# Inverse Square Law Calculator

URL: https://speedycalculator.com/calculators/physics/inverse-square-law/
Last updated: 2026-10-30

> The inverse square law calculator finds how the intensity of light, sound, radiation or gravity changes with distance from a point source, solving for the new intensity or the distance.

## Inputs

- Find
- Intensity I₁ at distance r₁
- Distance r₁ (m, cm, mm, km, in, ft, yd, mi)
- Distance r₂ (m, cm, mm, km, in, ft, yd, mi)
- Intensity I₂

## Results

- Intensity I₂
- Distance r₂
- Change in level

## Formula

```
I₁·r₁² = I₂·r₂²
```

## Explanation

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

FieldWhat to enterFindChoose one: Intensity at the new distance, Distance for a given intensityIntensity I₁ at distance r₁A numberDistance r₁Units: m, cm, mm, km, in, ft …Distance r₂Units: m, cm, mm, km, in, ft …Intensity I₂A 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 r₁Intensity I₂5012.57518.751002512531.2515037.520050

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)