New Hampshire is about 8 times smaller than South Dakota.

South Dakota is approximately 196,540 sq km, while New Hampshire is approximately 23,227 sq km, making New Hampshire 11.82% the size of South Dakota. Meanwhile, the population of South Dakota is ~814,180 people (502,290 more people live in New Hampshire).
Tip: This to-scale comparison of South Dakota vs. New Hampshire uses the Mercator projection, which distorts the size of regions near the poles.