There are several factors to consider.
What temperature rise above what ambient?
What is the conductivity of the conductor (an old book shows two types of aluminum EC - 61%IACS and EC-T61 - 57%IACS)?
What is the orientation of the bars, flatwise or on edge?
Are bars mounted above each other (stacked)?
For example:
30 deg C rise over 40C ambient, still but unconfined air
EC-T61 aluminum
Edgewise orientation, bars spaced at least one thickness apart.
AC 60hz current
3/8 x 4 = 1170A
1/4 x 4 = 960A