10 January, 2010

Ancient Weights from South Asian civilization


Chandrakant Doshi

email: jignashi@yahoo.co.uk

Key words: Harappa, Indus, weights


The ancient Harappan or Indus civilization, now widely known as the South Asian civilization, came to light with the excavations at Harappa in Punjab and Mohenjo Daro in Sindh, both now in Pakistan. The civilization flourished in the third millennium BCE. The first report on the excavations there listed, among various objects, a number of weights. These are exquisitely cut and polished pieces, weighing from about half a gram to over 11 kilograms. They are made of various materials: chert, a hard stone, being the most popular. They come in many different shapes: cubical, cylindrical, pyramidal, conical, barrel and truncated spheres.

A. S. Hemmy reported on these weights, defining the unit weight and scale of the system. The weights from the first four excavation reports are examined in this paper using tables and charts to show not only the systematic nature of the weight system but also the level of accuracy attained.


The excavation report of John Marshall1, “Mohenjo Daro and the Indus Civilization,” lists weights from both Mohenjo Daro and Harappa. Later excavations by M. S. Vats2 at Harappa and John Mackay3, 4 at Mohenjo Daro and Chanhu Daro have listed additional finds of weight specimens from these sites. Details of these are given in respective excavation reports.

Marshall`s report included weights from both Harappa and Mohenjo Daro. Further sessions at these sites produced additional reports. Details about the weights in each report vary considerably. For ease of reference these weights from the first four excavation reports are defined as Lists. Table 1 identifies each List. The details of the site, excavation report and the number of weight specimens are given for each List.

Information included for the weight specimens differs in each report. No information besides the weight is recorded in List 1 while List 2 makes mention of material and condition of some of the specimens. List 3 includes, besides the weight and material of each specimen, shape of each piece. List 4 provides the most comprehensive information: weight, condition of the specimen, shape, size, material and location of each piece. List 5 records only the weight and condition of each specimen.

In Lists 1 and 2, three damaged weights were corrected by completing the geometric shape. Fortunately, the original, uncorrected weight for each of these three pieces is also recorded in the reports and these are the values used here.


In a chapter included in ' Excavations at Chanhu Daro '5, published in 1943, Hemmy stated that... "From the much larger number of specimens collected at Mohenjo Daro and Harappa the value of the standard has been calculated as 13.625 gms."

Hemmy originally used the lowest weight as the unit of the weight system but later shifted to 13.625 grams as the unit, resulting in fractional ratios. I have used his earlier scheme in Table 2. The range of weight ratios6 runs from 1 to 12800. This set constitutes the nominal values of the Harappan system of weights and is referred to as such throughout this paper.

The accuracy of the weight system can be shown by a frequency distribution chart or histogram. The number of pieces within a narrow band or interval of weight values are tabulated. When the band of values is constant over the whole range then the frequency distribution chart is also a histogram.

Each band could be a small percentage of the nominal value. Simplest way to achieve this is to first normalise all the weight values.

Normalisation is the process of converting a set of data to a range centred around unity. This involves dividing each specimen by an appropriate nominal value from Table 2. The process of normalisation returns a value of 1 for each of the nominal values.

The binary scale runs, in segments, throughout the whole range of the weights, as can be seen from Table 2. The division should result, for most part, in normalised values between 0.75 and 1.5.

As it happens, 694 out of 697 specimens do indeed fall within this range. The three non-compliant weights occur in the range 54.5 grams and 136.25 grams. Rather than exclude them, their ratios to 54.5 grams, the attainable target value, are included in the complete list of normalised values.

The range of normalised values runs from 0.75 to 1.77, resulting in 102 equal steps, each spanning 1% of the nominal values. The first interval is centred around 1. Its boundaries are 0.995 and 1.005, giving a mean deviation of zero from the nominal values. The remaining steps are equally spaced either side of this central value.

A histogram of the normalised values, plotting the number of specimens in each interval, can be seen in Chart 1. The horizontal axis represents normalised values. The vertical axis represents the number of weight specimens in the given interval.

The peak frequency is 175 and is centred around the nominal values.

A. S. Hemmy used a procedure similar to the normalisation described above but his objective was to arrive at a more accurate value of the standard for the system of weights. All specimen were assigned a ratio with respect to the (then determined) standard value of 13.64 grams and the specimens within 7% of the corresponding standard values were divided by the assigned ratio. The results were then plotted to show the frequency distribution of the weights.

A selection was applied when arriving at the plot. As he writes5 … “All doubtful specimens were rejected, including those with unlikely ratios, as well as all weights below 6 gms.”

In preparing Chart 1 no weight specimens are left out. This removes the subjective element present when excluding some weight specimens.

Close to the nominal values, the distribution is fairly symmetrical. Of the 697 pieces, 608 are within +/- 10% of the nominal values and 533 are within +/- 5%. Outside of the 10% boundary there are many pieces with a frequency of just one. For clarity a magnified central section of the above chart is displayed in Chart 1a.

In Lists 4 and 5 an important detail included is the condition of each specimen. In List 4 these are classified under four categories: perfect, slightly chipped, chipped, badly chipped. In List 5 there are seven categories: perfect, good, slightly chipped, badly chipped, unfinished, burnt, dubious. Criteria for the classification are not included in any of the reports.

Perfect specimen is an undamaged specimen. The other categories represent various degrees of damage and are referred to, collectively, as damaged pieces. There are 90 perfect weight specimens in List 4 and 12 in List 5. Chart 2 is a histogram of the perfect and damaged specimens from List 4.

The peaks for both the perfect and damaged pieces occur at the nominal values. The largest of the weight value, a perfect piece, occurs at 177% of the nominal weight value.

The range covered in the chart is wide, from 75% to 177%. This results in a crowded central region. Chart 2a displays a restricted range of normalised values to improve matters.

There are 90 perfect and 130 damaged specimens in List 4; within the 10% range centred on the nominal values, the figures are 84 and 123, respectively.

In List 5 the number of perfect specimen is only 12 out of a total of 118. Chart 3 is a histogram of the prefect and damaged specimens from List 5 with Chart 3a displaying the central section.

From charts 2 and 3 it is clear that some of the perfect pieces appear far removed from the nominal values, though mostly singly. Perfect pieces would have been shaped and polished. In the next stage the pieces would be trimmed to the required weight. An insight into the stages involved in manufacturing these specimens is provided by two photographs included in separate excavation reports.

The image below appears in Marshall’s excavation report7, where Ernest Mackay writes: “They were first flaked into shape and then ground, and finally polished.”

Another photo appears in the report by Vats8, Plate CXVIII, shown below. In the report, Vats writes: “… they were first roughly chipped into shape and then ground and polished. The first process of chipping into shape is illustrated by No. 12 (1095) in Plate CXVIII ….”

Damage to a few of the pieces is visible in the photo. While most of the items in the photo are cubical, the last three are examples of cylinder, truncated sphere and cone.

One of the perfect pieces, farthest from nominal values, weighs in at 177% of a nominal value. A lot of effort would be required to trim it down to the required value.

Two of the prefect pieces appear at 93% of the nominal values. This could easily represent the lower end of the range of accuracy to which these pieces were being manufactured. If that is not the case then they can only be trimmed to a lower value. In that case they are weighing in at 186% of the lower nominal values. In view of a piece at 177% of a nominal value that could easily be the case.


A determination of the range of accuracy achieved by the ancients would be a clear step forward in understanding their technology in the manufacture of weights as well as their metrology. The weights have been manufactured to a great accuracy, as the charts show.

A collection of damaged and perfect weight pieces does not make it easy to establish the exact level of accuracy of the weight system. Examining the perfect pieces, identified in Lists 4 and 5 only, does not help in establishing the accuracy band either as there are perfect pieces far higher than the nominal values. These can be trimmed to the nominal value and are incomplete pieces. The number of such perfect pieces is rather small, as can be seen from Charts 2 and 3. Examination of weights from later excavations should help clear the picture.

In Chart 1 the peak frequency at the nominal values is impressive. However, as the Charts 2 and 3 show, both the perfect and damaged pieces are present in that peak. Also, in the same charts, the peaks for perfect and damaged pieces occur at the nominal values. Despite the collection being a mix of damaged and perfect pieces, the accuracy of the weight system is remarkable. What could be the reason for such accuracy? Did it happen routinely or did the ancients go to great lengths to achieve it?

Damage to some of the pieces is slight. This can be seen in Plate CXVIII, illustrated above, from Excavations at Harappa by M. S. Vats. In the records 35 pieces in List 4 are classified as slightly chipped while 53 pieces in List 5 are classified as good or slightly chipped (distinction between these two categories is not specified in the report). Specimens from these classifications contribute to the peak frequencies observed for the damaged pieces at the nominal values.

Since the majority of specimens are cubical in shape, an estimate of the weight of these damaged pieces, by completing the geometry, should be possible. However the exercise is unlikely to be easy or cheap.

In this collection of perfect and damaged weights statistical information like average and standard deviation may not mean much. However, as an exercise, this is calculated for the entire collection and for a restricted collection within a band of 10% of the nominal values.

The average of the normalised values of all 697 pieces is 1.0237 with a standard deviation of 0.1060. For 608 pieces within a band of 10% centred around the nominal values the average of the normalised values is 0.9997 while the standard deviation is 0.0308.

Most of the pieces are cubical in shape. This is not a difficult shape to manufacture. Rubbing on a flat surface will ultimately produce a cube, though the symmetry may be slightly lost when trimming to the target value. Cylindrical shape too cannot be difficult to achieve. It is the manufacture of shapes like conical, barrel and spherical that is fascinating. How does one shape a sphere out of a stone with the technology of the third millennium BCE?

Modern facilities afforded by the computer has made the analysis of the long published data an easy exercise. In Hemmy’s time the task could not have been that easy, though I suspect he may have had assistance in analysing all the data.

Hemmy used four of the five Lists in Table 1 to determine the systematic nature of the weight system, including the nominal values and their ratios given in Table 2. For the weights in List 3, Vats9 wrote, “ … I have followed Mr. Hemmy’s designations and limits within which those designations apply.” Subsequent finds have all followed the designations established by Hemmy.

The analysis presented here deals with only the earliest finds of the weight specimens. This presents us with the opportunity to check the results of this analysis against weight specimens from later finds. With many sites reporting findings of weights it should prove a useful exercise and I hope this happens soon.


I would like to thank my son Samir and his wife Susan for various discussions and suggestions, which have proved helpful. My thanks also go to the librarians at the Keith Axon centre, Redbridge Libraries, for cheerfully obtaining those excavation reports without which this paper would not have been possible.


1/. Mohenjo-Daro and the Indus Civilization.

Being an official account of archæological excavations ... carried out by the Government of India between the years 1922 and 1927. Edited by Sir J. Marshall, Arthur Probsthain, London, 1931, pp 596-8

2/. Excavations at Harappa. Vats, Madho Sarup

Being an account of archælogical excavations at Harappa, carried out between the Years 1920-21 and 1933-34, etc.

2 vol. Delhi, 1940. pp 363-365

3/. Further Excavations at Mohenjo-daro. Mackay, Ernest John Henry

Being an official account of archæological excavations at Mohenjo-daro carried out by the Government of India between the years 1927 and 1931 ... With chapters by A. S. Hemmy ... and by B. S. Guha ... and P. C. Basu, etc

2 vol. Delhi, 1938, 37, Vol. 1, pp 607-612

4/. Excavations at Chanhu Daro, Mackay, Ernest John Henry, 1935-36, New Haven, 1943, pp 238-239

5/. Excavations at Chanhu Daro, op cit., p 236-7

6/. Excavations at Chanhu Daro, op cit., p 241

7/. Mohenjo Daro and the Indus Civilization, op. cit., p 462

8/. Excavations at Harappa, op. cit., p 361

9/. Excavations at Harappa, op. cit., p 360


*© 2010 Chandrakant Doshi