Inverse Square Law Calculator

The inverse square law states that a specified physical intensity is inversely proportional to the square of the distance from the source. Mathematically, the relationship is expressed as I_1 × d_1^2 = I_2 × d_2^2, where I represents intensity and d represents distance. If you need to find an unknown initial intensity (Intensity1), the rearrangement is Intensity1 = ((Distance2^2) / (Distance1^2)) × Intensity2. This conservation principle assumes energy radiates equally in all directions without absorption by the surrounding medium.

Imagine a light source emitting a specific brightness. Suppose we know that at a second distance (Distance2) of 4 meters, the measured intensity (Intensity2) is 10 lumens per square meter. If our initial distance of interest (Distance1) is 2 meters, we can calculate the initial intensity (Intensity1) as follows. First, square the distances: Distance2 squared is 16, and Distance1 squared is 4. Next, divide 16 by 4 to get a ratio of 4. Finally, multiply this ratio by Intensity2 (10), resulting in an initial intensity of 40 lumens per square meter.

Always ensure your distance measurements use the same unit (such as meters or feet) before performing calculations. Remember that doubling your distance from a source does not merely cut the intensity in half; it reduces it to one-fourth because of the squared relationship. Keep in mind that real-world measurements may deviate slightly from theoretical calculations due to environmental scattering, reflection, or atmospheric absorption.