The Skechers fitness shoes Kim Kardashian tried to convince you to buy don’t actually work … not even a little bit … so says the federal government.

The Federal Trade Commission has determined Skechers made unfounded claims about its Shape-Ups shoes … pushed by hot-bodied spokespeople like Kim K and Brooke Burke.

According to the FTC, Skechers lied about clinical studies which the company said proved the shoes help people lose weight and strengthen muscles in the ass, legs and stomach.

In fact, Skechers has agreed to pay $40 million in settlement costs … and anyone who bought the shoes will be eligible for a refund.

Still, Skechers is reportedly disputing the FTC decision — and plans to conduct more research on the effects of the shoe.