. Courtesy Dept. of Archaeology and Museums, Gov't of Pakistan.


satellite photo of Indus Valley, 2012

world map showing location of Pakistan

The Indus Valley, 2012. It was wetter in 2200 bce.

From eosnap, courtesy Chelys srl.

The Harappan culture flourished in the Indus valley between 2600 and 1900 bce. Excavations have recovered a number of balance weights in the shape of cubes, often of chert, some from sites as early as 2800-2600 bce. Around 2200 bce, weights also began to be made in the form of spheres with two flat spots on opposite sides, but the cubic weights continued to be produced until about 1900 bce.

The discovery of impressive cities from a previously unknown ancient culture electrified archeologists in the 1920's. In analyzing weights recovered in the first excavations at Mohenojo-daro, A. S. Hemmy discovered a regular pattern¹: the smaller weights increased by a factor of two, and the larger were a decimal multiplier times one of the seven smaller weights.

Hemmy described the system in terms of multiples of the smallest weight, around 0.87 gram. Later researchers² took as the basic unit the weight of about 13.65 grams, because it is the one most commonly found, because the 13.65 g unit has a decimal relationship to the first “heavy”unit, and because units of about this size were later the basic units in South Asia.


multiples of the
smallest unit
1 2 4 8 16   32 64    
of the 13.65 g unit
1/16 1/8 ¼ ½ 1   2 4    
Larger by
a factor of 10
        160 200 320 640    
        10 12.5 20 40    
Larger by
a factor of 100,
100 unit increments
        1600   3200 6400 8000 12,800
        100   200 400 500 800


The Harappan's written language (if that is what the symbols found on Harappan seals are) has not been deciphered, so we do not know their names for these units.

Later excavations uncovered weights both larger and smaller than those Hemmy first worked with, but they are relatively rare. A few incorporate subdivisions by thirds.

Any process for producing standard weights has some tolerance, and the tolerances in 2200 bce were of course larger than they are today. To add to that, as Hendrickx-Baudot3 says, “We have to bear in mind not only the normal statistical spreading and standard deviation, but also the unknown from detrition or crumbling and chemical alteration.” Numerous workers4 have analyzed statistically the spread of weights around central values. As a rough estimate, taking all the weights from all sites, the measured mass generally comes within 6% of the ideal mass.

The tolerances are smaller if the weights of each city are analyzed separately. Probably each city's weight-makers worked from that city's prototype, and the prototypes themselves could be compared only with the precision of the day's balances. The astonishing thing is not that their tolerance was larger than ours, but that it is so small and that this probably pre-literate culture maintained the same tight standards for over seven centuries. Indeed, several scholars5 have thought that, though the use of cubical weights ceased, the system of weights continued. It appears again around 600 bce, when cities began to be built in northern India, and is reflected in units of weight used in South Asia today.

Kenoyer has speculated6 that the weights were primarily used in collecting taxes or tariffs, since finds are concentrated near the gates of cities, but he also feels that traders were instrumental in maintaining the standard. Weights of the same age, calibrated to the Harappan standard, have been found at distant trading centers, including Mesopotamia (Ur), Dilmun (modern Bahrain) and Magan (modern Oman).7

1. A. S. Hemmy.
Systems of Weights at Mohenjo-Daro.
J. Marshall, editor.
Mohenjo-Daro and the Indus Civilization. Vol. 2
London: A. Probsthain, 1931.

System of Weights.
E. J. H. Mackay.
Further Excavations at Mohenjo-Daro, being an official account of archaeological excavations at Mohenjo-daro carried out by the government of India between the years 1927 and 1931. Vol. 1.
Delhi: Manager of Publications, 1938.

The first excavation of a city of the Indus civilization. For a reproduction of Hemmy's list of the weight in grams of the weights found in the 1920's and 1930's, see www.safarmer.com/Indo-Eurasian/weightchart.jpg

2. Ardelia R. Hall.
The Cube Weights in Boston.
Ernest J. H. Mackay.
Chanhu-daro Excavations, 1935-36.
New Haven, CT: Pub. for American School of Indic and Iranian Studies and Museum of Fine Arts, Boston, by American Oriental Society, 1943.

3. M. P. Hendrickx-Baudot.
The weights of the Harrapa-culture.
Orientalia Lovaniensia Periodica, vol. 3, pages 5-34 (1972).

4. For example,
S. Iwata.
On the standard deviation of the weights of the Indus civilization.
Bulletin of the Society of Near Eastern Studies in Japan, volume 27, number 2, pages 13-36 (1974).

5. For example,
V. B. Mainkar.
Metrology in the Indus Civilization.
B. B. Lal and S. P. Gupta, editors.
Frontiers of the Indus Civilization.
New Delhi: Books and Books, 1984.

6. J. Mark Kenoyer.
Measuring the Harappan world: Insights into the Indus order and cosmology.
Ian Morley and Colin Refrew, editors.
The Archaeology of Measurement. Comprehending Heaven, Earth and Time in Ancient Societies.
Cambridge: Cambridge Univ. Press, 2010.

7. For a list of Harappan weights found elsewhere, see Table 1 of
Shereen Ratnagar.
Theorizing Bronze-Age intercultural trade: the evidence of the weights.
Paléorient, vol. 29, no. 1 (2003).



Jonathan Mark Kenoyer.
Ancient Cities of the Indus Valley Civilization.
Karachi: Oxford U. Press and American Institute of Pakistan Studies, 1998.

Jane R. McIntosh.
The Ancient Indus Valley. New Perspectives.
Santa Barbara, CA: ABC-Clio, 2008.

From a series intended for a wide audience, Understanding Ancient Civilizations. Contains extensive bibliographies.

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