Illuminance Distance Calculator
Enter an illuminance measured at one distance to get the illuminance at another distance, using the inverse-square law for a point source. You can also find the illuminance from a luminous intensity in candela.
The inverse-square law
The illuminance produced by a point source is inversely proportional to the square of the distance from the source.
- Illuminance = reference illuminance × (reference distance ÷ distance you want)²
- If the distance is doubled, the illuminance falls to 1/4 (2² = 4). If the distance is halved, the illuminance is 4 times as large.
A point source of luminous intensity I (cd) produces the following illuminance on a surface perpendicular to the light at a distance d (m):
- Illuminance (lx) = luminous intensity (cd) ÷ distance (m)²
Definitions of lx and cd
The definitions below follow the Japanese Order for Enforcement of the Measurement Act (Cabinet Order No. 357 of 1992), Appendix 1, whose original text was checked on October 26, 2026 when the Japanese version of this page was made. The definitions of the SI Brochure were not checked again for this page.
- Candela (cd): the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 10¹² hertz and has a radiant intensity in that direction of 1/683 watt per steradian.
- Lumen (lm): the luminous flux emitted within 1 steradian by a source of 1 candela.
- Lux (lx): the illuminance when a surface of 1 square meter is lit by a luminous flux of 1 lumen.
A source of 1 candela emits 1 lumen into 1 steradian. On a sphere at a distance d, 1 steradian covers d² square meters, so the illuminance is the intensity ÷ d² lux. At a distance of 1 m, a source of 1 cd gives 1 lx.
Source: Order for Enforcement of the Measurement Act (e-Gov Law Search, in Japanese)
Examples
- A place with 1,000 lx at 1 m, at 2 m: 1,000 × (1 ÷ 2)² = 250 lx (1/4)
- The same place at 0.5 m: 1,000 × (1 ÷ 0.5)² = 4,000 lx (4 times)
- The same place at 3 m: 1,000 ÷ 9 = about 111.1111 lx
- A source of 1,000 cd at 2 m: 1,000 ÷ 2² = 250 lx
Notes
- This is a rough estimate under ideal conditions: a point source (a source with no size), a space with no reflections, and a surface perpendicular to the light. Reflections from desks and walls, the colors of the ceiling and walls, the angle of the surface to the light and ambient light are not considered.
- A real luminaire has a different brightness in different directions (its light distribution), and close to the source it cannot be treated as a point, so the result departs from this formula. How close is too close, and by how much, depends on the luminaire, so no figure is given here.
- It cannot be used as a guaranteed value for lighting design. Check the manufacturer's photometric data or a measurement with a light meter.
- Distances must be greater than 0; illuminance and intensity must be 0 or more. You can enter up to 9 digits before the decimal point and 6 decimal places.
- Results are shown with 7 significant digits. You can copy the value as displayed or with 15 significant digits.
- For the sound equivalent, how sound weakens with distance, see the Sound Distance Attenuation Calculator.
Frequently asked questions
Why does doubling the distance quarter the illuminance instead of halving it?
Because the light spreads over four times the area when the distance doubles, so the brightness per unit area (the illuminance) falls to a quarter.
Why does the calculation not match my measurement up close?
A luminaire is not a point and has a light distribution. The closer you are to the source, the more the point-source formula departs from reality.
What is the difference between candela and lumen?
Luminous intensity (cd) is the strength of light in one direction; luminous flux (lm) is the total light a source emits. A source of 1 cd emits a flux of 1 lm into 1 steradian.