Inverse Square Law Calculator

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:

• I₁ is the intensity at distance r₁
• I₂ is the intensity at distance r₂
• r₁ and r₂ are the respective distances from 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 m

F₂ = 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:

• F is the force between two masses
• G is the gravitational constant
• m₁ and m₂ are the masses of the two objects
• r is the distance between their centers

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

Related Tools: