As this year is 365 days long, your half-birthday comes 182 and half days after your normal birthday.
For example, if you were 29 on May 28th, your 29 and a halfth half-birthday is today from noon today until noon tomorrow. If you were 50 on June 22nd, you’ll be 50 and a half on 21st December.
My half birthday is from noon on November 1st to noon on November 2nd. I was born at 3:45pm BST, so was ‘half a year older’ at 2:45am on November 2nd this year.