Finding the next occurrence of your birth date
For someone born 15 June 1995, counting from 14 September 2026: this year's 15 June has already passed, so the next occurrence is 15 June 2027 — 274 days away — and they'll be turning 32.
The 29 February exception
Someone born on 29 February only has a real birthday once every four years. Counting from 14 September 2026 for a birth date of 29 February 2000, the next occurrence lands on 28 February 2027 (2027 isn't a leap year, so the date is clamped down by one day) — 167 days away, turning 27.
When today is the birthday
If the reference date matches the birth month and day exactly — 14 September, counting from 14 September — the countdown shows 0 days until, and the turning age is whatever age is reached that same day.
Why this is a different question from a plain date countdown
A plain countdown needs the exact target date typed in. A birthday countdown only needs the birth date — it works out which year's occurrence is next on its own, since a birthday recurs annually rather than pointing at one single date the way a deadline or event does.