40 amps: the short answer
At 240 V single-phase over 100 feet,
a 40 amps copper load needs 8 AWG (about 2.55% drop). Both checks land on the same size: copper 8 AWG carries 40 amps at 75 °C and stays within the 3% voltage-drop target over 100 feet (about 2.55%).
Before you pull wire
This recommendation covers ampacity and voltage drop only, for copper at
75 °C. It does not apply ambient-temperature or conductor-count
derating, the 125% factor for continuous loads, conduit fill, or terminal ratings — any of
which can push the size up. Aluminum of the same load typically goes up one or two sizes.
Always confirm with a licensed electrician and your local code (AHJ).
Ampacity per NEC 310.16; voltage drop per NEC Ch.9 Table 8 (75 °C copper).