District of Columbia is about 637 times smaller than Louisiana.

Louisiana is approximately 112,825 sq km, while District of Columbia is approximately 177 sq km, making District of Columbia 0.16% the size of Louisiana. Meanwhile, the population of Louisiana is ~4.5 million people (3.9 million fewer people live in District of Columbia).
Tip: This to-scale comparison of Louisiana vs. District of Columbia uses the Mercator projection, which distorts the size of regions near the poles.