Approximately how much x-ray to gamma radiation penetrates the earth's current atmosphere? I am a science fiction writer with an undergrad level of understanding in this particular area. I am trying to figure out how the changes in the atmosphere will affect the higher end of the radiation spectrum. I know that as of now the amount of x-ray to gamma radiation that the atmosphere allows through is minute, but as the damage to the atmosphere continues that amount is surely going to change. I am particularly interested in specific numbers related to damage to the human body. I know the amount of radiation that is harmful to fatal to humans but I am looking at a future situation.(I know there are equations out there to calculate electron volts to rad or sievert but the math is a bit beyond me.{I also know that electron volts is a measurement of energy where sievert or rad is a measurement of energy per mass}). The current level of radiation on the higher end of the spectrum that penetrates the atmosphere would give me a good starting point, but the more information the better. 
Basically, would it be possible for the atmosphere to decay to the amount that the sun's gamma rays would harm humans, or would the environmental damage decimate life before that could even occur?
(Most of this is completely theoretical, but if you could give specific current numbers that would be very helpful)
P.S. If I am completely off base with my understanding of this topic please be kind in your corrections; I am totally open to constructive criticism and I am ultimately here for knowledge.
 A: You can get a pretty good idea of the answer by looking at the radiation exposure that people get when flying on transcontinental planes: they might be at an altitude of 10,000 to 12,000 m, and thus they are experiencing significantly less shielding than on earth (at 10 km, the pressure is about 26% of the pressure at ground level).
It is estimated that flying from New York to LA exposes you to about 40 uSv (see this beautiful chart) . Assuming the flight takes 6 hours, that would mean that an entire year at that altitude gives you a dose of 58 mSv - approximately the dose permitted for "US radiation workers" (that is, considered to be low risk of causing problems).
The problem is much worse near the poles, because charged cosmic ray particles (mostly from the Sun) are very effectively shielded by the Earth's magnetic field - except that they can "thread their way to Earth" along the magnetic field lines. This is of course the origin of the Northern lights.
By the time the atmosphere is so depleted that the atmospheric attenuation is a problem, people will choke from lack of oxygen before dying of radiation exposure: but if the magnetic field should fail, we're all going to be in trouble because of the much higher radiation levels that would penetrate (charged particles - which is not what your question was about).
To calibrate you - the solar wind at 1 AU is about $3\times 10^8$ particles/cm$^2$/s - mostly protons. The energy is roughly 1.5 erg/cm$^2$/sec (same source, table 2) or 1.5 mJ/m$^2$/s. The effect of this is nicely summarized in this article that shows that 6 months in the ISS gives you about 75 mSv of radiation dose - or 150 mSv per year. That's starting to be a little high... and that is in the protective capsule of the ISS which will stop quite a few of the incident rays.
In short - if you want a good story, make the earth's magnetic field fail...
A: The cosmic radiation that penetrates to the troposphere is secondary to high energy particle interactions with the upper layers of the atmosphere. That means that some highly energetic particle hits the upper atmosphere and generates a spray of particles. Most of those are very short lived and decay away in a few meters at most, but the muons (with their low mass, long lifetime, and relatively low interaction cross-section) are able to travel for kilometers or even tens of kilometers before decaying or undergoing another energetic interaction, so a non-trivial fraction of these make it to the ground or spawn tertiary radiation that does.
However, the particles that initiate these events must be orders of magnitude more energetic that either the direct ionizing photons from the sun or the solar wind.1 They originate in energetic astrophysical events elsewhere in the galaxy or even from extra-galactic sources.
The threat to the habitability of the planet from solar activity doesn't come from direct or secondary exposure of the biosphere to ionization, it comes from the ability of solar sources to remove atoms and molecules in the upper-most regions of the atmosphere from Earth orbit—from dribbling the atmosphere away into inter-planetary space. Earth escape velocity only corresponds to about $9 \,\mathrm{eV}$ of kinetic energy for a nitrogen atom which is well within the range that can be supplied by solar activity. Human life on the surface will require atmospheric support before direct ionization from solar sources is a threat.

1 The mean energy of secondary muons making it to sea level is around $1\,\mathrm{GeV}/c^2$ meaning that they have a Lorentz factor of 7–8: they are highly relativistic. Solar wind protons are not relativistic (meaning their kinetic energy is much less than $1\,\mathrm{GeV}/c^2$, and the energy of ionizing solar photons are typically measured in $\mathrm{keV}/c^2$).
