How old is Aragorn when he fights at Helm's Deep?

Question

In Jackson's movie Aragorn tells Eowyn he is 87 years old, but in Tolkien's book, Aragorn's age is not mentioned.

Or is it? And if it is, how old is Aragorn when he fights at Helm's Deep, at the end of the Two Towers?

Answer 1

Aragorn was technically 88 years old, but aged the equivalent of a 45-year-old.

Aragorn was born March 1st 2931.

2931 - Aragorn son of Arathorn II born on March 1st.
_{The Lord of the Rings - Appendix B - "The Tale of Years"}

The scene you refer to in the film takes place right after they set out from Edoras and two days prior to the Battle of the Hornburg (which was on March 3rd 3019). However in the books they only set out from Edoras one day before the Battle of the Hornburg. So depending on how you line up the film timeline to the book timeline, this will either be March 1st 3019 or March 2nd 3019.

3019 March:
2 - Frodo comes to the end of the Marshes. Gandalf comes to Edoras and heals Théoden. The Rohirrim ride west against Saruman. Second Battle of Fords of Isen. Erkenbrand defeated. Entmoot ends in afternoon. The Ents march on Isengard and reach it at night.
3 - Théoden retreats to Helm’s Deep. Battle of the Hornburg begins. Ents complete the destruction of Isengard.
_{The Lord of the Rings - Appendix B - "The Tale of Years"}

Thus Aragorn's real-time age was exactly 88 years.

However Aragorn is a Númenörean, and therefore ages at a different rate than ordinary Men.

Tolkien explains how to calculate this in a c.1965 work titled "Elvish Ages & Númenórean", which Tolkien notes "is the scheme followed in LR and Tale of Years".

The Númenörean 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 × 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"}

Basically, they age at normal rate for their first 24 years, after which they only age one year every three years. So for Númenöreans over the age of 24, you'd find their age by subtracting 24, dividing by three, and then adding back 24.

In this same work Tolkien applies the calculation to show Aragorn's age at his wedding:

In 3019, when [Aragorn and Arwen] were married, ... Aragorn would have lived 88 years and 4 months. His “age” would however be about “45”.
_{The Nature of Middle-earth - "Elvish Ages & Númenórean"}

We're looking for Aragorn's age two days before Helm's Deep, which is nearly the same.

1. 88 years [March 1st 2931 to March 1st 3019]
2. 64 years [subtract 24]
3. 21 years, 4 months [divide by 3]
4. 45 years, 4 months [add back 24]

Answer 2

Aragorn was born on 1 March 2931 Third Age. The Battle of the Hornburg took place on 3 March 3019 Third Age, making Aragorn 88 years old (and 2 days) at the Battle of Helm's deep.

The Third Age turned into the fourth age in the year 3021, when Aragorn assumed the throne at the age of 90. He died, thus vacating the throne to his son Eldarion, in 120 Fourth Age at the age of 210. He, like all the descendants of Isildur, were long-lived for men.

I don't remember if it is actually mentioned in the texts, but his age is mentioned in the Appendices at least.