Closer than most people guess: Australia (7,706,009 km² km²) is only about 22%% larger than United States (9,439,424 km² km²).
Australia sits in Oceania, United States in North America. On the old Mercator map the latitude gap distorted how large each felt beside the other; at true size the answer is simply 1.2×.
The old map muddied it further: Mercator inflates Australia about 1.2× and United States about 2×, so on a Mercator-style map this pair appears 2× apart instead of the true 1.2×.
Australia fits 1× into United States.