In same measures: Harappa to Taj

K. S. Jayaraman

doi:10.1038/nindia.2009.227 Published online 8 July 2009

Balasubramaniam in front of the Sun Temple in Konark, Orissa.

A researcher analysing designs of historical buildings and monuments of India has made a profound discovery. He has shown that the unit of length used by the builders through the ages surprisingly remained the same for over 3900 years. This reveals a new dimension in metrology — the science of measurement — in the Indian subcontinent.

From the Harappan settlements of 2000 B. C. and the Delhi Iron Pillar of Gupta period (320–600 AD) to the 17th century Taj Mahal, the unit 'angulam' had remained the standard of measurement in engineering plans, says Ramamurthy Balasubramaniam from the Indian Institute of Technology (IIT) in Kanpur.

Angulam and its multiples vitasti (12 angulams) and dhanus (108 angulams) find mention in the Indian treatise Arthasastra by Kautilya who codified the metrology that was prevalent around 300 B.C. But the exact value of angulam was derived only in 2008 by Michel Danino, the French author who made India his home.

Danino who studied the Dolavira settlement — the largest Harappan civilization site in India — found1 that the dimensions used were exact multiples of 1.904 metre, a unit that he assumed to be the dhanus mentioned in Arthasastra. Further, taking dhanus to be 108 angulams, Danino derived the value of angulam to be 1.763 cm.

Balasubramaniam, a professor of materials and metallurgical engineering, says he got interested in metrology after Danino's derivation of the value of angulam and his own observation2 that a terracotta scale of Harappan civilisation from Kalibangan, that was given to him for analysis, indicated markings of 1.75 cm.

"Seeing 1.75 cm markings on the Harappan scale and Danino's derived value of 1.763 cm for angulam no doubt excited me," Balasubramaniam told Nature India. "That prompted me to carry out dimensional analysis of some of India's historical structures to see if their builders used a standardised unit of measurement," he said.

Balasubramaniam who studied the 1600 year old Delhi Iron Pillar3 found that its dimensions "matched remarkably well" with the units of angulam and dhanus of the Harappan civilization. "For example, the total height of the pillar is precisely four dhanus and several measures come out as whole numbers of vitasti," he said.

The IIT professor had also carried out dimensional analysis of the earliest engineered caves at Barabar and Nagarjuni Hills in Bihar (Ashokan period, 300 B. C.), the Gupta Temple at Deogarh in Uttar Pradesh (6th century AD) and very recently4 the Taj Mahal in Agra.

"All these studies confirm the use of a constant basic measurement unit of angulam," the IIT professor said. "What is surprising is the fact that the constant of 1.763 cm, when matched for the angulam, leads to the realisation of the other multiples," Balasubramaniam said, "and surprisingly, important historical structures of the Indian subcontinent show a more than good match with these multiples."

For instance he found4 that the modular plan of the Taj Mahal complex is based on use of grids of sides measuring 60 and 90 vitasti. The mausoleum was designed on a master square of 270 vitasti to the side – a number that allows the area to be divided into nine smaller squares of side 90 vitasti.

"Further subdivision of the 90 vitasti length in thirds is evident in the length of the large arched doors (60 vitasti) and the small arched doors (30 vitasti) on each (outer) face of the mausoleum," Balasubramaniam explained. "We now know that the modular design and architecture of the Taj is based on Indian principles and there is nothing foreign in the design plan," Balasubramaniam said.

According to Balasubramaniam, the important outcome of his research is that it has establishes the continuity of metrological tradition from the Harappan civilisation down to pre-modern India indicated by the fact that the unit of angulam matches so well the dimensions of important monuments.

"This implies an unbroken engineering tradition in the use of the angulam over a period of more than 3900 years which is really amazing," he said. The tradition was broken with the adoption of British units in early twentieth century. "With the new knowledge we can now analyse all the important ancient structures in India, using 1.763 cm as the standard with different multiplying units. This work will open a new chapter in metrological studies," he said.

But how did the angulam knowledge get transmitted through the ages to maintain continuity? "It is reasonable to propose that the workers were following some kind of scale that was handed over through generations," says Balasubramaniam. "Otherwise, such a good match of the dimensions cannot be due to chance."


  1. Danino, M. New insights into Harappan town-planning, proportions, and units, with special reference to Dholavira. Man Environ. 33, 66-79 (2008)
  2. Balasubramaniam, R. et al. Analysis of terracotta scale of Harappan civilization from Kalibangan. Curr. Sci. 95, 588-589 (2008)
  3. Balasubramaniam, R. On the mathematical significance of the dimensions of the Delhi Iron Pillar. Curr. Sci. 95, 766-770 (2008)
  4. Balasubramaniam, R. New insights on the modular planning of the Taj Mahal. Curr. Sci. 97, 42-49 (2009)