Since different radiation types have different biological effects for the same deposited energy, a corrective radiation weighting factor W, which is dependent on the radiation type and on the target tissue, is applied to convert the absorbed dose measured in the unit gray to determine the equivalent dose. The result is given the unit sievert.
The equivalent dose is calculated by multiplying the absorbed energy, averaged by mass over an organ or tissue of interest, by a radiation weighting factor appropriate to the type and energy of radiation. To obtain the equivalent dose for a mix of radiation types and energies, a sum is taken over all types of radiation energy dose.
where
: is the equivalent dose absorbed by tissue T,
: is the absorbed dose in tissue T by radiation type R and
: is the radiation weighting factor defined by regulation.
Thus for example, an absorbed dose of 1 Gy by alpha particles will lead to an equivalent dose of 20 Sv.
This may seem to be a paradox. It implies that the energy of the incident radiation field in joules has increased by a factor of 20, thereby violating the laws of conservation of energy. However, this is not the case. The sievert is used only to convey the fact that a gray of absorbed alpha particles would cause twenty times the biological effect of a gray of absorbed x-rays. It is this biological component that is being expressed when using sieverts rather than the actual energy delivered by the incident absorbed radiation.