The Bible doesn't say how old Isaac was at the Akedah (the 'binding' of Isaac)--at least not in so many words. To find a definite answer, you need to consult the literature of early Judaism, whose authors, like some modern readers, were curious about the question, and searched the text for any clues it might provide.
It turns out there are several different definite answers:
One common rabbinic suggestion, apparently first attested in Targum Pseudo-Jonathan (3rd cent. CE+??), is that Isaac was 37 years old. It's pretty simple really:
- Sarah was 90 years old when she conceived Isaac (Gen 17:17).
- Sarah was 127 years old when she died (Gen 23:1).
- Since Sarah's death is mentioned in Gen 23:1 immediately after the account of the Akedah, it follows that Sarah died when she heard about Isaac's near-death experience.
- Subtract 90 from 127 and you have 37 years.
Josephus, writing toward the end of the first century CE, states baldly that Isaac was 25 (Ant. 1.227).
How far back do these traditions go in our extant literature? In a recent article that discusses references to the Akedah in the 2nd BCE book of Jubilees, the Dead Sea Scrolls, and the Targumim, Joseph Fitzmyer claims that speculations about Isaac's age "appear for the first time in the Christian era [i.e. in Josephus]" ("The Sacrifice of Isaac in Qumran Literature," Biblica 83 :222).
This may be true for direct statements, but an earlier answer is found already in Jubilees:
Jubilees, is concerned, as one might expect, to date the events narrated in Genesis by 49 year Jubilee cycles. Jub 15:1 dates Isaac's conception to the 6th month of the 6th year of the 4th sabbatical week of years (cf. 16:16)--in other words, the 27th year of that particular jubilee cycle. Presumably Isaac was born in the 7th year of the 4th sabbatical week of years (that is, in year 28). Jub 17:1 says he was weaned in the first year of the 5th sabbatical week (i.e., year 29). According to Jub 17:15, God tested Abraham in the first year of the 7th Sabbatical week (year 43). This means that Isaac was around 16 years old at the Akedah.
(N.B. Although my earlier total of 13 was more exciting, it was also incorrect. My numbers now agree with James C. VanderKam, "Studies in the Chronology of Jubilees," pages 522-544 in From Revelation to Canon [ed. James C. VanderKam; Leiden: Brill, 1999]. I take comfort in the fact that VanderKam points out several chronological errrors in Jubilees itself.)
I would not have bothered to (try to) do the math if I had not been working on an edition of the Greek textual evidence for Jubilees for the Online Critical Pseudepigrapha. What I originally imagined would be a straightforward project consisting of the rearrangement of the excerpts presented in Denis' Fragmenta, became more complicated when I realized that many of the texts do not actually quote Jubilees. This sent me looking for the texts of the Christian Greek authors who preserve Jubilees traditions--a few of which I have found on Google Books. I am still using Denis, the standard printed collection of Jubilees references, as a starting point, but I am also looking at the wider context in the source text, and frequently adding additional parallels. This means that I have to scan the Greek text I am transcribing and then read parts of Jubilees more carefully than I have before.
So when I found Cedrenus, an 11th century Byzantine chronicler, stating Isaac's age explicitly I decided to see whether Jubilees does the same. Cedrenus, by the way, asserts that Isaac was 25 at the Akedah. I presume he got this information from Josephus.