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 ≈ 0.00694A 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 lumensWhat 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) / r²Where:
- 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 NRelated Tools:
