Rhode Island is about 9 times smaller than New Hampshire.

New Hampshire is approximately 23,227 sq km, while Rhode Island is approximately 2,706 sq km, making Rhode Island 11.65% the size of New Hampshire. Meanwhile, the population of New Hampshire is ~1.3 million people (263,903 fewer people live in Rhode Island).
Tip: This to-scale comparison of New Hampshire vs. Rhode Island uses the Mercator projection, which distorts the size of regions near the poles.