Inverse Square Law Calculator
Calculate intensity changes with distance for light, gravity, sound, and electromagnetic radiation
Calculate Inverse Square Law
Intensity or force at the first distance point
Distance from source to first measurement point
Intensity or force at the second distance point
Distance from source to second measurement point
Inverse Square Law Results
Formula used: I₁/I₂ = r₂²/r₁²
Physical principle: Intensity is inversely proportional to the square of distance from point source
Physics Analysis
Solar Irradiance Example
Earth to Mars Comparison
Solar irradiance at Earth: 1361 W/m²
Earth distance: 1.0 AU
Mars distance: 1.53 AU
Formula: I₂ = I₁ × (r₁/r₂)²
Calculation
I₂ = 1361 × (1.0/1.53)²
I₂ = 1361 × 0.427
I₂ = 581.4 W/m²
Mars receives ~43% of Earth's solar energy
Physical Applications
Light & Radiation
Illuminance, irradiance
Point light sources, stars
Electric Field
Coulomb's law
Point charges
Gravitational Force
Newton's law
Planetary masses
Sound Waves
Acoustic intensity
Point sources
Physics Tips
Works for radial propagation from point sources
Total power/flux remains constant
Surface area increases as 4πr²
Double distance = quarter intensity
Understanding the Inverse Square Law
What is the Inverse Square Law?
The inverse square law describes how physical quantities that propagate radially from point sources diminish with distance. The intensity decreases proportionally to the square of the distance from the source, following the mathematical relationship I ∝ 1/r².
Why Does This Happen?
- •Energy spreads over spherical surfaces
- •Surface area increases as 4πr²
- •Total flux remains constant
- •Intensity per unit area decreases
Mathematical Formula
I₁/I₂ = r₂²/r₁²
I₁ × r₁² = I₂ × r₂² = constant
- I₁, I₂: Intensities at distances r₁ and r₂
- r₁, r₂: Distances from point source
- Constant: Total flux through sphere
Geometric Dilution: As distance doubles, intensity becomes 1/4 of original value
Real-World Examples
🌟 Stellar Light
Star brightness decreases with distance squared. A star at 2 light-years appears 1/4 as bright as the same star at 1 light-year.
🔊 Sound Intensity
Moving away from a speaker doubles the distance, sound intensity drops to 1/4, equivalent to about 6 dB reduction.
⚡ Electric Field
Electric field strength from a point charge follows Coulomb's law: E ∝ 1/r², where r is distance from the charge.