The **inverse square law calculator** is used to compute the **intensity** of a physical property is **inversely proportional** to the **square** of the distance from its source.

**Light intensity**from a**point source****Gravitational force**between two**masses****Sound intensity**from a**point source****Electric field strength**from a**point charge**

A light source has an intensity of **1000 lumens** at **1 meter**, the intensity at **2 meters** can be calculated as follows:

**Intensity at 2 meters** = (1000)/(2^2) = (1000)/(4) = 250 lumens.

## Inverse Square Law Calculator

Initial Intensity (I₁) | Initial Distance (r₁) | New Distance (r₂) | Calculated Intensity (I₂) |
---|---|---|---|

100 lumens | 1 m | 2 m | 25 lumens |

500 N | 2 m | 5 m | 80 N |

1000 dB | 3 m | 9 m | 111.11 dB |

200 V/m | 0.5 m | 1.5 m | 22.22 V/m |

50 W/m² | 4 m | 8 m | 12.5 W/m² |

1500 W/m² | 2 m | 6 m | 62.5 W/m² |

2500 N | 3 m | 9 m | 31.11 N |

300 J/m² | 1 m | 3 m | 33.33 J/m² |

8000 dB | 5 m | 10 m | 2000 dB |

1000 V/m | 1 m | 4 m | 62.5 V/m |

75 W/m² | 6 m | 12 m | 18.75 W/m² |

1200 N | 2 m | 8 m | 18.75 N |

5000 J/m² | 1.5 m | 3 m | 111.11 J/m² |

200 lumens | 1 m | 5 m | 8 lumens |

10,000 dB | 10 m | 20 m | 2500 dB |

## Inverse Square Law Formula

The **formula** for the inverse square law is:

**I₂ = I₁ * (r₁² / r₂²)**

Where:

I₁is theintensityat distancer₁I₂is theintensityat distancer₂r₁andr₂are therespective distancesfrom the source

If the **light intensity** at 2 meters from a bulb is **100 lumens**, the intensity at 4 meters would be:

I₂ = 100

(2² / 4²) = 100(4 / 16) =25 lumens

## How to Calculate Inverse Square Law

**Identify the known values:**Initial intensity (**I₁**), initial distance (**r₁**), and the new distance (**r₂**).**Apply the formula:**I₂ = I₁ * (r₁² / r₂²)**Solve for the unknown intensity (I₂)**

Calculate the **gravitational force** between two objects when their distance **doubles**.

Initial force (

F₁) =100 N,r₁=1 m,r₂=2 mF₂ = 100

(1² / 2²) = 100(1 / 4) =25 N

The **gravitational force** decreases to **25 N** when the distance **doubles**.

## What is the Inverse Square of 12?

The **inverse square** of a number is **1 divided** by the **square** of that number.

**Inverse square of 12 = 1 / 12² = 1 / 144 ≈ 0.00694**

A **light source** has an intensity of **1000 lumens** at 1 meter, its intensity at **12 meters** would be:

`I₁₂ = 1000 `*(1² / 12²) = 1000* (1 / 144) ≈ **6.94 lumens**

## What is the Inverse Square Force Law?

The **inverse square force law** applies to forces that **decrease** with the **square** of the distance, such as **gravity** and **electrostatic forces**.

**F = G ***(m₁* m₂) / r²

Where:

Fis theforcebetween two massesGis thegravitational constantm₁andm₂are themassesof the two objectsris thedistancebetween theircenters

Calculate the **gravitational force** between **Earth** (5.97 × 10²⁴ kg) and the **Moon** (7.34 × 10²² kg) at their **average distance** (3.84 × 10⁸ m).

`F = (6.67 × 10⁻¹¹) `*(5.97 × 10²⁴* 7.34 × 10²²) / (3.84 × 10⁸)² ≈ **1.98 × 10²⁰ N**

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