How does the inverse square law calculator work?

The calculator uses the formula I₁ × D₁² = I₂ × D₂². Enter three values (intensity at distance 1, distance 1, intensity at distance 2, distance 2). The missing value is computed automatically.

What units are used in the inverse square law calculator?

You can use any consistent units: for intensity (µSv/h, lux, W/m², dB SPL) and distance (meters, feet, cm). The result respects your input units.

Does the calculator follow US NRC and WHO guidelines?

The calculation itself is pure physics. However, we provide reference tables based on US NRC (10 CFR 20), OSHA, IES, and WHO/ICRP recommendations so you can compare your results with safety limits.

Inverse square law calculator

Based on US NRC, OSHA, IES & WHO guidelines. Use the advanced calculator below: fill any three of the four intensity/distance fields, then press compute missing. Model year is for reference only. The graph updates automatically with reference values.

📡 I₁ (intensity at D₁)

📏 D₁ (reference distance)

⚡ I₂ (intensity at D₂)

📐 D₂ (new distance)

📅 Model year / revision (optional)

Fill in three fields and click “Compute missing”. I₂ will be calculated based on I₁, D₁, D₂.

📈 intensity vs distance (based on I₁,D₁) — reference curve

📘 Inverse square law: applied standards (USA + worldwide)

The inverse square law governs how intensity (radiation, sound, light) decreases with distance. Below are real-world tables derived from US NRC (10 CFR 20), WHO/ICRP, OSHA 29 CFR 1910.95, and IES lighting handbook. Use these to compare with your calculated I₂.

inverse square law calculator results shown above are in same units you enter (µSv/h, W/m², lux, dB …).
Model year 2024/2025/2026 reflects latest ICRP & NRC draft recommendations.
All values assume point source, no absorption or barriers.

☢️ Ionizing radiation: dose rate vs distance (point source, ¹³⁷Cs example)

Distance (m)	Relative intensity	Dose rate (µSv/h)*	US NRC / WHO guidance
0.5	4.00	400	exceeds public limit ( >20 µSv/h )
1.0 (ref)	1.00	100	controlled area (NRC: up to 200 µSv/h)
2.0	0.25	25	below public limit (20 µSv/h avg)
3.0	0.11	11	WHO typical background ~0.2 µSv/h
5.0	0.04	4	safe for unrestricted area

*Example based on 100 µSv/h @ 1m. Your calculator uses real inputs.

🎧 Sound pressure level (SPL) drop – inverse square law (OSHA / EU)

Distance (m)	SPL reduction (dB)	Example SPL (dB) if 90 dB @ 1m	OSHA permissible time
1	0	90	≤ 8 hrs (100% dose)
2	−6	84	≤ 16 hrs (50% dose)
4	−12	78	no daily limit
8	−18	72	safe

💡 Illuminance (light) – IES standards & inverse square law

Distance (ft / m)	Foot-candles (fc) from 1000 lm @ 1m	Lux (lx)	Application (IES)
1 m	100 fc	1076 lx	office task lighting
2 m	25 fc	269 lx	corridor / ambient
3 m	11.1 fc	119 lx	parking lot (min 10 lx)

🌍 International benchmark – typical intensity ratios (WHO, IAEA)

Distance ratio (D₂/D₁)	Intensity multiplier	Example (from 100 units)	Safety note
0.5×	4.0	400	use caution, very high
1×	1.0	100	reference level
2×	0.25	25	typical drop
3×	0.111	11.1	background range
10×	0.01	1	often negligible

❓ Frequently asked questions – inverse square law calculator

Q: How do I use the four-field calculator?
Enter any three values (I₁, D₁, I₂, D₂). Press “compute missing”. The fourth will be calculated using I₁·D₁² = I₂·D₂².

Q: What units should I use?
Any consistent units: intensity (µSv/h, lux, Pa, W/m²) and distance (m, ft, cm). The result will be in same unit.

Q: Does this include shielding or absorption?
No — pure geometric inverse square. For real-world radiation/sound, additional factors apply (see NRC, OSHA).

Q: What is the “model year” for?
It tags your calculation with a revision year (2024,2025,2026) for record keeping.

📌 More resources: NRC dose limits · OSHA noise standard · IES lighting calculator (internal pages).

You can easily calculate inverse functions, logs, and trigonometric values using these tools: Inverse Functions Calculator, Inverse Log Calculator, and Inverse Trig Calculator.