The pragmatic test is simpler.  It is what is used in mountain strip flying.  Identify/mark a point half way down the runway.  The plane must accelerate to at least 70% of takeoff speed at that point.  If it has not reached it,  you are not going to make it.  Chop power and brake.  Lighten the load, wait for cooler weather, install a turbo.  Be safe.