How old were Aragorn and Arwen when they were married?

Question

After the one ring was destroyed and Aragorn was crowned King of Gondor and Arnor, he and Arwen were married. Though he looks older than his bride, I'm learning that Arwen is actually older than Aragorn by at least 2,600 years. She's obviously robbing the cradle, but I can't get an exact fix on exactly how old they were when married.

Answer 1

Both Aragorn and Arwen's births, and their marriage, are listed in the Third Age section of The Tale of Years (Appendix B, at the back of Return of the King). Arwen was born in the year 241. Aragorn was born on March 1 of 2931. Since they were married at the end of June in 3019, this means Aragorn was 88 years old when they were married, and Arwen was either 2778 or 2777 (depending on whether she was born in the first or second half of the year).

Answer 2

Aragorn was 88 (having aged 45 years) and Arwen 2778 (having aged 33 years)

As far as I can tell, Tolkien's last known writings about Arwen's growth is the work "Elvish Ages & Númenórean" written in 1965 and published in The Nature of Middle-earth.

Tolkien begins by describing the nature of elvish growth in Middle-earth in the Third Age, before giving examples of how it applies for different characters.

Elves' ages must be counted in two different stages: growth-years (GY) and life-years (LY). The GYs were relatively swift and in Middle-earth= 3 Löar. The LYs were very slow and in Middle-earth = 144 löar. ... They reached "full growth" of body in 24 GY. ... They then had 48 LY of youth, and then 48 LY of "full age" or "steadfast body", by which time their knowledge ceased to increase. ... If we neglect the difference of speed and call each unit a "year", we then see that an elf reached maturity at 24, end of "youth" at 72, and "old age" at 120. In mortal equivalents the age in physical and other characteristics indicated can be found approximately by multiplying by ¾.
_{The Nature of Middle-earth - "Elvish Ages & Númenórean"}

Basically, for the first 72 years of an elf's life they age one elf year every 3 normal years, until they turn "24" (72). After that they only age one elf year every 144 normal years. However, each of these aforementioned elf years is really the equivalent of what a mortal grows in 3/4 of a year.

So to get an understanding of how old an elf is you need to figure out how many total Growth-Years and Life-Years they've lived, and then multiply that number by 3/4.

The case of Arwen. Taking her birth as T[hird]A[ge] 241, she will then be "full-grown" in TA 313 (241 + 72). In 2951, when she first meets Aragorn, she will be (in Elven Growth- and Life-years) 24 + 18⅓ (nearly); (2951-313)/144 = 42⅓ = mortal equivalent 31¾. Aragorn was only 20.

In 3019, when they were married, she would have aged very little and would be nearly Elvish 43 (24 + (3019-313)/144) = mortal equivalent 32-3. But Aragorn would have lived 88 years and 4 months. His "age" would however be about "45". ...

The Númenórean scale fixed by the Valar (for other than Elros) was for a life in full (if not "resigned" earlier) of thrice that of ordinary men. This was reckoned so: A "Númenórean" reached "full-growth" at 24 (as with Elves; but this was for them reckoned in Sun-years); after that, 70 x 3 = 210 years were "permitted" = total 234. But decline set in (at first slow) at the 210th year (from birth); so that a Númenórean had an expectation of 186 fully active years after reaching physical maturity.
_{The Nature of Middle-earth - "Elvish Ages & Númenórean"}