engine-eer
You need a set of mach tables for standard atmosphere to calculate the pressure at the compressor face. A proper set of mach tables has the total pressure ratio and total temperature already calculated. I couldn't find a set on the web, but I did find a link to a NASA calculator that gives you what you are looking for. Plug in your flight conditions (and push the enter key with the cursor in either the altitude or the speed box) and this will tell you what you want. The units are funky, you have to calc the pressure ratio after you convert the total pressure back from lbs/sq ft back to psi, but it is all there.
It doesn't seem to make any mention of being Mac compatible...
What you want to remember is that there is a pressure loss in any inlet, so the calculated inlet pressure has to be multiplied by the inlet recovery. Low speed inlets (like on a big turbofan) are typically about 98% efficient or better, but long high mach inlets like on a fighter can be as bad a 92 or 93%.
So that's why very high speed aircraft like the XB-70 and SR-71 tended to have a slower initial acceleration rate than you would expect?
The faster you go, the higher the inlet pressure, but also, the higher the inlet temperature becomes. As you go to high mach numbers (above three) the inlet temperature will be closing in on 800 degrees F.
I thought stagnation temps tended to produce around 600-F at Mach 3?