At what age can you determine a child developmental delay?

That really depends on WHAT is delayed.

In some cases, a developmental delay can be diagnosed as early as four months of age if the baby has not shown the correct signs of developing certain muscle skills and movements.  For example, if a baby still can't support their own head at four months old - then a developmental delay for motor skills would be investigated to determine what health issues might be causing that delay.

In other cases, a developmental delay may not be obvious until sometime between the age of two to three years old.  Speech delays are often diagnosed a little late since there is a wide age range for what is acceptable speech development.  

There are many sources for "baby milestone" lists and most of them are fairly close in what they list as timelines for "normal development".  All of these milestones have an AGE RANGE for each development because every child does develop slightly differently.  For example, the milestone range for a baby walking is 12 months on the AVERAGE but some babies walk before 9 months while other babies don't walk until around 18 months.  Because of this range for this particular development, a baby that has not walked at 14 months would not be diagnosed as have a developmental delay unless there have been other issues that justify it.  But, if the child wasn't walking at 18 months, then it would be considered a developmental delay.  The doctor would decide what age to start running extra tests.  If there is a family history of certain health issues, tests might start sooner. 

Basically - a developmental delay would be diagnosed at a point in which a child has failed to do something that should have happened by that point in the child's development.    It would not be diagnosed at the early side of the milestone point.  It would be diagnosed at the later point of the milestone range.  (just because the average baby walks at 12 months does not mean another baby is "delayed" because they didn't walk until 15 months - both ages are in what is considered the NORMAL milestone range for that developmental skill.)