Distance Attenuation Calculator

Distance attenuation describes how energy from an ideal point source spreads as it travels outward. In free space, the same emitted power is distributed over the surface of an ever-larger sphere. Because a sphere's area increases with the square of its radius, intensity decreases according to the inverse-square law. This calculator applies I2 = I1 × (d1 / d2)², where I1 is intensity measured at reference distance d1 and I2 is the predicted intensity at target distance d2. It also reports the corresponding distance ratio in decibels as 20 × log10(d2 / d1). Doubling the distance produces one quarter of the original intensity and approximately 6.0206 decibels of attenuation. Tripling distance produces one ninth of the intensity and about 9.5424 decibels of attenuation. Moving closer gives a negative loss value, representing gain relative to the reference location. The decibel expression uses a factor of twenty for distance because field amplitude falls inversely with distance while power intensity is proportional to amplitude squared. The equivalent power ratio calculation, 10 × log10(I1 / I2), gives the same result. The model is appropriate for an isotropic source radiating uniformly in unobstructed three-dimensional space. Common examples include approximate sound, light, radio, and radiation intensity away from a source when the observation distances are large compared with source dimensions. Actual transmitters and speakers are directional, and nearby measurements may occur in a near field where the simple law is not valid. Walls, terrain, reflections, absorption, scattering, atmospheric effects, and antenna gains can all change real measurements. Use the same length unit for both distance fields; meters are shown for clarity, but any matching unit gives the same ratio. Initial intensity must describe the value at the stated reference distance, not total source power. This calculator isolates geometric spreading and does not add material absorption or system losses. It is useful for quick link intuition, acoustic planning, optical estimates, and inverse-square homework checks. For compliance, exposure, communications, or safety decisions, use calibrated measurements and a domain-specific propagation model that includes the source pattern and environment.