Inverse Square Law Calculator
Find how intensity changes with distance.
Many physical quantities spread out, falling off as the inverse square of distance.
How the Math Works
The Inverse Square Law Calculator uses the formula I₂ = I₁·(d₁ ÷ d₂)² to determine how light or wave intensity changes with distance. This equation shows that intensity (I) is inversely proportional to the square of the distance (d) from the source. When you double the distance from a light source, the intensity becomes one-fourth of its original value. The formula multiplies the initial intensity (I₁) by the square of the ratio between initial distance (d₁) and new distance (d₂) to calculate the resulting intensity (I₂).
Practical Applications
To use this calculator practically, input your starting intensity measurement and the distances involved in your scenario. For example, if you have a light source with 100 lux intensity at 2 meters, and want to know the intensity at 5 meters, enter I₁=100, d₁=2, and d₂=5. The calculator will compute I₂ = 100·(2÷5)² = 16 lux. This is essential for photographers adjusting exposure settings, engineers designing lighting systems, or physicists measuring radiation intensity at different distances from a source.
Day-to-Day Use
Understanding the inverse square law helps explain why car headlights appear dimmer the farther you are from them, or why sound from a speaker seems quieter when you move away. It's why street lights are spaced the way they are, ensuring adequate illumination without excessive energy use. The principle also explains why sunscreen protection is most critical close to the skin's surface, and why astronomers can calculate distances to stars using apparent brightness. Even everyday observations like why a campfire's warmth decreases rapidly as you move away relates to this fundamental physical law.
Worked example
100 units at 1 m → about 11.1 units at 3 m.
FAQ
What follows this law?
Light, sound, gravity and radiation from a point source.