District of Columbia is about 581 times smaller than Kentucky.

Kentucky is approximately 102,896 sq km, while District of Columbia is approximately 177 sq km, making District of Columbia 0.17% the size of Kentucky. Meanwhile, the population of Kentucky is ~4.3 million people (3.7 million fewer people live in District of Columbia).
Tip: This to-scale comparison of Kentucky vs. District of Columbia uses the Mercator projection, which distorts the size of regions near the poles.