How many cores in my GPU?

Question

How can you tell how many cores are available in any given GPU?
I would prefer a Windows/UI based answer, but API (DirectX?) is also nice to know.

Solution

No such API. Even term "core", applied to graphics hardware cannot be defined in a universal way: different vendors have very different architectures (even on desktop platforms). So, we can have 384 "CUDA cores" in nVidia GPU, 1024 "shader ALUs" in AMD GPU and 20 "blocks" in Intel GPU of the same price/performance/transistor count category. Sometimes you don't even have a dedicated GPU. So, it does not make sense to compare those numbers.