At which battle did Alexander the Great defeat the Persian king Darius III for the final time?

Alexander the Great defeated the Persian king Darius III for the final time at the Battle of Gaugamela.

Fought in 331 BC in northern Mesopotamia, Gaugamela was the second and final battle between Alexander and Darius. Alexander’s Macedonian and allied Greek forces were heavily outnumbered, but his controlled advance and sudden cavalry attack created a gap in the Persian line. Darius fled when the battle turned against him, leaving the Persian army to collapse.

The victory opened the road to Babylon, Susa, and Persepolis and effectively destroyed the Achaemenid Empire’s ability to resist Alexander. Darius escaped eastward but was later murdered by the Persian satrap Bessus, so Gaugamela was his final battlefield defeat—not the moment of his death.

A common mix-up is the Battle of Issus in 333 BC, where Alexander defeated Darius earlier. Gaugamela is also sometimes called the Battle of Arbela, although the battlefield was near Gaugamela rather than directly at Arbela.