Inverse Square Law Calculator

The inverse square law describes a quantity that spreads from a point source through three-dimensional space. At distance r, the same emitted power is distributed over a spherical surface with area 4πr squared. Because that area grows with the square of distance, intensity equals source power divided by 4πr squared. Moving twice as far away spreads the energy over four times the area, reducing intensity to one quarter. Moving three times as far away reduces it to one ninth. This calculator evaluates absolute intensity at an initial and a final distance for an ideal isotropic source. It also calculates the final-to-initial ratio, which depends only on the distance ratio: final intensity divided by initial intensity equals initial distance squared divided by final distance squared. Source power cancels from that comparison. The displayed intensity uses watts per square meter when power is entered in watts and distance in meters, but the ratio is dimensionless. Many physical fields follow this geometry under suitable conditions. A bare lamp approximates inverse-square illumination when its dimensions are small relative to distance. Acoustic power from a compact source approximately follows it outdoors before reflections and atmospheric absorption become important. Radiation fluence from a localized emitter, gravitational field strength outside a spherical mass, and electric field magnitude from a point charge also contain inverse-square dependence, although their absolute formulas use different source quantities and constants. Real measurements often depart from the ideal result. Directional antennas, reflectors, lenses, walls, floors, and shielding redirect energy rather than spreading it uniformly. Sound can be absorbed by air and reflected by surfaces. Light can be attenuated by fog or scattering. A source that is physically large compared with the measurement distance cannot be treated as a point. In the near field of an antenna or acoustic radiator, wave behavior may be more complicated than simple spherical spreading. Use source power only when the quantity of interest truly spreads across a spherical area. For comparing measured intensity at two distances, the ratio remains useful even when absolute power is unknown. Keep both distances in the same unit. Distance is measured from the effective center of the source, not from an arbitrary enclosure edge. The calculator is therefore valuable for quick physics checks, sensor placement, lighting estimates, radiation planning, and classroom demonstrations, while detailed engineering work should include directionality, attenuation, boundaries, and applicable safety standards.