The township is drained by the Grand River, which crosses from the southern border to the northwest corner.

A portion of Meridian-Baseline State Park is located within Rives Township.

As of the census[1] of 2000, there were 4,725 people, 1,677 households, and 1,319 families residing in the township.

There were 1,745 housing units at an average density of 48.6 per square mile (18.8/km2).

16.2% of all households were made up of individuals, and 5.6% had someone living alone who was 65 years of age or older.