South Dakota is about 1.3 times smaller than Wyoming.

Wyoming is approximately 251,489 sq km, while South Dakota is approximately 196,540 sq km, making South Dakota 78.15% the size of Wyoming. Meanwhile, the population of Wyoming is ~563,626 people (250,554 more people live in South Dakota).
Tip: This to-scale comparison of Wyoming vs. South Dakota uses the Mercator projection, which distorts the size of regions near the poles.