This web page gives a detailed timeline of the Mahabharata, based on the text of the Mahabharata and its associated commentaries. Here is the basic method of calculating the ages of the Pandavas. First of all, as I discuss in this answer, Krishna departed the Earth after he was shot by a hunter who mistook his foot for the mouth of a deer. This event marks the beginning of the Kali Yuga, and it took place in 3102 BC. Now we use the description of the birth of Yudhisthira given in this chapter of the Adi Parva of the Mahabharata:
Then the handsome Kunti was united (in intercourse) with the god of justice in his spiritual form and obtained from him a son devoted to the good of all creatures. And she brought his excellent child, who lived to acquire a great fame, at the eighth Muhurta called Abhijit, of the hour of noon of that very auspicious day of the seventh month (Kartika), viz., the fifth of the lighted fortnight, when the star Jyeshtha in conjunction with the moon was ascendant.
It can be determined using astrological calculation that this took place in 3229 BC, 127 years before the start of the Kali Yuga. So Yudhisthira was 127 years old at the time of Krishna's death. But we know from the Sauptika Parva of the Mahabharata that Krishna died 36 years after the Mahabharata war.
Thus Yudhisthira was 91 years old at the time of the Mahabharata war. And each of the Pandavas were born a year apart. So at the time of Mahabharata war, Yudhisthira was 91 years old, Bhima was 90 years old, Arjuna was 89 years old, and Nakula and Sahadeva were 88 years old.
By the way, as I discuss in this answer, the Matsya Purana says that Krishna was 89 years old at the time of the Mahabharata war, making him younger than Yudhisthira and Bhima, the same age as Arjuna, and older than Nakula and Sahdeva. That is confirmed by the relations of respect described in the Srimad Bhagavatam:
After the Lord bowed down at the feet of Yudhiṣṭhira and Bhīma and firmly embraced Arjuna, He accepted obeisances from the twin brothers, Nakula and Sahadeva.
In any case, using similar astrological calculations, it can be shown that Bhishma was born in 3278 BC, and was thus 140 years old at the time of the Mahabharata war.
By the way, it may seem odd to you that everyone was so old, but you have to keep in mind that people were much longer-lived in the Dwapara Yuga.