Calculate Intensity Drop at Divergence

Calculator for the strength of spherical expanding signals, like light, radio and sound, at certain distances, with the inverse-square law. The signal expands as a spherical shell, the intensity decreases to the square of the distance. At twice the distance, the signal has one fourth of the strength. This is in theory, if the signal doesn't get reflected. Please enter both values of measuring point A and one value of measuring point B, the other value will be calculated.

The formula for the inverse-square law is: I₁ / I₂ = r₂² / r₁²
I is the intensity (strength), r is the radius Radius (distance).

Divergence

The declining signal strength at a spherical expansion. Theoretically, the signal range is infinite, at least for electromagnetic waves like light. Sound, in contrast, needs a medium like air to spread out. But even the strongest signal won't be measurable at a long enough distance.

Example: for a signal to reduce its intensity to a tenth, it takes 3.162 times the distance (square root of 10).

Divergence occurs in space, i.e., in three dimensions. The diverging signal, however, is only located in the outermost layer of the expanding sphere; this layer is a surface, i.e., two-dimensional. This applies, for example, to electromagnetic waves and impulses, which travel without loss. However, since in reality there is always a greater or lesser loss, the calculated value is theoretical. Electromagnetic rays can, of course, encounter shielding obstacles that disrupt their divergence.
One can also calculate in other dimensions. If the signal spreads in two dimensions, then the divergence is circular, and the outermost layer is one-dimensional. The strength then decreases linearly, so double the distance means half the strength. In a four-dimensional space, the outer layer would be three-dimensional, where double the distance would mean one-eighth the strength.

Measuring point A	distance:	strength:
Measuring point B	distance:	strength: