Inverse Square Law Calculator (Radiation)

Enter a known intensity (I₁) and its distance (r₁) from the source, then provide a second distance (r₂) to calculate the radiation intensity at that new distance (I₂). You can also solve for distance instead of intensity. The Inverse Square Law Calculator applies the formula I₁r₁² = I₂r₂² to show how radiation, light, or sound diminishes as you move away from a point source.

Choose the unknown value you want to solve for.

Known radiation intensity at the first distance.

Distance from the source at which I₁ was measured.

Known intensity at the second distance (required if solving for r₂ or I₁).

Distance from the source at the second point.

Results

Calculated Result

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Intensity Ratio (I₁ / I₂)

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Distance Ratio (r₂ / r₁)

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% Change in Intensity

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Intensity at Distance 1 vs Distance 2

Results Table

Frequently Asked Questions

What is the inverse square law?

The inverse square law states that the intensity of radiation (or any radially emitted energy) from a point source decreases proportionally to the square of the distance from that source. If you double the distance, the intensity drops to one-quarter of its original value. The relationship is expressed as I₁r₁² = I₂r₂².

How do I calculate the inverse square law for radiation?

Use the formula I₂ = I₁ × (r₁ / r₂)². Enter the known intensity I₁ at a reference distance r₁, then specify the new distance r₂ to find I₂. This calculator does the math automatically once you fill in the known values and select what you want to solve for.

What is the reduction in intensity when moving from 1 meter to 3 meters?

At 3 meters the intensity drops to (1/3)² = 1/9 of the original value — roughly an 88.9% reduction. So if the intensity at 1 m is 100 mR/hr, at 3 m it would be approximately 11.1 mR/hr.

Which phenomena follow the inverse square law?

Many physical quantities follow the inverse square law, including gamma radiation, X-ray exposure, visible light intensity, sound pressure level (in free field), gravitational force, and electrostatic force. Any energy radiating equally in all directions from a point source obeys this relationship.

Why does intensity decrease with the square of distance rather than linearly?

As radiation spreads outward from a point source, it covers the surface area of an expanding sphere (A = 4πr²). Because area grows as r², the same amount of energy is spread over a proportionally larger surface, so intensity per unit area falls as 1/r².

Can I use this calculator for light or sound instead of radiation?

Yes. The inverse square law applies to any isotropic point source — light (lux or W/m²), sound in a free field, and electromagnetic radiation. Simply select the appropriate intensity unit from the dropdown and the calculation is identical.

What distance units are supported?

The calculator supports meters, feet, centimeters, and inches. As long as both distances use the same unit, the ratio and the result will be correct. The calculator enforces consistent units automatically.

Does the inverse square law apply to shielded or directed sources?

No — the inverse square law assumes a point source radiating uniformly in all directions (isotropic) with no shielding, collimation, or absorption. For collimated beams, shielded sources, or situations where the medium absorbs radiation, additional correction factors are required.

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