Radiation in the form of a fast-moving particle is dangerous to life forms like us because each particle can ionize a lot of molecules. When a radioactive nucleus decays, the alpha, beta, or gamma particle released generally has an energy of hundreds of keV or even MeV. Ionizing a molecule takes only a few eV, so a fast-moving particle can easily ionize thousands of molecules.

Ionized molecules inside a cell are bad news because they change the chemistry, which can seriously affect how the cell behaves. A little radiation is generally fine; all of us receive some radiation exposure. A lot of radiation is generally to be avoided, however.

From a biological perspective, it makes most sense to talk about radiation from the point of view of absorbed dose. This is the absorbed energy divided by the mass of the material that is exposed to the radiation.

absorbed dose (Gy) = absorbed energy (J) / mass (kg)

The SI unit for absorbed dose is the gray (Gy). A more commonly used unit is the rad, which is a hundredth of a gray.

1 rad = 0.01 gray

Different kinds of radiation have different levels of effectiveness when it comes to ionizing molecules in living tissue. The absorbed dose really needs to be corrected for this, and the correction is an easy one. Different types of radiation are measured relative to 200 keV x-rays, and assigned a multiplication factor known as the relative biological effectiveness (RBE) based on how effective they are relative to 200 keV x-rays. The biologically-equivalent dose is measured in rem, and is given by:

Biologically-equivalent dose (rem) = Absorbed dose (rad) x RBE

Different RBE values are given here: