Lumens Distance Calculator
A bulb’s lumen rating describes all the light it emits, but almost none of that light lands where you are standing. This calculator applies the inverse-square law to a point source: give it the total lumens and the distance in meters, and it returns the illuminance in lux on a surface at that distance, assuming the light spreads evenly in every direction with nothing in the way.
Illuminance at that distance
0.00 lux
Spread assumed:
In US units:
Quick Answer
An 800 lumen source at 2 meters delivers 15.92 lux: the 800 lumens spread over the 50.27 m² surface of a sphere with a 2 meter radius. Double the distance to 4 meters and the same source gives 3.98 lux, one quarter as much. The calculator above is pre-filled with this example.
- Quick Answer
- How to use the lumens distance calculator
- Worked examples, verified against the tool
- The inverse-square formula, and where the 4π comes from
- How fast light falls off with distance
- How much lux do you need, and how this helps you get it
- Not the same as a distance calculator
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
How to use the lumens distance calculator
Two inputs, one honest assumption: the source radiates evenly in all directions, like a bare bulb, with no shade, reflector or lens redirecting it.
- Enter the total lumens. Use the lumen figure on the bulb or fixture specification, not the wattage and not a candela beam rating. A standard household bulb is about 800 lumens; a bright floodlight runs to 5,000 or more.
- Enter the distance in meters. Measure from the source to the surface you care about: desk, floor, workbench, plant canopy. Working in feet? Multiply by 0.3048 first (6 feet is 1.83 meters).
- Read the lux, then the verdict. The result box also shows the sphere area your light was spread over and the same illuminance in foot-candles, and it places your number in a band from dim ambient to detailed-work bright so you can judge it without a reference table open.
- Test distances, not just bulbs. Because of the square in the formula, moving a fixture from 3 meters to 2 meters raises the lux from 8.84 to 19.89 for a 1,000 lumen source, a bigger gain than most bulb upgrades deliver.
Worked examples, verified against the tool
Each row below is a real run of the calculator above, including the classic coincidence in the first two rows: a weak source close up and a strong source far away can deliver exactly the same lux.
| Lumens | Distance | Illuminance | What it represents |
|---|---|---|---|
| 800 | 2 m | 15.92 lux | A household bulb read at desk distance underneath it |
| 5,000 | 5 m | 15.92 lux | A floodlight at garden distance: same lux, very different setup |
| 1,200 | 1.5 m | 42.44 lux | A studio softbox rating at portrait distance (idealised, before diffusion losses) |
| 10,000 | 2 m | 198.94 lux | A high-output work light: general workshop territory |
| 806 | 0.75 m | 114.03 lux | A desk lamp close overhead: bright for paperwork, short of office targets |
The inverse-square formula, and where the 4π comes from
Lux = lumens / (4 × π × distance²). The denominator is the surface area of a sphere, and that single detail is where most quick calculators go wrong.
A lux is one lumen landing on one square meter, a definition set out in the BIPM SI Brochure. A point source sends its lumens outward in every direction, so at distance r they are spread across a sphere of radius r, whose area is 4πr². Divide the total lumens by that area and you get lumens per square meter at that distance: lux. Doubling r quadruples the area, which is the whole inverse-square law in one sentence, and the same geometry HyperPhysics uses for its inverse-square treatment of light.
The formula also runs backwards by hand, which this tool deliberately does not automate: distance = √(lumens / (4π × target lux)). To get 500 lux from a 10,000 lumen source, √(10,000 / (4π × 500)) = √1.59 ≈ 1.26 meters. And lumens needed = target lux × 4π × distance², so holding 300 lux at 2 meters takes about 300 × 50.27 ≈ 15,080 lumens of bare-bulb output.
Lumens are not candela
The most common error in rival tools is feeding lumens into the candela formula, E = I / d². Candela measures light sent in one direction; lumens measure all of it. A source’s candela in a given direction equals its lumens divided by the solid angle it spreads over, and for a full sphere that solid angle is 4π steradians, which is exactly where the 4π in this page’s formula comes from. If a manufacturer gives you a candela rating for a spotlight, use E = I / d² with that rating and ignore this page’s lumen input; mixing the two units overstates the light by up to 12.6 times.
When this formula is the wrong tool
Three real-world effects sit outside the model, and the honest answer is to name them rather than hide them. Directional fixtures (reflectors, lenses, shades) concentrate light, so in-beam lux runs far above this estimate. Surfaces at an angle receive less than surfaces square to the source, by the cosine of the angle. And rooms give some light back: pale walls and ceilings reflect flux onto your surface, which is why a real room usually measures a little above the bare point-source figure at working distance.
How fast light falls off with distance
For a fixed 1,000 lumen source, illuminance collapses quickly: by 5 meters you are under 5% of the 1-meter value, and by 10 meters about 1%.
| Distance | Illuminance from 1,000 lumens | Share of the 1 m value |
|---|---|---|
| 1 m | 79.58 lux | 100% |
| 2 m | 19.89 lux | 25% |
| 3 m | 8.84 lux | 11.1% |
| 5 m | 3.18 lux | 4% |
| 10 m | 0.80 lux | 1% |
Key takeaways
- The denominator is a sphere area, 4πr². Any lumens-to-lux tool that skips the 4π is pricing candela, not lumens.
- Distance beats brightness: halving the distance quadruples the lux, while doubling the lumens only doubles it.
- Judge the result against a target band (offices 300 to 500 lux, workshops 500 to 1,000) before buying anything.
- For spotlights and flashlights, switch to the candela rating and E = I / d²; this page models bare, all-direction sources.
How much lux do you need, and how this helps you get it
Recommended illuminance depends on the task, and the ranges below follow the Illuminating Engineering Society’s recommended practice, published in the IES Lighting Library.
| Space | Target illuminance | Notes |
|---|---|---|
| Hallways and corridors | 100 to 150 lux | Safe movement, no detailed tasks |
| Living areas | 100 to 300 lux | General activity, with task lamps for reading |
| Offices and classrooms | 300 to 500 lux | Sustained paperwork and screen work |
| Workshops and inspection | 500 to 1,000 lux | Fine detail, tools, quality checks |
Two applied cases show how readers use this in practice. For plant lighting, the question is fixture height over a canopy, and the grow light distance calculator covers that horticultural version of the same trade-off, while the grow light cost calculator prices the electricity once the height is set. For rooms, fixture count and spacing come first, and the ceiling light calculator plans the layout; this page then checks what one fixture actually delivers at floor or desk level.
Not the same as a distance calculator
The shared word is a trap: this page never measures how far apart two things are. The site’s distance calculator finds the length between two points in a plane or in space, a geometry question. This page starts where that answer ends: you already know the distance, and you want to know how much light survives the trip. If your question is “how far”, use the geometry tool; if it is “how bright when it gets there”, you are in the right place.
What competing calculators miss
The formula is one line, so rivals separate themselves mostly by getting it subtly wrong or stopping at the number:
- Tools that divide lumens by distance² (or by π × distance²): both circulate widely, and both overstate the light, by about 12.6 times and exactly 4 times respectively, because they treat a lumen rating as a candela rating. This page prints the sphere-area reasoning next to the result so the figure can be checked, not just trusted.
- BraveCalculator’s lumens distance calculator: the closest clone, with the same correct 4π formula, but the answer arrives with no context: no target bands, no falloff table, no foot-candle figure, so a reader holding “42.44 lux” has no way to judge whether that is good.
- Photometric suite calculators (Firgelliauto, NUM8ERS): thorough engineering tools, but they start from candela, solid angles and beam geometry. A homeowner holding a bulb box that says “800 lumens” has no input they can honestly type in.
- Guide-style pages (UMA Technology and similar): worked examples that switch between the area method and the inverse-square method mid-article, producing numbers that cannot be reproduced either way.
- The gap this page fills: the correct sphere formula for a lumen-rated source, a verdict band on every result, a verified falloff table showing the quartering rule, and the candela boundary stated plainly so directional fixtures are not mispriced.
Frequently asked questions
It computes illuminance in lux at a distance from a light source: lux = lumens / (4 × π × distance²), with distance in meters. That is the inverse-square law for a point source spreading its total lumens evenly over the surface of a sphere. It does not run backwards: to find the distance that delivers a target lux, rearrange the same formula by hand, as the formula section on this page shows.
Because they use a different denominator. Dividing lumens by π × distance² gives a result exactly four times higher than this page, and dividing by distance² alone gives one about 12.6 times higher. Both shortcuts quietly treat your lumens as if they were candela, the unit for light sent in one direction. For a bare bulb or any source rated in total lumens, spreading the flux over the full sphere area, 4πr², is the correct treatment.
The illuminance falls to one quarter, because the same lumens spread over four times the sphere area. An 800 lumen source gives 15.92 lux at 2 meters and 3.98 lux at 4 meters. Halving the distance does the opposite and multiplies the lux by four, which is why moving a lamp a short distance changes a room more than buying a slightly brighter bulb.
Not directly. The distance field expects meters, and the answer is wrong if you type feet into it. Convert first: multiply feet by 0.3048, so 3 feet is 0.91 meters and 10 feet is 3.05 meters. The result is in lux; to read it as foot-candles, the unit common in US lighting practice, divide by 10.764.
No, not exactly. The formula assumes a bare point source radiating equally in all directions. A reflector or lens concentrates the same lumens into a beam, so the lux inside the beam is much higher than this estimate and the lux outside it is lower. For directional fixtures, use the manufacturer's candela rating with the candela form of the law, illuminance = candela / distance².
It depends on the task. Common planning ranges put hallways and corridors at 100 to 150 lux, offices and classrooms at 300 to 500 lux, and workshops and detailed inspection work at 500 to 1,000 lux. Compare your result against the band for your space, then remember that surface colours, glare and how evenly the light spreads matter as much as the single number at one point.
The tool only checks that both entries are positive numbers. A tiny distance such as 0.1 meters with 100,000 lumens returns 795,774.72 lux, which is the honest output of the formula even though no real bulb behaves as a perfect point source that close up. Very large or very small results are a prompt to sanity-check the setup, not a tool error.
Yes, illuminance adds. Run the calculator once per light, using that light's lumens and its own distance to the surface, then add the lux values together. Two identical 800 lumen bulbs, each 2 meters from a desk, give about 15.92 + 15.92 = 31.84 lux where their light overlaps, before accounting for angles, shades and obstructions.
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References
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure): the lux as one lumen per square metre. Accessed October 22, 2026.
- National Institute of Standards and Technology. Metric (SI) Units. Accessed October 22, 2026.
- Illuminating Engineering Society. The Lighting Library: IES standards and recommended practice for illuminance levels. Accessed October 22, 2026.
- National Institute of Standards and Technology. The International System of Units (SI), SP 330, Section 2: photometric units (candela, lumen and lux). Accessed October 22, 2026.
- U.S. Department of Energy, Energy Saver. LED Lighting. Accessed October 22, 2026.
- Occupational Safety and Health Administration. 29 CFR 1926.56: Illumination (construction). Accessed October 22, 2026.
- Georgia State University, HyperPhysics. Inverse Square Law for Light. Accessed October 22, 2026.