Inverse Square Law Calculator

Calculate how light, sound, radiation, or gravity intensity changes with distance using the inverse square law, with dB change and distance tables.

About the Inverse Square Law Calculator

The inverse square law is one of the most universal relationships in physics: the intensity of a point source's radiation decreases with the square of the distance. This applies to light, sound, gravity, electric fields, radio waves, nuclear radiation, and any other phenomenon that spreads uniformly in three dimensions.

When you move twice as far from a light source, the brightness drops to one-quarter. Triple the distance and it drops to one-ninth. This geometric spreading has profound consequences for lighting design, acoustics, telecommunications, radiation safety, and astrophysics.

This Inverse Square Law Calculator computes the intensity at any distance given a reference measurement, along with the dB change, distances for half and one-tenth intensity, flux from source power, and a comprehensive distance-intensity table. Preset buttons cover lighting, sound, radio, and gravitational scenarios. The visual decay chart shows how rapidly intensity falls off with distance.

Use the preset examples to load common values instantly, or type in custom inputs to see results in real time. The output updates as you type, making it practical to compare different scenarios without resetting the page.

Why Use This Inverse Square Law Calculator?

This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows. This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.

How to Use This Calculator

  1. Enter the known intensity at a reference distance.
  2. Enter the reference distance (distance 1).
  3. Enter the target distance (distance 2) where you want to know the intensity.
  4. Select the distance unit.
  5. Select point source (1/r²) or line source (1/r).
  6. Optionally enter the source power for flux calculations.
  7. Review intensity at the target distance, dB change, and the distance table.

Formula

I₂ = I₁ × (d₁ / d₂)² Ratio in dB = 10 × log₁₀(I₂ / I₁) Half-intensity distance: d = d₁ × √2 Flux: Φ = P / (4πd²) for isotropic point source

Example Calculation

Result: I₂ = 11.11 W/m², Ratio = −9.54 dB

At 3 meters from a source measured at 100 W/m² at 1 meter, the intensity drops to about 11.1 W/m² — a 9.5 dB reduction.

Tips & Best Practices

Practical Guidance

Use consistent units throughout your calculation and verify all assumptions before treating the output as final. For professional or academic work, document your input values and any conversion standards used so results can be reproduced. Apply this calculator as part of a broader workflow, especially when the result feeds into a larger model or report.

Common Pitfalls

Most mistakes come from mixed units, rounding too early, or misread labels. Recheck each final value before use. Pay close attention to sign conventions — positive and negative inputs often produce very different results. When working with multiple related calculations, keep intermediate values available so you can trace discrepancies back to their source.

Tips for Best Results

Enter the most precise values available. Use the worked example or presets to confirm the calculator behaves as expected before entering your real data. If a result seems unexpected, compare it against a manual estimate or a known reference case to catch input errors early.

Frequently Asked Questions

Why does intensity follow 1/r²?

A point source radiates uniformly in all directions. The same power is spread over the surface area of a sphere (4πr²), so intensity decreases as r² increases.

Does the inverse square law apply to sound?

Yes — in open air with no reflections, sound intensity follows the inverse square law. In rooms, reflections modify this behavior.

What about laser beams?

Lasers are highly directional and do not spread isotropically, so the inverse square law does not apply to coherent beams (though it applies to the diffraction-limited divergence). Use this as a practical reminder before finalizing the result.

How does this apply to gravity?

Newton's law of gravitation follows the inverse square law: F = GMm/r². Gravitational field strength drops as 1/r².

What is the 6 dB rule for sound?

Doubling the distance from a point source reduces sound pressure level by 6 dB (intensity by ~75%), consistent with the inverse square law. Keep this note short and outcome-focused for reuse.

Does it apply to nuclear radiation?

Yes — radiation from a point source follows 1/r². This is the basis of the distance rule in radiation protection.

Related Pages