Inverse Square Law Intensity Calculator

Model spreading waves and light over distance accurately. Switch between reference and power based methods. Get clear intensity ratios and downloads for reports today.

Choose the model that matches your measurements.
Tip: In reference mode, units cancel in the ratio, but keep them consistent.

Formula used

For an inverse-square field, intensity falls with the square of distance: I ∝ 1 / r².

  • Reference scaling: I₂ = I₁ × (r₁² / r₂²)
  • Isotropic point source: I = P / (4πr²)
  • Level change: ΔdB = 10 log₁₀(I₂/I₁) (power-like intensity)

These relations assume free-space spreading and no absorption.

How to use this calculator

  1. Select a calculation mode that matches your data.
  2. Choose whether to solve for intensity or distance.
  3. Pick distance and intensity units, then enter values.
  4. Press Calculate to show results above the form.
  5. Use Download CSV or Download PDF for reporting.

Example data table

Scenario I₁ r₁ r₂ Computed I₂
Sound level proxy 100 (relative) 1 m 2 m 25 (relative)
Radiant intensity 12 W/m² 0.5 m 1.5 m 1.333 W/m²
Light proxy 800 Lux 1 m 4 m 50 Lux

Real environments add reflections and absorption, so measured values may differ.

Practical notes

  • Near-field: Very close to a source, the model may not hold.
  • Extended sources: Large emitters behave differently at short ranges.
  • Medium losses: Air, fog, and water can add exponential loss.
  • Safety: Compare outputs with local exposure standards.

Inverse Square Law Intensity: Professional Notes

1) Why distance changes intensity so quickly

Point-like sources spread energy over a growing sphere. When distance doubles, surface area becomes four times larger, so average intensity falls to one quarter. A 10× distance increase gives about 1/100 intensity.

2) The governing relationship used here

The calculator applies I2 = I1(r1/r2)2 and rearrangements to solve for intensity, distance, or required source level for a target intensity.

3) Practical units and consistency

Intensity is “power per area,” often W/m². In optics you may see irradiance (W/m²) and, for visible light, illuminance (lux). Any consistent units work in ratio form because the square-distance factor is unitless. Measure distances from the same reference point on the source. Keep the same medium and line-of-sight path.

4) Data-driven scaling examples

If a sensor reads 8 W/m² at 2 m, then at 4 m the estimate is 8×(2/4)² = 2 W/m². Moving from 1 m to 5 m gives 1/25 of the 1 m intensity. From 3 m to 6 m, intensity drops to one quarter. These checks help catch entry errors.

5) Light planning with quick estimates

For lamps that are approximately point sources at the measurement distance, inverse-square scaling helps plan coverage. Example: 600 lux at 1.5 m becomes about 150 lux at 3.0 m. Large panels and optics can deviate, so confirm with a meter for critical work.

6) Sound interpretation and the 6 dB rule

In free space, 1/r² intensity corresponds to about 6 dB drop in level for each distance doubling (ideal spherical spreading). Indoors, reflections and standing waves often reduce the drop.

7) Radiation and stand-off distance decisions

Increasing distance is an effective control when the source is roughly isotropic. A 3× distance increase reduces intensity to 1/9. Use target mode to estimate a minimum stand-off distance, then compare with limits and instrument uncertainty. For shielding or absorption, apply an additional attenuation factor.

8) Limits and common causes of mismatch

The model weakens in the near-field, for extended sources, or when barriers and absorption dominate. Reflections, sensor angle response, fog, and water can shift real measurements. Treat inverse-square as the geometric factor; if you know transmission T, estimate I ≈ Igeo×T. Record assumptions when exporting.

FAQs

1) What does the inverse square law mean?

It states that intensity from a point-like source decreases with the square of distance. Doubling distance reduces intensity to one quarter, while tripling distance reduces it to one ninth.

2) Can I use this calculator with any units?

Yes. Use one consistent distance unit for r and one consistent unit for intensity. In reference mode, units cancel in the ratio, so the scaling remains valid.

3) Does the law work indoors?

It can be a rough estimate, but reflections and room modes often keep levels higher than free-space predictions. Measure on site when accuracy matters, especially in small or reflective rooms.

4) When should I solve for distance instead of intensity?

Use distance solving when you have a limit or target intensity (such as a safe exposure level) and want the approximate range needed from a known source level.

5) Is sound always inverse-square?

In open space with spherical spreading, intensity follows 1/r². Near walls, in corridors, or close to large sources, the field may be closer to cylindrical or complex, so results become approximate.

6) What if the medium absorbs energy strongly?

Then inverse-square alone underestimates losses. Add absorption or transmission effects separately, especially in fog, water, or material shielding where exponential decay can dominate.

7) Why are my measured results different from the estimate?

Differences commonly come from reflections, non-point source geometry, sensor angle response, and near-field effects. Use the calculator as a baseline model and validate with measurements.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.