At what age does the average human reach half their full adult height?

Just over two years of age. The average height of an adult American male is 1.77 meters, so half that would be 88.5 cm. This level is reached at about 2 years 3 months. For females, who grow at similar rates as small children but have a slightly lower end height, the threshold will be reached a little earlier.

Three quarters (134 cm for boys) is reached around age 9.

The numbers are taken from this chart:

https://www.cdc.gov/growthcharts/data/set1clinical/cj41l021.pdf