Double the distance from a point source and its intensity drops to a quarter, because the same energy spreads over four times the area. It applies to light bulbs, speakers, radiation sources and gravity.
How to use the Inverse Square Law Calculator
- Find
- Intensity I₁ at distance r₁
- Distance r₁
- Distance r₂
- Intensity I₂
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose what to find and enter the other values (in the same units of intensity).
Common mistakes to avoid
- Mixing units between fields.
- Using a rule outside the range where it applies.
- Expecting fun estimates to be exact predictions.
Inputs explained
| Field | What to enter |
|---|---|
| Find | Choose one: Intensity at the new distance, Distance for a given intensity |
| Intensity I₁ at distance r₁ | A number |
| Distance r₁ | Units: m, cm, mm, km, in, ft … |
| Distance r₂ | Units: m, cm, mm, km, in, ft … |
| Intensity I₂ | A number |
What each result means
- Intensity I₂ = [Intensity I₁ at distance r₁]×([Distance r₁]÷[Distance r₂])^2
- Distance r₂ = [Distance r₁]×sqrt([Intensity I₁ at distance r₁]÷[Intensity I₂])
Example values
How the main result changes when Intensity I₁ at distance r₁ changes and everything else stays at the example values above:
| Intensity I₁ at distance r₁ | Intensity I₂ |
|---|---|
| 50 | 12.5 |
| 75 | 18.75 |
| 100 | 25 |
| 125 | 31.25 |
| 150 | 37.5 |
| 200 | 50 |
Formula
I₁·r₁² = I₂·r₂²
Worked example
Inputs — Find: Intensity at the new distance; Intensity I₁ at distance r₁: 100; Distance r₁: 1 m; Distance r₂: 2 m.
Results — Intensity I₂ = 25; Change in level = -6.0206 dB.
Key terms
- Point source
- Source radiating equally in all directions.
Frequently asked questions
Why the square?
The surface area of a sphere grows with r².
Does it apply to lasers?
No – a collimated beam doesn't spread like a point source.
How does it apply to radiation safety?
Doubling your distance quarters the dose rate.
Is gravity an inverse-square force?
Yes, in Newton's theory.