Botswana is about 2,597 times bigger than American Samoa.

American Samoa is approximately 224 sq km, while Botswana is approximately 581,730 sq km, making Botswana 259,601% larger than American Samoa. Meanwhile, the population of American Samoa is ~45,443 people (2.3 million more people live in Botswana).
Tip: This to-scale comparison of American Samoa vs. Botswana uses the Mercator projection, which distorts the size of regions near the poles.