North Carolina is about 3.9 times smaller than Turkmenistan.

Turkmenistan is approximately 488,100 sq km, while North Carolina is approximately 126,161 sq km, making North Carolina 25.85% the size of Turkmenistan. Meanwhile, the population of Turkmenistan is ~5.6 million people (3.9 million more people live in North Carolina).
Tip: This to-scale comparison of Turkmenistan vs. North Carolina uses the Mercator projection, which distorts the size of regions near the poles.