Inverse Square Law Calculator — Light, Sound & Radiation
Find how the intensity of light, sound, radiation or any point-source field changes as distance changes. Enter the intensity at a known distance and the new distance to get the result instantly.
Physical quantity
Intensity at the new distance, scaled by (r₁/r₂)²
- 1
Distance ratio r₁ ÷ r₂
1 ÷ 2 = 0.5 - 2
Ratio squared (r₁/r₂)²
0.5² = 0.25 - 3
Intensity at r₂
I₁ × (r₁/r₂)² = 100 × 0.25 = 25Intensity falls with the square of distance from a point source.
How does this calculator work?
The inverse square law states I₂ = I₁ × (r₁/r₂)² — intensity falls as the square of distance from a point source. Doubling distance quarters intensity; tripling it reduces it to one-ninth. Applies to light, sound, gravity, radiation and electric fields from compact sources in free space.
Formula
How this is calculated
The inverse square law describes how the intensity of any physical quantity radiated from a point source in three-dimensional space decreases in proportion to the square of the distance from the source. As a sphere of radius r has surface area 4πr², the same total power is spread over a larger and larger area, so intensity (power per unit area) falls as 1/r². Doubling the distance reduces intensity to one-quarter; tripling it reduces intensity to one-ninth.
The law applies to many phenomena: illuminance from a point light source (lux), sound intensity from a point source in free field (W/m²), gravitational field strength, electric field intensity, and ionising radiation flux from a compact source. In practice, real sources are rarely perfect points — extended sources, reflective surfaces, wave diffraction and atmospheric absorption all introduce deviations — so the law is most accurate in the far-field (distance much larger than source size) under free-space conditions with no reflections.
For sound, the inverse square law applies to intensity (W/m²). To convert to decibels: L₂ = L₁ − 20·log₁₀(r₂/r₁). For light, the law governs illuminance (lux) from a point source but not luminance of an extended surface. For radiation shielding, distance is one of three key protections (alongside time and shielding material).
Frequently asked questions
Energy from a point source spreads over the surface of an expanding sphere. Surface area grows as r², so the same energy is divided over r² times more area as distance doubles — hence intensity ∝ 1/r².
Yes, for a point source in free field (open air, no reflections). In a reverberant indoor space reflections add energy, so the actual drop is less steep. The rule-of-thumb for a free-field point source is that doubling the distance drops the sound pressure level by about 6 dB.
Yes — as long as both distances use the same unit and both intensities use the same unit, the ratio is dimensionless and the formula applies. The calculator does not assume SI units; metres, feet, kilometres, etc. all work.
Also known as
TG we-Calculate Editorial Team. (2026). Inverse Square Law Calculator — Light, Sound & Radiation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/inverse-square-law-calculator
TG we-Calculate Editorial Team. "Inverse Square Law Calculator — Light, Sound & Radiation." TG we-Calculate. 2026. https://we-calculate.com/calculator/inverse-square-law-calculator.
TG we-Calculate Editorial Team, "Inverse Square Law Calculator — Light, Sound & Radiation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/inverse-square-law-calculator
@misc{wecalculate_inverse_square_law_calculator, title = {Inverse Square Law Calculator — Light, Sound & Radiation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/inverse-square-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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