How many kilometers equals to a Yojana

Question

After reading this answer, I am curious to know how many kilometers or miles are equal to one yojana.

Below is some of the information taken from the above link. Here a league equals one yojana

The sphere of the earth (or Bhúr-loka), comprehending its oceans, mountains, and rivers, extends as far as it is illuminated by the rays of the sun and moon; and to the same extent, both in diameter and circumference, the sphere of the sky (Bhuvar-loka) spreads above it (as far upwards as to the planetary sphere, or Swar-loka). The solar orb is situated a hundred thousand leagues from the earth; and that of the moon an equal distance from the sun. At the same interval above the moon occurs the orbit of all the lunar constellations. The planet Budha (Mercury) is two hundred thousand leagues above the lunar mansions. Śukra (Venus) is at the same distance from Mercury. Angáraka (Mars) is as far above Venus; and the priest of the gods (Vrihaspati, or Jupiter) as far from Mars: whilst Saturn (Sani) is two hundred and fifty thousand leagues beyond Jupiter. The sphere of the seven Rishis (Ursa Major) is a hundred thousand leagues above Saturn; and at a similar height above the seven Rishis is Dhruva (the pole-star), the pivot or axis of the whole planetary circle. Such, Maitreya, is the elevation of the three spheres (Bhúr, Bhuvar, Swar) which form the region of the consequences of works. The region of works is here (or in the land of Bhárata).

I am very desperate to know how much our ancients know about mathematics, I want to compare those calculations with the current ones.

Answer 1

I'll stick to 1 yojana = 8 miles because Hanuman chalisa gives the distance between earth and sun as - जुग सहस्र योजन पर भानू. लील्यो त्याही मधुर फल जानू. (Sun's जुग सहस्र योजन away.) जुग = 12,000 सहस्र = 1,000 Thus 12,000 * 1,000 = 12,000,000 yojana. Sun is approx 96,000,000 miles away. Thus we can conclude that 1 yojana = 8 miles.

Answer 2

Different Values have been interpreted for yojana from our ancient texts.

The British set it at 5 miles which was felt smaller. There have been various contradictory conclusions ranging from 5 miles to 8 miles. A good history about multiple values are present at this site:

The Arthaśāstra (4th century BCE) says that 1 yojana = 4 gorutas; 1 goruta = 1000 dhanus; 1 dhanu = 96 angulas. Taking the angula as ¾ inch makes the yojana about 4.54 statute miles. During the colonial period the British administration set the yojana at 5 miles; however, this seems to be smaller than its usual value. The ancient commentator on the Arthaśāstra says the goruta is 2000 dhanus, which would make the yojana about 9 miles.

T. W. Rhys Davids complied a list of occurrences of the term and compared each with distances on modern maps. He concluded:

The conclusion to which I come is that we have no data as yet for determining the sense in which the word yojana is used in the Three Piṭakas; that in fifth-century Páli literature it means between seven and eight miles, and that the traditions preserved by Ceylon authors of that date as to distances in North India in the time of Gautama agree pretty well, except in the cases of Kapilavastu and Sankassa, with the sites fixed by General Cunningham.

Answer 3

As per Wikipedia.

A Yojana (Sanskrit : योजन ) is a Vedic measure of distance that was used in ancient India. It is equivalent to about 8.0 km (5 mi) as per modern measures of distance, although the exact value is disputed among scholars (between 8 and 13 km (5 and 8 mi).

Answer 4

Garuda Purana, Dharma Kanda Chapter XXXIII has a shloka which says

The distance between the mortal world and the region of Yama is eighty six thousand yojanas (one million, thirty two thousand kilometres).

If this conversion is correct then 1 yojana is equivalent to 12 kilo meters.

Answer 5

Yojana is measurement of distance equal to 6.06/8 miles approximately

Saint Srila Vadiraja Tirtha Swami, a master of Vedic mathematics, gives its divisions and calculations:

7 sarsapas(mustard seeds) = 1 Vrhi (length of a paddy seed) 3 Vrhis - 1 Angula 24 Angulas - 1 Hasta or 1 cubit (=2 feet) 4 Hastas = 1 Danda, staff length(=8 feet = 96 inches) 1000 Dandas = 1 Krosa (=4000 Hastas=8000feet=96000 inches) 4 Krosas = 1 Yojana(=32000 feet or 384000 inches)

COnsidering 1 mile = 1609 meters or 5278.87 feet

1 Yojana = 32000/5278.87 = 6.06 miles.

Thus scholars of Madhva accept 6.06 miles/Yojana for all calcualations referred in book "Bhugola Varnanam".

Srila Vishwanath Chakravarthy Thakur, Srila Prabhupada and many other acharyas used 8 miles per yojana for calculations in Bhagavatam.

The Madhva scholars reconcile this as follows:

The fact that seeds and the like were bigger in previous ages and as time progresses their sizes are reduced as indicated in SB 12.2.1. For the same reason, a man's cubit or Hasta measured 24 inches then as against 18 inches now obtained.

By considering the above change in Hasta measurements,

1 Yojana = 16000 Hastasx24/18 = 21333.33 Hastas = 42667 feet

Thus 1 Yojana = 42667/5279 = 8 miles

To justify reductions in scale, Vamsidhara observes that yojana is defined on the basis of human body, Thus a yojna is 16000 hastas and a hasta is 24 finger widths. Also, a hasta can be defined as one fifth the height of a man standing with his arms stretched up. As the bodies of infants, children and adults vary greatly in size, so the yojana also varies and in this way one can explain differences between various estimates of distance.

Reference: Bhagavata Cosmology

Answer 6

1 yojan is distance travelled by sound in 1 second which is 343 meters when sound travells through air as medium

Ram setu was 100 yojan = 34300 meteres or 34.3 KM which is almost same as calculated by scientists as length of ram setu (adam's bridge)