@zeccano So basically it depends how much detail you want to go into what equation you use. Here is the simple equation for just the gravity and its effect on time dilation. That is good enough to understand the experiment I did but keep in mind if you want more accuracy then you would do a few things extra
1) calculate in the time dilation due to the slight velocity difference between the two clocks, this isnt hard but it also is a less significant part of the math and it works if its left off too, just not as accurately.
2) instead of modeling the mass of the earth as uniform (which is easier and usually good enough) you can actually measure the strength of gravity where you are. By doing so you can get really hyper accurate results, which are what most studies do.
In our case lets stick with the simpler and less accurate equation just so you can understand it.. it looks like this
\(t_0 = t_f \sqrt{1 - \frac{2GM}{rc^2}} } \)
If you want to see how to calculate an approximation for G at a particular altitude then you can use this:
https://www.vcalc.com/equation/?uuid=9eed23e3-ec77-11e5-9770-bc764e2038f2
Now just need to look up the height of the mountain I was on as well as my home's altitude where the control clock was set and we can get the numbers.