# Inverse square law - Radiation protection widget

**Published:** Mar 16, 2024

For formal radiation safety advice, visit our **Radiation Protection Adviser (RPA)** services page.

The inverse square law in radiation protection, and in other related physics subjects, is fairly simple. It can be explained / taught in various ways. One way is to simply state the following (which works for accumulated dose and dose rate depending on what you are intending to measure / observe).

- Double the distance will quarter the dose (or dose rate).
- Half the distance will lead to four times the dose (or dose rate).

We have spent years saying this to delegates. Take a look at the widget below.

#### Inverse square law radiation protection widget

Please have a play (**move the slider**) - each time you load / reload the page the widget will pick a new starting dose rate.

#### Discussion

Using the widget you can see that:

\[\text{ Dose (or Dose rate)}\propto \frac{1}{r^{2}}\]

where ** r** is the distance from the source. This can be expanded to consider two dose rates at two different distances in the following form:

\[\frac{D_{1}}{D_{2}}=\frac{r_{2}^{2}}{r_{1}^{2}}\]

Here **D _{1}** is dose rate at distance

**r**and

_{1}**D**is dose rate at

_{2}**r**(some greater distance from the source). Mathematically these expressions work, and for gamma / x-ray point sources they can be observed by measurement.

_{2}However, in a training environment there is little opportunity to take real measurements. This is where the radiation protection widget comes in. It allows the training delegate (or visitor to our site) to simulate what they would observe if they were taking real measurements. This interaction helps to reinforce the concept!

Look closely at the graphic as you move the slider and increase the distance. You see the edge of a sphere moving outwards (**4Πr ^{2}**). You can also see a volume of material (air in this case) represented which grows (or shrinks if you move the other way).

Also note that intensity of the radiation field at a distance is represented by the leading edge which changes from dark red very close to the source to light translucent pink at the furthest extent. In addition, note the real time calculation being performed at each distance and the resulting dose rate. The attenuation (of the dose rate at 1m) can be clearly seen as you move away from the source.