How to Use Inverse Square Law Calculator
The Inverse Square Law Calculator finds intensity or distance in three steps.
- Select the Solve Mode — Choose whether you want to find the new intensity at a different distance, or find the distance that gives a target intensity.
- Enter the Known Values — Provide the reference intensity I₁, the reference distance d₁, and the second distance or intensity. Any consistent units work (metres, feet, dB, lux, mW/cm², etc.).
- Read the Result — The Inverse Square Law Calculator instantly displays the unknown quantity and shows the ratio I₁/I₂ = (d₂/d₁)² so you can verify the calculation.
- Use the Comparison Table — Optionally enter a range of distances to see how intensity scales across the whole spectrum at a glance.
Formula & Theory — Inverse Square Law Calculator
The Inverse Square Law Calculator is built on the fundamental relationship:
I₁ / I₂ = (d₂ / d₁)²Rearranged to solve for the two most common unknowns:
I₂ = I₁ × (d₁ / d₂)² (find new intensity)
d₂ = d₁ × √(I₁ / I₂) (find new distance)| Symbol | Meaning | Unit |
|---|---|---|
| I₁ | Intensity at reference distance | lux, mW/cm², dB… |
| I₂ | Intensity at new distance | same as I₁ |
| d₁ | Reference distance | m, ft, … |
| d₂ | New distance | same as d₁ |
Decibel Form for Sound
For sound pressure level (SPL), the inverse square law becomes:
SPL₂ = SPL₁ − 20 × log₁₀(d₂ / d₁) [dB]Every doubling of distance reduces SPL by approximately 6 dB in free-field conditions.
Point Source Assumption
The inverse square law is exact only for ideal point sources with no reflections or absorption. Real-world environments (walls, atmospheric absorption, directional speakers) cause deviations; the calculator provides the free-field baseline.
Use Cases for Inverse Square Law Calculator
The Inverse Square Law Calculator is used wherever intensity decays with distance:
- Sound and acoustic engineering — Calculate how far a speaker must be placed to achieve a target SPL, or predict noise levels at different distances from a source.
- Stage and architectural lighting design — Find the illuminance (lux) at a given distance from a light fixture to meet lighting standards.
- Radiation safety — Estimate dose rate at an increased distance from an X-ray or gamma source to determine safe working distances.
- Photography and flash exposure — Determine how moving the flash changes exposure on subjects at different distances from the strobe.
- Astronomy — Relate a star’s luminosity to its apparent brightness (flux) at Earth’s distance using the same inverse-square principle.
- Physics education — Verify textbook inverse-square-law problems and build intuition for how rapidly intensity drops with distance.