Is there a standard distance between steps and bottom of porch step railings? What I am referring to is if you measure the distance from a step to the railing above it. The distance I measured was around 10 inches.
Without an illustration, I presume you mean the sloped bottom rail that the balusters rest on of the stair hand rail system.
If I remember right, this is pretty much standard everywhere in the US.
This is a copy and paste from the pdf referred to by nobyman. His was handy, it saved time...
R312.3 Guard opening limitations. Required guards shall not have openings from the walking surface to the required guard height which allow passage of a sphere 4 inches (102 mm)in diameter. Exceptions: 1. The triangular openings at the open side of a stair, formed by the riser, tread and bottom rail of a guard, shall not allow passage of a sphere 6 inches (153 mm) in diameter. 2. Guards on the open sides of stairs shall not have openings which allow passage of a sphere 4 3/8 inches (111 mm) in diameter.
The International Code Council says in the International Building Code that a 4" sphere shall not pass through a "guard" for stairs over 30" above finish floor...except for the triangular space formed by the riser, tread and bottom of the guardrail. In which case, it cannot allow a 6" sphere to pass. (There are other exceptions, but none that pertain to your issue.) See Section 1013.4, Exception 2 of the IBC.