A "GPS" will not add elevation gain/loss to your total distance traveled. That's a pretty common misconception and why I pointed it out here.

Estimates of satellite heights can be off a lot so you just can't use those to determine your elevation. Some GPS units have a built-in altimeter that increases accuracy but those readings can lose accuracy if a weather front changes the atmospheric pressure quickly.

And elevation gain/loss measurements are given separately so you have do the math yourself to calculate that part of the equation.
_________________________
--

"You want to go where?"