I agree with Crystal, 100%, though I would add that context is important. If I say, "My arm hurts," we understand that I'm talking about the length from my shoulder to my wrist. If it was my hand, I would say, "My hand hurts," never "My arm hurts."
So when you're specifically talking about limbs, as in "I have two arms, two legs, and a head," we're referring to the shoulder til the ends of the fingertips (just like "leg" is referring to the hip til the ends of the toes). But if you're referencing something specifically about the appendage, it can mean shoulder to wrist. Another example, "I got a tattoo on my arm." We know they didn't get the tattoo on their hand. We don't count anything past the wrist as "arm" in these instances.