Physics · Photometry
Inverse square law for light calculator.
Find the illuminance a point source puts on a surface at a distance, or work backward to the candela or distance. See how moving the lamp changes the lux.
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Inverse square law for light
For a small light source, the illuminance on a surface facing it is E = I / d², where I is the luminous intensity in candela, d the distance in metres and E the illuminance in lux. If the surface is tilted so the light arrives at angle θ from the surface normal, multiply by cosθ: E = I cosθ / d². Doubling the distance cuts the illuminance to one quarter.
Worked example. A 100 cd source 2 m from a surface facing it gives E = 100 / 4 = 25 lx. Move it to 4 m and E = 100 / 16 = 6.25 lx, a factor of 0.25. If the surface is tilted 60°, E = 25 × cos 60° = 12.5 lx.
The law needs the source to be small compared with the distance (a point source). For a large panel or a strip light it overstates the effect at close range.
Frequently asked questions
What is the inverse square law for light?
Illuminance from a point source falls with the square of the distance: E = I / d squared. Twice as far gives a quarter of the lux.
How do I get lux from candela and distance?
Divide candela by the distance in metres squared. 100 cd at 2 m is 25 lux.
What does the cosine do?
When the surface is tilted so light hits at an angle from the normal, the lux drops by cos(angle). At 60 degrees it halves.
When does the law fail?
Close to a large or extended source, such as a light panel or a long tube, because the source is not a point.
Is candela the same as lumens?
No. Candela is lumens per steradian, the intensity in one direction. Lumens are the total light output.
Sources
Checked
- NIST SP 330 (2019), Table 4: SI derived units with special names (lumen = cd sr, lux = lm/m2)
- Wikipedia: Illuminance (point-source formula E = Iv cos(theta) / D^2, citing ANSI/IES LS-1-22 and CIE S 017:2020)
- BIPM: The candela
NIST gives lux and lumen in terms of candela. The point-source distance and cosine laws are quoted from the Illuminance article, which cites IES and CIE standards; the worked numbers are arithmetic on that formula. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Idealised point-source model for study. Not a lighting design or compliance calculation.