What R-value does a 2x4 wall have?

What R-value a 2x4 wall has depends on whether you mean just the cavity insulation or the whole assembly including framing, sheathing, drywall, and air films. A 2x4 wall is 3.5 inches deep. With standard R-13 fiberglass batts installed perfectly, the cavity itself is R-13, but the whole wall assembly including wood studs that are only R-4.4, plus exterior sheathing, drywall, and air films, typically averages only R-9 to R-11 whole-wall due to thermal bridging through studs every 16 inches. With high-density R-15 batts designed for 2x4 walls, the whole-wall is about R-11 to R-13. With closed-cell spray foam filling the 3.5 inch cavity at R-6.5 per inch, you get about R-22 cavity and about R-15 to R-17 whole-wall. If you add 1 inch of R-5 continuous exterior foam over the sheathing, you can bring a 2x4 wall up to R-18 to R-20 whole-wall, which is comparable to a standard 2x6 wall. Older 2x4 walls from the 1960s with no insulation have only R-3 to R-4 total. So a modern code-built 2x4 wall with R-13 batts is typically considered R-13 nominal but only R-10 effective.