Excuse me as my understanding of this level of physics is not my area of expertise. It is my hope someone will be able to satisfy me with an explanation.

 

According to Einstein's theory of relativity time slows down as you approach the speed of light relative to a stationary body. The protons in the LHC are traveling close to that velocity. So the accelerated protons will experience time differently to 'stationary' proton outside the accelerator.

So how long will pass for the accelerated proton in one of our 'stationary' seconds?

And is there a simple equation for calculating this effect?

Yes. The value is equal to one over the Gamov factor (in seconds). In this case, a good approximation for the Gamov factor is taking the energy of the protons and divide it by 1 GeV, the mass of a proton.