Inverse Square Law Calculator (Light, Sound & Radiation)
By Santaji GadepatilinUpdated November 3, 2026
Energy spreading out from a point source covers an area that grows with the square of distance, so its intensity falls as 1/d². This inverse square law calculator scales a measured intensity, illuminance, sound intensity or radiation dose rate from one distance to another and gives the change in decibels.
How to use the inverse square law calculator
Enter the intensity measured at distance 1 in any unit, then the two distances. The calculator returns the intensity at distance 2 in the same unit, the ratio as a percentage and the level change in decibels. To find how far away a target intensity occurs, enter I₂ and clear distance 2.
Inverse square law formula
I2 = I1 × (d1 ÷ d2)² · ΔL = 20 log10(d2 ÷ d1) dB
Example
A lamp gives 100 lux at 1 m. At 3 m:
- I₂ = 100 × (1 ÷ 3)² = 11.11 lux (11.11% of the original)
- Level change = 20 × log₁₀(3) = 9.54 dB
Intensity versus distance multiple
| Distance multiple | Remaining intensity | Drop in dB |
|---|---|---|
| 1.5 × | 44.44% | 3.52 dB |
| 2 × | 25.00% | 6.02 dB |
| 3 × | 11.11% | 9.54 dB |
| 4 × | 6.25% | 12.04 dB |
| 5 × | 4.00% | 13.98 dB |
| 10 × | 1.00% | 20.00 dB |
| 20 × | 0.25% | 26.02 dB |
| 50 × | 0.04% | 33.98 dB |
| 100 × | 0.01% | 40.00 dB |
Notes
- Decibels use 10 log₁₀ of an intensity ratio, which equals 20 log₁₀ of the distance ratio.
- The same 1/r² rule governs gravity and electric fields — see the gravitational force calculator.
Frequently asked questions
What is the inverse square law?
The intensity from a point source is inversely proportional to the square of the distance, I ∝ 1/d². Doubling the distance cuts the intensity to one quarter.
How many decibels does sound drop when distance doubles?
About 6 dB (20 × log₁₀ 2 = 6.02 dB) for a point source in free field. Indoors, reflections make the drop smaller.
How does the inverse square law apply to radiation safety?
Dose rate from a small gamma source falls as 1/d², so moving from 1 m to 2 m cuts exposure to 25%. Distance is one of the three basic protections, with time and shielding.
When does the inverse square law not apply?
Close to large sources (a line or area source), with focused beams such as lasers or spotlights, and where the medium absorbs energy (fog, water). A rule of thumb is that it holds beyond about five times the source's largest dimension.