Animated family movie “Rango” topped box offices with $38 million over the weekend, according to studio estimates yesterday — coming in at the low end of expectations as moviegoing remains sluggish since the start of 2011.

“Rango,” which features Johnny Depp as the voice of a colorful chameleon trying to bring law and order to a town in the old Wild West, had been estimated to bring in anywhere from $38 million to $42 million by distributor Paramount Pictures.

Elsewhere, Matt Damon thriller “The Adjustment Bureau” — also in its debut weekend in theaters — took in $21 million to land in the No. 2 spot.

Another newcomer, “Beastly,” which is a modern retelling of the classic tale “Beauty and the Beast,” took hold of No. 3 with $10.1 million.

Comedy “Hall Pass” and animated movie “Gnomeo & Juliet,” which held the No. 1 and No. 2 spots last weekend, respectively, fell out of the top 3 positions. “Hall Pass” dropped to No. 4 with $9 million, while “Gnomeo” landed at No. 5 with $6.9 million.