At tree level, the magnetic moment of the electron, , is equal to 2 (this can be obtained from the Dirac equation). However, higher order corrections due to quantum fluctuations slightly change the value from 2.
The latest experimental measurement from Harvard gave:
This is a precision of 0.24 parts per billion!
A group calculated the order theoretical correction and got the following value:
A couple things to note: first, this is amazing theoretical precision. Second, it took a lot of work. The group had to calculate 12,672 diagrams! I am amazed that experimentalists can design experiments with such incredible exactness, and that the Standard Model (specifically QED) matches up this well with the experiment. If someone tries to tell you that the math behind theoretical particle physics is just “pie in the sky” that doesn’t really mean anything, point them to this measurement.
Here is the reference:
Aoyama, Tatsumi and Hayakawa, Masashi and Kinoshita, Toichiro and Nio, Makiko, "Tenth-Order QED Contribution to the Electron and an Improved Value of the Fine Structure Constant," Phys. Rev. Lett. 109 (2012)