Three websites where you can find the compatibility of two specific birthdays are CafeAstrology.com, Keisan.casio.com and TokenRock.com. Each of these sites uses the exact birthday of each person, year of birth included, and calculates unique compatibility reports.
CafeAstrology.com's Compatibility Rating Tool provides a percentage of compatibility and also a brief write-up of the particulars of the relationship by examining each person's astrological chart and sun sign.
Keisan.casio.com's Biorhythm Compatibility Calculator uses two birthdays to measure their biorhythm compatibility in the form of percentages for emotional, physical and intellectual compatibility.
TokenRock.com uses a Numerology Compatibility Calculator to measure each person's Life Path Number by adding up the numbers in each date of birth and comparing them in a written compatibility report.