calculating lunar phases
A new moon occurs 2017/7/23 09:45:34 UTC. Instantly after that it is waxing. 

A crescent won't be visible for a few days. It reaches first quarter about 7 days later. The moon will appear to be about half full for maybe a couple of days. Nevertheless, first quarter, full moon, third quarter and new moon are moments in time, not intervals. 

It may, sometimes be convenient to refer to "the day that new moon occurs", and in casual use people will say the moon is full while it appears as a circle to the naked eye (usually lasting several nights) These are casually defined for casual use. For precise terminiology say "it is now 3 days 4 hours after New Moon" or similar.