# Distance-Intensity Calculation

I1/ I2 = D22/ D12

 Where: I1 = Intensity 1 at D1 I2 = Intensity 2 at D2 D1 = Distance 1 from source D2 = Distance 2 from source

## Example Calculation 1

The intensity of radiation is 530 R/h at 5 feet away from a source. What is the intensity of the radiation at 10 feet?

Rework the equation to solve for the intensity at distance 2
I2 = I1 x D12 / D22

Plug in the known values
I2 = 530R/h x (5ft)2 / (10ft)2

Solve for I 2
I2 = 132.5 R/h

In this instance the distance has been doubled and the intensity at that point has decreased by a factor of four.

## Example Calculation 2

A source is producing an intensity of 456 R/h at one foot from the source. What would be the distance in feet to the 100, 5, and 2 mR/h boundaries.

Convert R/hour to mR/hour

456R/h x 1000 = 456,000 mR/h

Rework the equation to solve for D2

$D_{2}=\sqrt{\frac{I_{1}D_{1}^{2}}{I_{2}}}$

Plug in the known values and solve

$D_{2}=\sqrt{\frac{456,000mR/h \times (1ft)^{2}}{100mR/h}}$

D2= 67.5 feet

Using this equation the 100mR/h boundary would be at 68 feet, the 5mR/h boundary would be at 301.99 feet, and the 2mR/h boundary would be at 477.5 feet. Sources are seldom operated for an entire hour, and collimators are often used which reduce these distances considerably.