Is 13 cm big?
No — 13 cm (5.1 in) erect is almost exactly average: the clinician-measured mean is 13.12 cm (Veale 2015, n=15,521), which puts 13 cm at the 47th percentile.
No. 13 cm (5.1 in) erect is not big — it is, within about a millimeter, the average. The largest clinician-measured dataset (Veale et al. 2015, BJU International, n up to 15,521) reports a mean erect length of 13.12 cm, which places 13 cm at the 47th percentile.
Statistically, that is as unremarkable as a measurement gets: about half of men are shorter, about half are longer. Anyone attempting to design the most typical possible penis would miss this number by roughly a millimeter.
Perception is a separate matter. Self-reported surveys run 1–2 cm above clinical measurements, and adult media selects for outliers, so the reference point many men carry in their heads is inflated. Judged against that imaginary standard, 13 cm reads as small. Judged against actual measured men, it is the exact middle of the pack.
Where other lengths fall is laid out in the penis size chart, and the full context in what the average penis size is.