What wire size for a 125 ft run to a shed on a 30 amp breaker?
Table 310.16 says #10 copper handles 30 amps at 75 degrees C. But at 125 ft, voltage drop is the real sizing driver, and the smart answer is #8 copper.
The voltage drop math
On a 240V feeder pulling the full 30 amps through #10 copper at 125 ft, drop is about 9.3 volts, which is 3.9 percent. On a 120V circuit the same run doubles to nearly 8 percent, which is unusable. The NEC informational notes at 210.19 and 215.2 recommend keeping a feeder to 3 percent and the total to the farthest outlet at 5 percent. Stepping up to #8 copper brings the 240V full load drop to about 5.8 volts, or 2.4 percent, comfortably inside the recommendation. If the shed will run a welder, compressor, or EV charger near the full 30 amps for sustained periods, #8 is not optional in any practical sense.
Detached building rules
A shed fed from the house follows 225.30: one feeder or branch circuit to the structure, with limited exceptions. At the shed you need a disconnecting means per 225.31, located at a readily accessible location nearest the point of entrance per 225.32. If the feeder supplies more than one branch circuit, the shed needs a grounding electrode system connected per 250.32(A), so plan on driving rods at the shed. Run four wires: two hots, neutral, and equipment grounding conductor, and keep neutral and ground separated at the shed panel per 250.32(B)(1).
Burial and materials
Direct burial UF cable needs 24 in of cover for this circuit per Table 300.5, while conductors in PVC need 18 in. Many installers trench once and lay 3/4 in or 1 in PVC with THWN so the shed can be upgraded later by repulling; at 125 ft that future flexibility is worth the conduit cost. Size the equipment grounding conductor per Table 250.122, #10 copper for a 30 amp device, and if you upsize the hots for voltage drop, upsize the EGC proportionally per 250.122(B).