What's my altitude?

My regular walk to the Beverly Hills Public Library seems like a
gradual uphill climb -- nothing on par with San Francisco, but a very
slight incline most or all of the way. As you might expect, the walk
back home is a breeze. According to my handheld Garmin GPS, it's
exactly 1.75 miles each way. But I wondered exactly how much height I
was achieving on my walk, in addition to the distance. How can I tell?
Can a handheld device measure something like that? It could be several
feet or, I suppose, it could be more. I have utterly no idea. Any
ideas?