📡 Electromagnetic Waves & Radiometry
Inverse Square Law & Path Loss Calculator
Compute geometric wave intensity drop-off ($I_2 = I_1 \left(\frac{d_1}{d_2}\right)^2$), Free Space Path Loss ($\text{FSPL}$ in dB), optical illuminance (lux), and radiological dose attenuation.
💡 Studio Light (1000 lux at 1m)
☢️ Gamma Source (50 mR/hr)
📡 RF Antenna (100 W/m²)
☀️ Sun at Jupiter (5.2 AU)
Source & Distance
Received Intensity at Target Distance (I₂)
40.00 Lux
Intensity Ratio
4.00%
1 / 25th
Decibel Loss
-13.98 dB
20 log10(d1/d2)
Distance Factor
5.00× Further
d2 / d1
💡 Inverse Square Calculation:
$$I_2 = I_1 \times \left(\frac{d_1}{d_2}\right)^2 = 1000 \times \left(\frac{1}{5}\right)^2 = \frac{1000}{25} = 40.0\text{ Lux}$$
The Physical Law of Inverse Squares
Because a point source radiates spherically into $4\pi r^2$ surface area, flux density drops quadratically:
- Universal Equation: $$I_2 = I_1 \left(\frac{d_1}{d_2}\right)^2$$
- Decibel Path Loss: $$\Delta L_{\text{dB}} = 10 \log_{10}\left(\frac{I_2}{I_1}\right) = 20 \log_{10}\left(\frac{d_1}{d_2}\right)$$
- Doubling Distance: Moving twice as far away ($2\times$) reduces intensity to exactly 25% (1/4th), or a -6.02 dB drop.