Three strokes on a par 5 make an eagle, as do two on a par 4. A hole-in-one on a par 3 is also an eagle. The name describes the score relative to par, so the number of strokes changes with the hole.1
The name belongs to the same family as birdie. The USGA's historical explanation describes eagle as an extension of birdie for a score one stroke better. Its later terminology history records A. B. Smith and his companions claiming credit for the word.23
In standard Stableford scoring, an eagle earns four points when par is the target. The comparison uses the hole score after any applicable handicap strokes in a handicap competition. The committee can set a different target, so the points depend on the competition's conditions.4
A double eagle has a different meaning from simply doubling an eagle's two-stroke advantage. It means three under par on a hole, also called an albatross. The sequence is birdie at one under, eagle at two under, then albatross at three under.12