The lumen to lux calculator above does something no unit converter can do. Lumens and lux are not two scales of the same quantity, so there is no fixed number to multiply by. Lumens measure the total light a source emits in every direction it emits into. Lux measures how much of that light lands on a square metre of surface. Getting from one to the other requires geometry — how tightly the beam is aimed, and how far the surface is from the source.
Arb Digital builds free tools that pick one job and finish it. This page relates all three photometric quantities at once: luminous flux in lumens, illuminance in lux, and luminous intensity in candela. It also runs the question backwards, so you can start from the light level you want and find the lamp output that would deliver it, either at a single point or across a whole room floor.
What This Lumen to Lux Calculator Does
In its first mode you give it a lamp's rated lumen output, the beam angle printed on the box, and the distance from the lamp to the surface. It returns the illuminance directly under the beam centre in lux, plus the luminous intensity in candela, the solid angle the beam occupies, the diameter of the lit circle, and the average lux across that circle. Those five numbers describe the lit patch completely.
In its second mode the question flips. You state the illuminance you want and the geometry you are stuck with, and it returns the lumen output the lamp must have. This is the mode that matters when you are shopping, because lamps are sold by lumens and specifications are written in lux.
The third mode leaves point-source geometry behind and treats a room. Given a floor area, a target lux level on the working plane, and a combined utilisation and maintenance factor, it returns the total lumen output the room needs and divides that across the number of luminaires you plan to fit. Room lighting is not a single-lamp problem, so it deserves its own path rather than a fudge applied to the point-source answer.
How to Use It
- Pick the mode that matches your question. Two of the three are point-source questions about one lamp aimed at one surface. The third is a room question and ignores distance entirely.
- Enter the full beam angle, not the half angle. This is the single most common input error. Manufacturers quote the full cone angle at which intensity has fallen to half its centre value, so a "60 degree" downlight means 30 degrees either side of the axis.
- Measure distance along the beam axis. If a downlight is 2.4 metres above the floor and you care about a desk at 0.75 metres, the distance is 1.65 metres, not 2.4.
- Set a realistic utilisation and maintenance factor for room mode. Very little of a lamp's output reaches the working plane untouched. A figure between 0.4 and 0.7 covers most real rooms, with dark walls and deep fittings at the low end.
- Read the average lux as well as the centre lux. The hero figure is the brightest point. The grid figure is what the whole lit circle averages, and the gap between them tells you how even the pool of light is.
The Formula: How Lumens Become Lux
Three quantities, three definitions, and two links between them. Luminous flux Φ in lumens is the total visible light emitted. Luminous intensity I in candela is flux per unit solid angle. Illuminance E in lux is flux per unit area received. The candela is the SI base unit here, and the other two are derived from it; the NIST page on the SI unit of luminous intensity states that the candela is defined by fixing the luminous efficacy of monochromatic radiation at a frequency of 540 × 1012 hertz to 683 lumens per watt. The lumen and the lux appear in the SI Brochure published by the BIPM as coherent derived units, the lumen being the candela steradian and the lux the lumen per square metre.
The first link is the beam cone. A cone of full angle θ subtends a solid angle Ω = 2π(1 − cos(θ/2)) steradians. Dividing flux by that solid angle gives intensity: I = Φ ÷ Ω. The second link is the inverse square law: E = I ÷ d2, because the same cone of light spreads over an area that grows with the square of distance.
Work the defaults. A 60 degree beam has a half angle of 30 degrees, so Ω = 2π(1 − cos 30°) = 2π(1 − 0.8660) = 0.8418 steradians. A 1,000 lumen lamp aimed into that cone gives I = 1,000 ÷ 0.8418 = 1,188 candela. At two metres, E = 1,188 ÷ 22 = 297 lux. The lit circle has a radius of 2 × tan 30° = 1.155 metres, so a diameter of 2.31 metres and an area of 4.19 square metres. Spreading 1,000 lumens evenly over that area would give 239 lux, and the fact that the centre reads 297 lux is exactly what tells you the pool is not even.
Why a Unit Converter Cannot Answer This
Arb Digital already publishes a luminous flux converter and a luminous intensity converter, and it is worth being precise about what they do and do not do. A converter rescales a value within a single physical quantity: lumens to millilumens, candela to candlepower. The number changes, the quantity does not. Every conversion factor is fixed and unconditional.
Flux, intensity and illuminance are three different quantities with three different dimensions. There is no fixed factor from lumens to lux any more than there is a fixed factor from litres to metres. The bridge between them is geometry, and geometry is an input, not a constant. That is the boundary: the converters rescale, this page derives. If you already have candela and want millicandela, use the converter. If you have lumens and want lux, you also need a beam angle and a distance, and that is what this page is for.
Beam Angle Is Not the Same as Field Angle
Lighting datasheets often quote two angles, and they are not interchangeable. The beam angle, sometimes written as the fifty per cent angle, is the cone within which intensity is at least half its on-axis value. The field angle, or ten per cent angle, is the wider cone within which intensity is at least a tenth of the centre value. Field angle is typically one and a half to two times the beam angle for the same lamp.
Use the beam angle in this calculator. It gives the useful, well-lit cone, and it is the figure that matches how the inverse square calculation is normally presented. If you enter a field angle instead, the solid angle comes out far too large, the intensity too small, and the lux too low — often by a factor of two or three, which is enough to make a lighting scheme look impossible on paper when it would have worked.
For a bare lamp with no reflector, the honest answer is 360 degrees, and the tool handles that: the solid angle becomes the full 4π steradians and intensity falls to flux divided by 12.57. Most household bulbs are somewhere between, radiating strongly to the sides but weakly backwards through the base, which is why manufacturers quote a beam angle of about 200 to 270 degrees for them. The angle converter handles radians and gradians if your datasheet uses them.
Why the Centre Reading Beats the Average
The two lux figures this page reports look like they should agree, and the fact that they do not is the most useful thing on the results panel. The hero number applies the inverse square law along the beam axis, so it describes the single brightest point on the surface. The grid number divides total flux by the area of the lit circle, so it describes what a perfectly even pool of the same total light would read.
Real beams are not even. Intensity falls off from the axis outward, and by definition it has halved by the time you reach the edge of the beam cone. So the centre always reads higher than the average, and the ratio between the two is a rough measure of how harsh the light will look. A narrow spot has a big gap and produces a bright disc with sharp falloff. A wide flood has a small gap and produces a soft wash.
Which one you design to depends on what the light is for. Task lighting is usually specified at the centre point, because that is where the work happens. General area lighting is specified as an average, because nobody stands in one place. Quoting a centre reading as though it were an area average is misleading and is worth watching for on product pages.
Room Lighting Is a Different Calculation Entirely
Point-source geometry breaks down for a room because light bounces. A lumen that leaves a downlight, misses the desk, hits a pale wall and reflects onto the desk anyway has still done useful work. The standard approach handles this with a lumen method calculation: total flux required equals target illuminance times floor area, divided by a utilisation factor and a maintenance factor.
The utilisation factor accounts for room geometry and surface reflectance — how much of what leaves the fittings ever reaches the working plane. A tall narrow room with dark walls wastes far more light than a low wide room with white walls. The maintenance factor accounts for time: dust on the fitting, dirt on the walls, and the gradual lumen depreciation of the lamp itself. This tool combines the two into one figure because they multiply together anyway.
Working the room defaults: 300 lux across 20 square metres needs 6,000 lumens landing on the floor, and with a combined factor of 0.6 the fittings must emit 10,000 lumens. Divided between four luminaires that is 2,500 lumens each, which is a realistic output for a modern LED downlight. Use the area converter if your floor plan is in square feet, and the rectangle area calculator or the wall area calculator if you have dimensions rather than an area.
Lumens, Watts and What Actually Costs Money
Lumens per watt is the efficacy of a lamp, and it is the number that decides your electricity bill for a given light level. Incandescent lamps sit around 15 lumens per watt, halogen a little higher, fluorescent near 60 to 100, and current white LEDs commonly reach 100 to 160. The theoretical ceiling for white light is far lower than the 683 lumens per watt of the candela definition, because that figure applies to a single green wavelength the eye responds to most strongly.
Buying by watts made sense when almost every lamp was an incandescent with the same efficacy. It is now meaningless: a 9 watt LED and a 60 watt incandescent both produce about 800 lumens. Once you have a total wattage, price it with the electricity bill calculator, and the power converter handles unit changes on the way.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Entering the half angle — beam angles are quoted as the full cone, so halving one before entering it inflates the intensity by roughly a factor of four.
- Using mounting height as distance — the distance that counts is from the lamp to the surface you care about, which for a desk is the mounting height minus the desk height.
- Applying point-source geometry to a room — the inverse square law describes one lamp on one spot and ignores every reflected lumen, so it badly understates a room with pale surfaces.
- Treating lumens as a brightness rating — lumens are total output. The same output through a narrow beam looks dazzling and through a wide beam looks dim.
- Forgetting the maintenance factor — a scheme designed to exactly hit its target on day one will be under target within a year as fittings collect dust and lamps age.
Related Free Tools From Arb Digital
Rescale single quantities with the luminous flux converter and the luminous intensity converter, and handle geometry with the angle converter, the area converter and the length converter. For the electrical side, the LED resistor calculator sizes the current-limiting resistor on a discrete LED, the power converter rescales wattage, and the electricity bill calculator prices a running load. Room geometry comes from the rectangle area calculator and the wall area calculator. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
There is no single answer, because lux depends on how the light is spread and how far it travels. A 1,000 lumen lamp with a 60 degree beam gives about 297 lux at two metres directly under the beam. The same lamp with a 15 degree beam would give roughly 4,700 lux at the same distance.
Yes. One lux is exactly one lumen falling on one square metre. The reason a conversion still needs geometry is that you have to know how many square metres the light actually lands on, and that depends on beam angle and distance.
The beam angle, which is the cone where intensity is at least half the on-axis value. Field angle is the wider ten per cent cone and is typically one and a half to two times larger, so using it in place of the beam angle understates the lux considerably.
Use 360 degrees for a genuinely omnidirectional source, which makes the solid angle the full sphere. Most household bulbs radiate mainly sideways and forwards rather than back through the base, so manufacturers usually quote something between 200 and 270 degrees for them.
The hero figure is the illuminance at the brightest point, on the beam axis, from the inverse square law. The grid figure is the total flux divided by the area of the lit circle, which is what an even pool would read. Real beams fall off from the centre, so the average is always the lower of the two.
The converter rescales lumens into other units of the same quantity, such as millilumens. This page moves between three different quantities — flux, intensity and illuminance — which is only possible once you supply the beam angle and distance that link them.
It is the combined share of emitted lumens that reaches the working plane after losses to fitting design, room geometry, wall reflectance, accumulated dirt and lamp ageing. Values between 0.4 and 0.7 cover most real interiors, with dark surfaces and deep fittings at the lower end.
This tool is provided for educational and estimating use. It is not a substitute for a lighting design carried out to an applicable standard, and nothing on this page is installation or safety guidance.
