A 40 amp breaker takes 8 AWG copper, and at this rating the kind of wire doesn't change the copper answer. In NM-B cable, which NEC 334.80(A) holds to its 60 °C rating, 8 AWG copper carries exactly 40 A, with nothing to spare. With THHN in conduit and 75 °C terminals the same wire is rated 50 A, but no smaller copper size qualifies: 10 AWG is listed at 35 A in the 75 °C column, and 240.4(D) limits it to a 30 A breaker anyway.
Aluminum is where the column decides. At 60 °C, 8 AWG aluminum is rated 35 A, 5 A under the breaker, so the 60 °C size is 6 AWG, rated 40 A. In the 75 °C column 8 AWG aluminum reaches 40 A and qualifies. Both aluminum sizes land exactly on the breaker rating, with no margin above it.
Cooking is the code's own 40 A case. NEC 210.19(C) sets a 40 A minimum branch-circuit rating for a household range of 8¾ kW or more, and the 2026 NEC's Annex D works an 8,000 VA range demand (Table 120.55, Column C; 2023: Table 220.55) out to 33 A and supplies it with 8 AWG copper on a 40 A circuit. Ranges are commonly put on 40 A or 50 A circuits, but only the 40 A figure is a code minimum; the nameplate and installation instructions (110.3(B)) set what a given range needs. A separate cooktop or wall oven also falls under 210.19(C), but the 40 A minimum is written for ranges. One cooktop or one oven is figured at its nameplate rating (Table 120.55 notes; 2023: Table 220.55, Note 5).
For loads sized at 125%, a 40 A circuit is the match for 32 A. The 2026 NEC treats EV charging as a continuous load (625.41; 2023: 625.41 and 625.42), and the breaker and wire for a continuous load are sized at 125% of it under 210.20(A) and 210.19(A)(1). An EV charger set to 32 A therefore needs 32 × 1.25 = 40 A, while one set to 40 A needs a 50 A circuit. A storage water heater of 120 gallons or less is sized the same way under 422.13, so a 40 A circuit covers one drawing up to 32 A, which is 7,680 W at 240 V.
Air conditioners and heat pumps are sized from their nameplate, not from a breaker rating. Under Article 440 the nameplate gives a minimum circuit ampacity (MCA) and the maximum rating of the breaker or fuse, often shown as MOP or MOCP (440.4(B)). The wire has to carry at least the MCA, which already includes the 125% that 440.32 applies to a motor-compressor, so it isn't added a second time. The breaker or fuse may not exceed the marked maximum (440.22(C)). For this equipment the electrician starts from those two nameplate figures rather than from the tables on this page.
Length moves the copper size only on longer runs. At 240 V and the full 40 A, 8 AWG copper drops 6.11 V over 100 feet, 2.55%, and reaches 3% at about 118 feet one way. At 150 feet it would drop 3.82%, so the length table moves both copper columns to 6 AWG, which brings the drop to 2.40%; at 200 feet it is 4 AWG. Aluminum at 75 °C runs out sooner: 8 AWG aluminum reaches 3% at about 71 feet, which is why the table gives 6 AWG from 75 feet. The table puts the whole 40 A at the far end. A charger drawing 32 A drops a fifth less, and on 8 AWG copper it stays within 3% to about 147 feet. The 3% figure comes from an NEC informational note and is a recommendation, not a requirement.