what information's needed to find the machining rate of a Planer and convert it to inches per minute?

There is some potential for confusion here since metal working and woodworking planers operate differently, and in is not unusual for a metal working planet to be fitted with milling heads. However I'm going to guess we are talking about a basic metal working machine with stationary single point tool. You'll need to know the speed of the table, both on the cutting stroke and the return (non cutting) stroke, or perhaps that would be better stated as the time to take one complete cycle, the cutting stroke length, also the chip width and thickness.

I don't really have any experience with planers, so the numbers I going to use might be strange, but the math is what you are asking about, not specific numbers.

Supposing we have a 100inch cutting length and, with the reversing, accelerating and decelerating, one complete table stroke takes one minute, also imagine the depth of cut is 0.5 inch and the chip is 0.05 inches thick (0.05" feed per stroke). To determine tho volume of metal removed we multiply stroke times depth times thickness (100 * 0.5 * 0.05 = 2.5 inches³) then divide that by the time it took (1 minute in this example) to determine the rate

60 divided by time (in sec) of single stroke gives strokes per minute then times length of stroke gives inches per minute.

I assume this is for feed rate calculations and should be fine.

Are you talking about Milling or turning. What material.

What cutter size. Size of Planar.

I am going to assume you are referring to a milling operation.