The tricky part about understanding Yugas in a historical context is that time is relative. Yugas pertaining to the mechanics of the universe and affairs of the gods have a different scale than those pertaining to human history. I’ve studied the definition of yugas in Visnu Purana, Surya Siddhanta and Manu Samhita. They very similar, but the difference in emphasis in Manu Samhita is important to note.
Here is the definition given in Surya Siddhanta (I will note where Manu Samhita differs):
Time creates, maintains and destroys everything.
There are two types of time, finite and infinite.
Infinite time has no no beginning or end.
We are currently aware only of finite time, which has beginnings and endings.
There are two types of finite time: practical and philosophical.
Measurable time is practical.
Time too small to be measured is “philosophical time.”
Practical time begins with a unit called “respiration” (prANa).
Philosophical time begins with an “atomic” unit (truTi).
Note, Surya Siddhanta does not discuss philosophical time, although the Puranas do. It is full of extremely small theoretical divisions of time. Surya Siddhanta is concerned only with practical time:
6 repirations = 1 “semi-pulse” (vinADI)
60 semi-pulses = 1 “pulse” (nADI)
A sidereal “day” (which includes the night), has 60 pulses.
Note: The Purana’s and Manu Samhita have a slightly different system. They say practical time begins with a “twinkle” (nimeSa), 15-18 of which are in a “bit” (kASThA), 30 of which are in a “minute” (kalA), 30 of which are in an “hour” (muhUrta), 30 of which are in a day.
There are 30 sidereal days in a month.
[Another system:] A “common” month instead has 30 sunrises.
[Another system:] A “lunar” month instead has 30 “phases” (tithi [relative distance of the Moon and Sun]).
A “tropical” month begins when the Sun enters a new zodiac sign.
There are 12 months in a year.
A year = 1 “day” for the gods.
Day for the gods is night for the anti-gods, and visa versa.
360 years = 1 “year” for the gods.
12,000 divine years = a “quadruple-age” (catur-yuga)
It is the same as 4,320,000 solar years.
These figures account for the “dawns” and “twilights” in the ages.
Note: As will next be stated, without the dawns and twilights, there are 10,000 years in a quadruple-age, which is equivalent to 3,600,000 (360 x 10,000) years of the gods.
Here the Manu Samhita differs importantly by stating that 12,000 solar years constitute one “mahayuga” (the more standard term for catur-yuga).
Each of the four ages in the quadruple-age possesses on less “foot” of the “bull” named dharma. The duration of each age (“yuga”) is a tenth of the catur-yuga multiplied by the number of legs the age possess. The durations of the twilight and dawn are each a 10th of this.
10,000 is the base number for the calculation – the number of years in a quadruple-age, without the dawns and twilights. A tenth of this is 1,000.
“Age 4” (“kRta”) has 4 “legs” of dharma, therefore it lasts 4,000 years (4 x 1,000).
“Age 3” has 3 legs, therefore it is 3,000 years
“Age 2” has 2, therefore it is 2,000 years
“Age 1” (“kali”) has 1, therefore it is 1,000 years long.
The twilight and dawn for each age is a tenth of its length. So “Age 4” is 4,000 + 400 (for the dawn) and 400 (twilight) = a total of 4,800 years
Similarly Age 3 with dawn and twilight is 3,600 years.
Age 2 is 2,400.
Age 1 is 1,200 years long.
All accounting for the total, 12,000 years.
To express this on the gods or anti-gods timescale, multiply by 360. So on the gods timescale the age lenths are:
Age 4 = 1,728,000,000 solar years
Age 3 = 1,296,000,000
Age 2 = 864,000
Age 1 = 432,000 solar years.
71 quadruple ages = 1 “patriarch-epoch” (manvantara)
The dawn and twilight of each manvantara is each equal to the length of Age 4, there is a catastrophic flood during this time.
14 patriach-epochs = 1 “aeon” (kalpa)
The aeon has its own dawn – the same length as Age 4 – so that there are 15 sets of transitional periods altogether in an aeon.
An aeon is thus equivalent to the duration of 1,000 quadruple-ages.
Note: an aeon lasts for 12,000,000 years, which is 4,320,000,000 years on the gods time-scale.
Everything is destroyed at the end of an aeon.
1 aeon = 1 daytime for Brahma (the creator), and his night is the same length
He lives for 100 years of such days and nights.
Half his life is past, and we are now in the first aeon of his second half [i.e. the first day” of his 50th “year”]
In this aeon, six patriarch-epochs have past, along with their transitions.
In the seventh patriarch-epochs (where the partiarch is named Vaivasvata) 27 quadruple-ages have past.
In this 28th quadruple-age, Age 1 has already passed.
Try to calculate the time that has passed till now!
Note: This is the time at which the Surya Siddhanta claims to have been spoken. To calculate it:
Brahma’s “50th birthday” would occur 432 billion years after the universe began. Putting that aside for now, the current aeon began 4,800 years ago (the length of Age 4, which had passed so far when the book was created).
Previous to that 27 quadruple-ages passed, which is 324,000 years (27 x 12,000).
Previous to that, six patriarch-epochs passed, which is 5,140,800 years (6 x (12,000×71)).
Previous to that was the dawn of the aeon, another 4,800 years.
So the total amount of time since Brahma’s “50th birthday” was 5,474,400 years.
So the Surya-Siddhanta says it was first spoken after about 432 billion, 5 million, 474 thousand, 400 years since the beginning of this universe.
Since we are now somewhere within Age 1, we should add about another 7,200 years to get the more current approximate age of the universe – which is barely any different on this huge scale.
To express all this from the timescale of the gods, multiply by 360.
From the beginning of the current day of Brahma, he spent 47,400 years setting up the creation of plants, stars, gods, anti-gods, etc.
Note: From this point forwards the Surya Siddhanta mainly becomes entirely practical and describes the mathematics of how to calculate time via planetary positions relative to the stars and zodiac signs. It begins by describing a unique planetary conjunction that is supposed to mark the beginning of the current Age.