Analysis of information sources in references of the Wikipedia article "Hindu units of time" in English language version.
On the very day, and at the very moment the Lord [Krishna] left the earth, on that very day this Kali, the source of irreligiousness, (in this world), entered here.
The Parijata tree proceeded to heaven, and on the same day that Hari [Krishna] departed from the earth the dark-bodied Kali age descended.
Kali Yuga began on the day when Krsna passed on to heaven. Understand how it is calculated.
Kali Yuga had started on the very day when Krsna passed away.
It was on the day on which Krishna left the Earth and went to heaven that the Kali age, with time for its body set in.
* HINDUISM: Myths of time and eternity: ... Each yuga is preceded by an intermediate "dawn" and "dusk." The Krita yuga lasts 4,000 god-years, with a dawn and dusk of 400 god-years each, or a total of 4,800 god-years; Treta a total of 3,600 god-years; Dvapara 2,400 god-years; and Kali (the current yuga) 1,200 god-years. A mahayuga thus lasts 12,000 god-years ... Since each god-year lasts 360 human years, a mahayuga is 4,320,000 years long in human time. Two thousand mahayugas form one kalpa (eon) [and pralaya], which is itself but one day in the life of Brahma, whose full life lasts 100 years; the present is the midpoint of his life. Each kalpa is followed by an equally long period of abeyance (pralaya), in which the universe is asleep. Seemingly the universe will come to an end at the end of Brahma's life, but Brahmas too are innumerable, and a new universe is reborn with each new Brahma.
* YUGA: Each yuga is progressively shorter than the preceding one, corresponding to a decline in the moral and physical state of humanity. Four such yugas ... make up a mahayuga ("great yuga") ... The first yuga (Krita) was an age of perfection, lasting 1,728,000 years. The fourth and most degenerate yuga (Kali) began in 3102 BCE and will last 432,000 years. At the close of the Kali yuga, the world will be destroyed by fire and flood, to be re-created as the cycle resumes. In a partially competing vision of time, Vishnu's 10th and final Avatar, Kalki, is described as bringing the present cosmic cycle to a close by destroying the evil forces that rule the Kali yuga and ushering in an immediate return to the idyllic Krita yuga.
a day in the life of Brahma is divided into 14 periods called manvantaras ("Manu intervals"), each of which lasts for 306,720,000 years. In every second cycle [(new kalpa after pralaya)] the world is recreated, and a new Manu appears to become the father of the next human race. The present age is considered to be the seventh Manu cycle.
6.2.2: For all human, divine, and Brahma scales, one year equals 360 'days' of respective scale.
Each manvantara is preceded and followed by a period of 1,728,000 (= 4K) years when the entire earthly universe (bhu-loka) will submerge under water. The period of this deluge is known as manvantara-sandhya (sandhya meaning, twilight). ... According to the traditional time-keeping ... Thus in Brahma's calendar the present time may be coded as his 51st year - first month - first day - 7th manvantara - 28th maha-yuga - 4th yuga or kaliyuga.
catvāri trīṇi dve caikaṁ kṛtādiṣu yathā-kramam ।
saṅkhyātāni sahasrāṇi dvi-guṇāni śatāni ca ॥ 19 ॥
(19) The duration of the Satya millennium equals 4,800 years of the years of the demigods; the duration of the Tretā millennium equals 3,600 years of the demigods; the duration of the Dvāpara millennium equals 2,400 years; and that of the Kali millennium is 1,200 years of the demigods. PURPORT: As aforementioned, one year of the demigods is equal to 360 years of the human beings. The duration of the Satya-yuga is therefore 4,800 × 360, or 1,728,000 years. The duration of the Tretā-yuga is 3,600 × 360, or 1,296,000 years. The duration of the Dvāpara-yuga is 2,400 × 360, or 864,000 years. And the last, the Kali-yuga, is 1,200 × 360, or 432,000 years.
