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).

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.

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.

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.

Intensity at Distance 1

Distance 1 (reference)

Distance 2 (target)

Distance Unit

Source Type

Source Power (W, optional)

Intensity at Distance 2

11.1111

I₂ = I₁ × (d₁/d₂)²

Intensity Ratio

11.111%

-9.54 dB change

Change in dB

-9.54 dB

10 × log₁₀(I₂/I₁)

Distance for Half Intensity

1.414 m

d = d₁ × √2 — intensity drops to 50%

Distance for 1/10 Intensity

3.162 m

d = d₁ × √10 — intensity drops to 10%

Intensity at 2× Distance

25.0000

Doubling distance reduces intensity to 25%

Intensity Decay

0.5

1.0

2.0

3.0

5.0

10.0

Distance (m)	Intensity	Fraction	dB
0.50	400.0000	400.00%	6.0
1.00	100.0000	100.00%	0.0
2.00	25.0000	25.00%	-6.0
3.00	11.1111	11.11%	-9.5
5.00	4.0000	4.00%	-14.0
10.00	1.0000	1.00%	-20.0
20.00	0.2500	0.25%	-26.0
50.00	0.0400	0.04%	-34.0

Planning notes, formulas, and examples

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.

When This Page Helps

This calculator improves speed and consistency while reducing avoidable mistakes in practical workflows.

How to Use the Inputs

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

Formula used

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

Check that all inputs use the same scale and assumptions before trusting the result.
Compare the answer with the worked example or a rough estimate to catch entry mistakes.

When To Use This Calculator

Calculate how light, sound, radiation, or gravity intensity changes with distance using the inverse square law, with dB change and distance tables. Use it when you need a repeatable calculation in the physics / general category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Sources & Methodology

Last updated: January 15, 2025

Frequently Asked Questions

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.