I am 16 days late with my periods. What is the reason?

Could be many things.

Age;
Diet;
Exercise;
Rapid weight loss or gain;
Pregnancy, etc.

Just to name a few. Sometimes we are late or miss a period for no apparent reason.

If this will help, I am 29 years old. In a relationship. I have always been very regular with my periods. Although last month I was 5 days late, I started on 10th of July.
Was expecting to start 10th Aug or even 3-5 days late. BUT NOTHING YET.

Sexually active? Birth control?

Sexually active.
No birth control.

Have you taken a HPT using first morning urine?