There are a number of places where our chronology is not based on the pshat of the Tanach.
- Chumash - One can determine, using only the text of the Chumash, when the exile in Mitzraim began. One cannot, however, determine when it ended. Pirkei d'Rebbi Eliezer chapter 48, for example, asserts that Yocheved was born when Am Yisrael entered Mitzraim, and she was 130 when Moshe was born. But this is not in the Chumash. The Chumash leaves this open for drash.
- Shoftim Period - Melachim Alef, 6:1 states that the building of the 1st Beit HaMikdash began 480 years after the Exodus. The exact chronology of events, and duration of time the mishkan was in each location during this 480 year period seems to be from mesorah and not the text.
- Galut Bavel - The length of Galut Bavel is 70 years, but what does that mean precisely? As I have mentioned before, there are multiple 70 year periods at play. The period between the building of the 2nd Beit HaMikdash and the arrival of Ezra haSofer is made much shorter by Chazal's identification of Artachshasta as Daryavesh (Bavli Rosh Hashanah 3b).