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An X-ray for knee pain. A CT scan for a head injury. Mammograms every other year, starting at age 50. Over a typical lifetime of radiation exposure from medical tests, a person can start to wonder: How much is too much?

There’s no formula for answering that, experts say, in part because the health effects of radiation don’t add up in a linear way. And while massive doses of radiation are known to be harmful, the small doses used in routine tests are usually safe, especially compared with other health-care choices people make without thinking twice.

“Radiation does have some risk,” says Russ Ritenour, a medical physicist at the Medical University of South Carolina in Charleston. “But it is important for medicine. And in most cases, the risk is quite small compared to the risk of taking too much Advil over your life and other things like that.”

Ionizing radiation — the type that can damage cells — is a daily fact of life even for people who never go to the doctor. Rocks and soil contain radioactive materials, which also appear in our food, our bones and the air we breathe. Cosmic rays barrage us with radiation from space, with higher doses at altitude and on airplanes.

Overall, a person in the United States gets an annual average of about 3 millisieverts (mSv) of background radiation. (Millisieverts are units that measure radiation absorbed by our bodies.)

Added exposure, totaling another 3 mSV each year for the average American, comes from such man-made sources as power plants that run on coal and nuclear fuel, and consumer products including TVs and computer screens. But most of the extra radiation we get comes from X-rays and CT scans, Ritenour says.

Most routine diagnostic tests emit extremely small amounts of radiation. A patient will get about 0.001 mSv from an arm X-ray, 0.01 mSv from a from a panoramic dental X-ray, 0.1 mSv from a chest X-ray and 0.4 mSv from a mammogram, according to Harvard Medical School. (Those estimates vary somewhat, depending on the source and on the specific device used, the size of the patient and other factors.)

CT scans, which take multiple X-rays to create cross-sectional images, deliver higher doses: 7 mSv for a chest CT, and 12 mSV for a full-body scan, according to the National Cancer Institute. Studies have found doses of 25 mSv or more from a PET/CT, an imaging test that requires ingesting a radioactive substance.

With the increasing availability and affordability of imaging technologies, people are getting more tests than they used to. Today, Americans receive more than 85 million CT scans each year, compared with 3 million per year in the 1980s.

Many of those tests may be excessive, argue some researchers, who have been trying to quantify the risks of our increasing use of ionizing radiation in medical imaging. A 2009 study by scientists at the National Cancer Institute estimated that 2 percent — or about 29,000 — of the 1.7 million cancers diagnosed in the United States in 2007 were caused by CT scans. In a 2004 study, researchers estimated that a 45-year-old who planned to get 30 annual full-body CT exams would have a nearly 2 percent lifetime risk of dying of cancer. Other studies are underway to clarify risks, including in children.

But evaluating an individual’s chances of experiencing a bad outcome from any given test or a combination of tests is tricky. Some of the most definitive data on radiation’s health effects come from long-term studies of tens of thousands of people who survived the atomic bombings of Hiroshima and Nagasaki in 1945. Sudden exposure to 1,000 mSv, those studies have found, increased the risk of getting cancer by 42 percent and increased the risk of dying of cancer by 5 percent.

Risks of secondary cancers also rise with the high doses of radiation used in some cancer treatment — a trade-off that often makes sense because doing nothing would be even riskier.

Evidence is murkier about health consequences from lower doses. The Food and Drug Administration estimates that 10 mSv of radiation, an amount typical for a CT of the abdomen, increases lifetime cancer risk by 1 in 2,000. But that calculation assumes that risks are proportional to dose, which has not been proved. Below 10 mSv, there is not enough good data to draw clear conclusions.

There is also no absolute number of scans that constitute a tipping point for health,Ritenour says, in part because our bodies have repair mechanisms that can fix cells damaged by radiation. So while every scan adds to the chances that a problem will occur, radiation doesn’t build up in the body. And damage doesn’t accumulate like water poured into a glass. Theoretically, he adds, 10 mammograms in one day would be riskier than one mammogram a year for 10 years.

“All you can really say is that there’s very little chance a problem can happen” at low doses, says Ritenour, who often consults with patients who have questions about radiation. “It is very unsatisfying in a way. You can’t say, ‘You will definitely have no problems.’ ’’

Although health risks from most imaging tests are extremely small, fear can be hard for people to rationalize away. There is a one-in-a-million chance of getting cancer from a chest X-ray, Ritenour says, the same tiny chance of getting cancer from toxins in peanut butter.

Making decisions about diagnostic tests ultimately requires comparing their potential benefits with their potential harms. That balance can be easy to measure if someone has a broken leg or a bullet fragment lodged in their body. But decisions become more nuanced for tests such as mammograms, which catch breast cancers in some women but also produce false alarms that cause unnecessary anxiety and follow-up testing that entails even more radiation. Given the trade-offs, the U.S. Preventive Services Task Force offers evidenced-based advice about many screening tests, and those guidelines can be helpful starting points for conversations with your doctor.

Online calculators can also offer food for thought. When I entered my location, estimated miles traveled by airplane and other information into a tool maintained by the Nuclear Regulatory Commission, I learned that I absorb an estimated 318 millirems, or 3.18 mSv, of radiation each year. Each millirem, according to this government agency, equates to a 1.2-minute reduction in life span, the same accrued from eating 10 extra calories (assuming I’m overweight) or crossing the street three times. In other words, I am likely to die 4½ hours sooner than I would if I could avoid radiation altogether.

While some researchers work to better understand and communicate the risks of radiation, others are refining technologies and procedures, adds Louis Wagner, a diagnostic medical physicist at McGovern Medical School at the University of Texas Health Science Center at Houston. And the field has come a long way.

For example, after studies found an elevated risk of breast cancer among women who had received X-rays for childhood scoliosis, experts say, many health centers switched from taking images from the front of the body to taking images from behind to reduce the cancer risk.

Technicians have made mistakes, such as using higher doses of radiation than needed during scans, and some mistakes have led to expensive legal cases, Wagner says. But those cases are rare. And most machines are now equipped with safety features to avoid overexposure.

“The profession has sought to make use of radiation very, very beneficial to patients with minimal and, I believe, unrecognizable risks,” Wagner says. “I want patients to know the medical profession is avidly pursuing better ways to use radiation to increase the benefits-to-risks ratio. I think good progress is being made.”