The equipment grounding conductor is the fault-return path run with the circuit conductors: its job is to carry fault current long enough to trip the breaker. It is sized from the rating of the circuit’s overcurrent protective device per NEC Table 250.122, with ratings between rows rounding up to the next row exactly as 250.122(A) directs — a 45 A breaker uses the 60 A row, 10 AWG copper — and every answer exists in both a copper and an aluminum column.
The rule most charts skip is 250.122(B): when the ungrounded conductors are made larger than ampacity requires — long-run voltage drop being the classic reason — the EGC must grow by the same circular-mil area ratio, rounded up to the next standard size from Chapter 9 Table 8. A 40 A circuit upsized from 8 AWG to 6 AWG copper (ratio 1.589) pushes the table’s 10 AWG EGC to 8 AWG; without the rule, the fault-loop impedance of a long run could keep the breaker from tripping fast.
The EGC also has a box-fill identity: under NEC 314.16(B)(5), all equipment grounding conductors in a box together count as a single volume allowance based on the largest EGC present, and since the 2023 code each EGC beyond four adds a further quarter allowance — eight 12 AWG grounds count as two full allowances, 4.50 in³.