Too soon for baby kicks?

This is a question for the mommas and mommy to be's out there. When did you start to feel your baby actually kicking you? I am currently 20 weeks and 4 days, and I am pretty darn sure I have been feeling the baby "kick" for about a week or two now. My fiance can feel it too when he puts his hand on my belly. Isn't it a bit soon to be feeling it so much? It mostly happens at night when I lay down or when I'm sitting down relaxing after a meal. Is this normal at 20 weeks?