How to calculate the safe distance for a radiography

Updated July 20, 2017

The effects of electromagnetic radiation of the kind used in diagnostic radiography can build up in the human body over time, causing potentially cancerous damage to human DNA. Thus, maintaining a safe distance during radiographic treatments is critical to good workplace safety in any hospital. To calculate this distance, you should employ an equation known as the inverse square law for radiography. This relationship states that radiation exposure is inversely proportional to the square of distance. For example, doubling the distance between a person and a radiation source will cause radiation exposure to drop by a factor of four.

Consult the guidelines of your hospital to determine the permitted level of radiation intensity for the instrument you will be using. This figure could either be given as an intensity or as a total cumulative exposure. If the latter figure is used, divide the total cumulative exposure by the length of time you anticipate having to keep the instrument activated to calculate an intensity.

Consult the documentation of your instrument to find a value describing the radiation intensity of that instrument at a certain distance. The distance itself is not extremely important -- you simply need it as a reference point.

Note the inverse square law for radiography:

I_1/I_2 = (D_2/D_1)^2 = D_2^2/D_1^2

I_1 and D_1 are the respective intensity and distance at the reference point, and I_2 and D_2 are the respective intensity and distance at the second point you will be calculating. For your purposes, I_2 and D_2 will correspond to the intensity and distance at the minimum safe distance.

You are attempting to calculate the minimum safe distance (D_2), so rearrange the equation to solve for D_2:

D_2 = D_1 * (I_1/I_2)^.5

Plug in the reference point values for intensity and distance you got from the instrument's documentation for I_1 and D_1. Plug in the permitted level of radiation intensity as outlined by your hospital for I_2.

Solve for D_2. This is the minimum safe distance for your radiography instrument.


This article is not intended as a substitute for the protocols of your hospital or the guidance of its staff. Always consult hospital staff when unsure of how to safely operate a radiography instrument.

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About the Author

Brendan Conuel has been writing professionally since 2009. His first paper, “The CHilean Automatic Supernova sEarch (CHASE),” appeared in the physics research journal "AIP Conference Proceedings." Conuel holds a Bachelor of Arts in physics, astronomy, and religion from Wesleyan University.