Your boy will likely be 6 ft. 6 in. at age 18.
Young men often continue to grow a little past 18 until they reach 21, but their height at age 18 is very close to their final adult height. This prediction is a "best guess" but it's still just that -- a guess. Based on the formula we used* there is a 50 percent chance that your boy's full-grown height will be within 0.8 inches (above or below) of this prediction, and a 90 percent chance that it will be within 2.1 inches.
Sometimes a child will surprise everyone and turn out much taller or shorter than either parent. This calculator can't account for that possibility. It also won't work well for children who 1) are exceptionally tall, 2) are already taller than both their parents, or 3) have a condition that affects their height, such as growth hormone deficiency.
Predicting Adult Stature Without Using Skeletal Age: The Khamis-Roche Method
by H.J. Khamis and A.F. Roche
Pediatrics, October 1994