Modern mammography machines use low radiation doses to produce breast x-rays that are high in image quality. On average the total dose for a typical mammogram with 2 views of each breast is about 0.4 mSv (a mSv is a measure of radiation dose). Older mammography units delivered higher doses, and led to concerns about radiation risks. These older machines are no longer used.
To put dose into perspective, people in the US are normally exposed to an average of about 3 mSv of radiation each year just from their natural surroundings (this is called background radiation). The dose of radiation that a woman gets during a screening mammogram of both breasts is about the same amount of radiation she would average from her natural surroundings over about 7 weeks.
Strict guidelines ensure that mammography equipment is safe and uses the lowest dose of radiation possible. Many people are concerned about the exposure to x-rays, but the level of radiation from a mammogram today does not significantly increase the breast cancer risk for a woman who gets regular mammograms. In theory, repeated x-rays might have the potential to cause cancer, but the benefits of mammography outweigh any possible harm from the radiation exposure.
If there is any chance you are pregnant, let your health care provider and x-ray technologist know. Although the risk to the fetus is likely to be very small, screening mammograms aren’t routinely done in pregnant women.
http://www.cancer.org/treatment/understandingyourdiagnosis/examsandtestdescriptions/mammogramsandotherbreastimagingprocedures/mammograms-and-other-breast-imaging-procedures-mamm-radiation