The Harappan angulam

(Sudama and Lomas Rishi Caves at Barabar, Bihar, in 1870)

During the time of Emperor Asoka and his successor Dasaratha, seven caves were constructed in Barabar and Nagarjuni hills, about 47 km from Gaya; during the Mauryan times, these hills encircled the city of Rajagriha. In the thirteenth year of his reign Asoka donated two caves in Barabar hills to Ajivikas. He donated one more in the 20th year of his reign while the Third Buddhist Council was going on, and all these were documented carefully with inscriptions inside the cave. The caves in Nagarjuni hills were the work of Asoka’s successor – his grandson Dasaratha – and these caves, like the ones in Barabar hills were donated to the Ajivikas[5].
These caves had circular roofs and the surfaces were polished. When these caves were measured, it was found that they were not constructed to random dimensions, but to a well known measure from the Harappan period: the angulam[2].
The urbanized Harappan civilization with elaborate town planning had knowledge of geometry and standardized measures. Statistical analysis of various Harappan settlements has shown that the basic unit of measurement was 17.63 mm[3]. This is taken to be one angulam and 108 angulams one dhanus. Various dimensions in the Harappan site of Dholavira are  integral multiple of dhanus. Now at a different site — Kalibangan — a terracota scale was found and when the measure between the tick marks was analyzed, it was found to be 17.5 mm. This also matched the measurement found in ivory and metal scales and shell markings at other sites[1].
The angulam is approximately 1.763 cms in Harappa, 1.75 in Kalibangan, and 1.77 in Lothal. The Arthashashtra derives larger units from angulam: garhapatya dhanus is 108 angulams; 1 danda, 96 angulams.
In the Mauryan caves, it was found that the danda measured the cave perfectly. For example the Lomas Rishi cave was 6 dandas long and 3.5 dandas wide and the Sudaman cave, 10 dandas long and 3.5 dandas wide. There is some fine print here as the Arthashastra provides confusing descriptions for various measures: one hasta is either 24, 28, or 54 angulams and one danda is 96 or 192 angulams. Since 96 was used by later texts, that measure was chosen.
What makes this interesting is that while cutting caves through hard rock, the Mauryans did not randomly dig through; the caves were carefully planned and constructed with pre-determined dimensions. Two caves in  Nagarjuni hills had the same dimension, so did two caves in Barabar hills. This also reveals that the Harappan measures were used in the Gangetic plain, even after 2000 years.


  1. Analysis of terracotta scale of Harappan civilization from Kalibangan, Current Science, VOL. 95, NO. 5, 10 September 2008, R. Balasubramaniam, Jagat Pati Joshi
  2. New insights on metrology during the Mauryan period by R. Balasubramaniam in Current Science, VOL. 97, NO. 5, 10 September 2009
  3. Unravelling Dholavira’s Goemetry by Michel Danino
  4. New Insights into Harappan Town-Planning, Proportions and Units, with Special Reference to Dholavira, by Michel Danino, Man and Environment, vol. XXXIII, No. 1, 2008, pp. 66-79
  5. Asoka and the Decline of the Mauryas by Romila Thapar

Image Credit: Wikipedia

10 thoughts on “The Harappan angulam

  1. As Sankar says angulam is used in Telugu too..everyone assumes it’s an inch, but I think older masons would know it’s centimeter less than that 🙂
    Michel Danino, I think, also postulated that Taj Mahal was built on danda and angulam scale (I can’t remember where I saw that paper). So it was used until fairly recently in construction of buildings. I bet in some off beat districts, it’s still used by masons.
    It’s amazing how desi internationalists/scientists discard units of measurements that survived several millennium.

    1. From Danino’s paper:
      “Then, the Arthashastra defines a digit (angula in Sanskrit) as eight widths of barley grain (2.20.6) or “the maximum width of the middle part of the middle finger of a middling
      man” (2.20.7) (Kangle 1986: 138).”

  2. Here is the Nature article link that talks of Taj Mahal measurements that relate to Harappa. It was actually R. Balasubramaniam who made that link using Michel Danino’s derivations on Harappan measurements.

  3. I find this interesting because 14 angulams of 1.763cms = 0.24682m which is the length of a 1 sidereal second pendulum at about 36 degrees latitude. 28 such angulams is the length of the Arabic cubit used by Al Mamun to measure the length of the degree at Sinjar, Iraq when he found that the circumference of the earth was about 81 million such cubits. (56.25 Arabic miles to the degree, 4000 cubits to the mile) T.B.Jervis in his 1836 book on Indian measures noted that this cubit was common all thru India and also noted that the half of such a cubit was mentioned in Sanskrit literature. Surya Siddhanta verse 1.59 in which the earth’s circumference is calculated as 162 million “feet” , ie 2*81 million — assuming that they were using 1620/512 as their estimate of Sqrt(10). Jervis speculated that the Indians had received their cubit of 28 angulams from the Arabs and that the Surya Siddhanta could not then be as old as was thought. But if this evidence of an angulam of 1.763cm in Harappan civilization (==>foot of 24.682cms) is true, maybe the Arabs got their double foot (cubit) from the Harappans via the Sassanians of Ctesephon whom the Arabs conquered!

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