Synonyms for Height (same or very similar meaning)
WordNet sense 1 (the highest level or degree attainable; the highest stage of development):
acme, elevation, meridian, peak, pinnacle, summit, superlative, tiptop, top
WordNet sense 2 (the vertical dimension of extension; distance from the base of something to the top):
tallness
WordNet sense 3 (elevation especially above sea level or above the earth's surface):
altitude
WordNet sense 4 ((of a standing person) the distance from head to foot):
stature
From the ODE community, based on WordNet
add/edit