In his book Aryabhatiya, he mentions the following:

Meaning:
"When the three yugas Satya yuga, Treta yuga and Dwapara yuga) have elapsed and
60 x 60 (3,600) years of Kali yuga have already passed, I am now 23
years old".
Calculate accordingly:
- He said in his book that 3600 years of Kali have passed. It means
when he wrote the book, 3600 years of Kali have elapsed.
- He further added that he was 23 years old when he completed his book.
So, when he was born, 3577 (3600-23) years of Kali might have passed.
- In Panchankam, through astrology, it is mentioned that as of April
2018, 5119 years of Kali have passed. Now, subtract 3577 from 5119.
You will get the number 1542. It means, 1542 years have elapsed since
Aryabhatta was born.
- Now reduce 1542 from 2018. You will get 476. This is how, his date is
calculated.