Inverse Square Law Calculator
From a known intensity at one distance, find the intensity at any other distance — and see exactly how fast a point source fades as you move away.
Point source, same distance unit
The law holds for an ideal point source radiating freely; the intensity can be any unit, but the two distances must share one unit so the ratio is clean.
What is the inverse square law?
One intensity and two distances in, the new intensity out
The inverse square law says that the intensity of anything spreading out from a point source — light, sound, gravity, or radiation — falls with the square of the distance. The same energy spreads over a sphere whose area grows as the distance squared, so twice as far means a quarter of the intensity, three times as far means a ninth. This calculator turns a known intensity at one distance into the intensity at any other distance, which is exactly what you need for photography lighting, speaker placement, radiation safety, antenna and Wi-Fi planning, or any physics problem about a source fading with distance.
Enter a reference intensity, its distance, and a target distance to get the new intensity and the intensity ratio instantly.
One short formula: scale the reference intensity by the square of the distance ratio.
I₂ = I₁ × (d₁ / d₂)²I₁ is the known intensity at the reference distance d₁, and I₂ is the intensity at the target distance d₂. The factor (d₁/d₂)² is the intensity ratio: it is what multiplies the reference intensity. Because the distances appear only as a ratio, their shared unit cancels — so the intensity can be in lux, watts per square metre, or any other unit, and it comes back unchanged.
Suppose a lamp reads 100 lux at 1 metre and you want the reading at 2 metres.
Distance ratio
d₁ / d₂ = 1 / 2 = 0.5 — the target is twice as far, so the ratio is one half.
Intensity ratio
(0.5)² = 0.25 — squaring the distance ratio gives a quarter.
New intensity
100 × 0.25 = 25 — at 2 metres the lamp reads a quarter of its 1-metre value.
The headline insight is how steep the fall-off is: doubling the distance quarters the intensity, and tripling it cuts the intensity to a ninth. This is why a flash that lights a subject perfectly at one metre is far too dim at three, and why stepping back from a loud speaker brings rapid relief. The intensity ratio (0.25 in the example) is the multiplier you can carry around: read it as "a quarter of the source," whatever the unit. The relationship runs both ways — moving closer raises the intensity by the same square law, so halving the distance quadruples it, which matters for radiation and laser safety where a small step toward the source is a big jump in exposure. Because everything scales by the ratio (d₁/d₂)², only the relative distances matter, not the absolute numbers: going from 2 m to 4 m has exactly the same effect as going from 5 m to 10 m. Keep in mind this is the ideal free-field result; real reflections, absorption, and beam shaping soften it in practice.
The law is exact for an ideal point source, but a couple of practical points are worth keeping in mind.
Point sources, free field, consistent distance unit
The inverse square law assumes an ideal point source radiating equally in all directions into empty space, with no reflections, absorption, or focusing. Real sources are different: a focused spotlight, a laser, or a directional antenna beats the simple fall-off, while a room's walls, fog, or a sound-absorbing space change it the other way. Very close to a finite-sized source the law also breaks down, because the source is no longer "a point." The intensity can be any unit, but the two distances must share one unit — the ratio cancels it, so a mix of metres and feet gives a wrong answer.