Lux, Lumens and Candela Converter

Lumens, candela, lux and foot-candles in every direction, through the solid angle and the distance that actually connect them — with the θ/2 in the cone formula spelt out, the luminance units (nit, foot-lambert, apostilb) carried too, and a plain statement of why nothing photometric converts to watts.

Last updated 24 Sep 2026

Lumens, candela and lux, through the geometry

One quantity + geometry → all three

Which of the three have you got?These are three different quantities, not three units for one quantity. Whichever you have, the other two need the geometry below before they exist at all.

Its valueLumens, candela, lux or foot-candles, matching the choice above.

Beam angle — the full apex angle of the coneTrade labels. A bare bulb is 360°, a ceiling downlight about 120°, an MR16 spot 10 to 24°. This is the control that turns lumens into candela.

Or type the beam angle yourself, in degreesLeave at 0 to use the dropdown. Anything from 0.1° to 360° works; the manufacturer’s figure is usually the 50%-intensity angle.

Distance from the source, in metresStraight out along the beam axis. Illuminance falls as the square of this, so it is the other half of the geometry.

Surface reflectance, for the luminance rows0 to 1. White paint about 0.8, newsprint 0.6, dark carpet 0.1. Only the luminance rows use it, and only for a matte surface.

The beam cone, not a circuit. The apex is the source, the vertical line is the surface, and the three photometric quantities all appear at once: the total leaving the apex is the luminous flux in lumens, the flux per steradian of the cone is the luminous intensity in candela, and the flux per square metre arriving is the illuminance in lux. The cone is drawn at whichever of eight standard beam angles is nearest to yours, with the drawn HALF-ANGLE exact — so the drawing is to scale in the angle and not in the distance, and a wide cone comes out short and a narrow one long. The numbers are for your own angle and distance exactly. At 180 and 360 degrees the outline becomes a hemisphere or a sphere, drawn from straight segments because the renderer has no arc, and the sphere is drawn smaller than scale so that the surface still fits beside it.

63.7lxExample

an 800 lm LED downlight with a 120° beam, 2 m above a desk

The cone, the inverse square law, and the ring they close

Ω = 2π(1 − cos(θ/2)) · I = Φ / Ω · E = I / d² = Φ / (Ωd²) · L = ρE / π

Φ: luminous flux, in lumens — the total
I: luminous intensity, in candela — flux per steradian in one direction
E: illuminance, in lux — flux per square metre arriving at a surface
L: luminance, in cd/m² — what leaves a matte surface of reflectance ρ
θ: the FULL apex angle of the beam. The half-angle is what goes in the cosine
Ω: solid angle, in steradians. The whole sphere is 4π = 12.5664
d: distance from the source along the axis, in metres

Worked example

an 800 lm LED downlight with a 120° beam, 2 m above a desk
Ω = 2π(1 − cos 60°) = 2π × 0.5 = π = 3.1416 sr — 120° is the one beam angle whose solid angle is a round number
I = 800 lm ÷ 3.1416 sr = 254.6 cd
E = 254.6 cd ÷ (2 m)² = 63.7 lx on the axis
The beam lands on a circle 6.93 m across, and averaged over the whole of it the illuminance is 21.2 lx — exactly a third of the axis figure, because Ω/(π tan²60°) = 1/3
A white desk of reflectance 0.8 then has a luminance of 0.8 × 63.7 ÷ π = 16.21 cd/m², which is 4.73 fL
And 800 lm could not be made with less than 800 ÷ 683 = 1.1713 W of radiant power, even if every photon were green

Every photometric unit on this page, and what it is a unit of

The first three rows are the whole problem. A lumen is a total, a candela is a rate per unit solid angle and a lux is a rate per unit area, so no factor converts one into another — you need the geometry. The rest are old units that survive in particular trades, and every factor in the third column was rebuilt here from the exact foot of 0.3048 m and the definitions in Palmer’s SI appendix rather than copied from a conversion chart. The apostilb, lambert and foot-lambert all carry a factor of 1/π for the same reason: they were defined so that a perfectly matte surface lit to 1 lm/cm² has a luminance of 1 lambert.
Unit	Quantity	In SI units	Where you meet it
lumen (lm)	Luminous flux — total light out of the source	cd·sr	The number on a lamp box
candela (cd)	Luminous intensity — light per unit solid angle in one direction	SI base unit	Torches, LEDs, beacons; millicandela on an indicator LED datasheet
lux (lx)	Illuminance — light arriving per unit area	lm/m²	Light meters, workplace lighting standards
foot-candle (fc)	Illuminance	10.763910 lx	US lighting practice. 1 lm per square foot
phot (ph)	Illuminance	10 000 lx	Older continental European work. 1 lm per square centimetre
nox (nx)	Illuminance	0.001 lx	Very low light levels; a millilux under another name
candela per square metre (cd/m²), the nit	Luminance — how bright a surface looks	SI	Display specifications
stilb (sb)	Luminance	10 000 cd/m²	Older texts. 1 cd/cm²
apostilb (asb)	Luminance	0.318310 cd/m²	Perimetry in ophthalmology, and older lighting work
lambert (L)	Luminance	3,183.099 cd/m²	Older texts. 1 lm per square centimetre off a matte surface
foot-lambert (fL)	Luminance	3.426259 cd/m²	Cinema screen brightness: SMPTE asks for 14 fL
steradian (sr)	Solid angle — the size of a cone	dimensionless	The whole sphere is 4π = 12.5664 sr

What the beam angle does: solid angle and candela for 1000 lumens

Ω = 2π(1 − cos(θ/2)) with θ the FULL apex angle, so the half-angle is what goes inside the cosine. Putting the full angle there instead is the classic error and it is worth almost exactly a factor of four at small angles, which is why this column is tabulated: a 10° spot is 0.0239 sr and not 0.0955. Read down the fourth column and the page explains itself — the same 1000 lumens is 41 825 cd in a 10° spot and 79.6 cd from a bare bulb, a factor of 526. The 120° row is worth remembering: cos 60° is exactly a half, so a 120° cone is exactly π steradians. The solid angles here were checked against a numerical integration of sinα dα over the cap, not against another chart.
Beam	Solid angle, sr	Share of the sphere	Candela from 1000 lm	Lit diameter at 1 m, m	Lux on axis at 2 m
10 deg — very narrow spot	0.0239	0.19%	41,824.5	0.175	10,456.1
15 deg — spot	0.0538	0.43%	18,603.4	0.263	4,650.9
24 deg — narrow flood	0.1373	1.09%	7,283.2	0.425	1,820.8
36 deg — flood	0.3075	2.45%	3,251.8	0.650	813.0
60 deg — wide flood	0.8418	6.70%	1,187.9	1.155	297.0
90 deg — very wide flood	1.8403	14.64%	543.4	2.000	135.8
120 deg — typical led downlight	3.1416	25.00%	318.3	3.464	79.6
180 deg — hemisphere	6.2832	50.00%	159.2	—	39.8
360 deg — bare bulb	12.5664	100.00%	79.6	—	19.9

Why no number converts lumens to watts

The lumen is a weighted quantity: it counts radiant power multiplied by V(λ), the CIE spectral luminous efficiency function for photopic vision, and the candela is DEFINED by fixing that weighting at 683 lm/W for monochromatic radiation of frequency 540 THz. So the same radiant watt is 683 lumens at 555 nm, 26 lumens at 450 nm and 2.8 lumens at 700 nm. Given only a lumen figure there is no way back to watts without the source’s spectrum, and the last column is the reason: 800 lm needs 1.17 W of green light or 30 W of deep blue. The bottom row of the results above gives the ABSOLUTE FLOOR — what your flux would take if every photon were at 555 nm. No real source gets near it; a good white LED is around 30% of it.
Wavelength	V(λ)	Lumens per radiant watt at that wavelength	Watts needed for 800 lm
450 nm — deep blue	0.0380	26.0	30.82
510 nm — green	0.5030	343.5	2.33
555 nm — the peak of V(λ)	1.0000	683.0	1.17
590 nm — sodium yellow	0.7570	517.0	1.55
660 nm — deep red	0.0610	41.7	19.20
700 nm — far red	0.0041	2.8	285.68

Three quantities, one cone

Lumens, candela and lux are not three units for one thing. They are three different quantities, and that is the only fact you need to stop getting them wrong. A lumen is a total: all the light leaving the source, in every direction it goes. A candela is a rate: light per unit solid angle, in one particular direction. A lux is a different rate: light arriving per unit area. No multiplication turns one into another, which is why no search box can answer “how many lux is 800 lumens”. What connects them is geometry, and only you know the geometry.

The two geometric facts. First, a cone of full apex angle θ subtends a solid angle Ω = 2π(1 − cos(θ/2)) steradians, and luminous intensity is flux per steradian, so cd = lm / Ω. The half-angle inside that cosine is the whole trap: use the full angle and a narrow beam’s answer is wrong by a factor of very nearly four. Second, illuminance obeys the inverse square law, lx = cd / d², because the same cone covers four times the area at twice the distance. Put the two together and the three quantities close into a ring: the spherical cap the beam lands on has area Ωd², so lm / area and cd / d² are the same number, exactly. That identity is what lets one drawing carry all three.

The number a light meter gives you is the on-axis one. Hold it under the middle of a downlight and you read the peak. Move it out towards the edge of the lit circle and the reading falls, partly because the surface is further away and partly because the light arrives at a slant. For a flat surface the two effects together are a cosine-cubed law, and the average over the whole lit circle is Ω / (π tan²(θ/2)) times the axis figure — exactly a third for a 120° beam, 80% for a 60° one and 99% for a 15° spot. Both numbers are in the results, and the difference between them is the commonest reason a room that meets its lux target on paper is gloomy in the corners.

Where this page stops. It converts units and does geometry for one source. Designing the lighting for a room is a different calculation — room index, utilisation factor, maintenance factor, how many fittings and where — and the electronics section’s room lighting calculator does that; its companion lumens-to-watts converter handles efficacy by lamp type and the old-bulb equivalents. What this page owns is the unit relationships and the cone. It also refuses one thing outright: there is no conversion from any photometric unit to any radiometric one. The lumen is radiant power weighted by V(λ), the CIE curve for human photopic vision, and undoing a weighting needs the spectrum that was weighted. For plants the weighting is the wrong one entirely, which is what the lux to PPFD converter exists to deal with.

Frequently asked questions

How many lux is 800 lumens?

It has no answer until you say over what area, or at what distance from what kind of source. Spread 800 lm over a square metre and you have 800 lx. Spread it over a 12 m² room and you have 67 lx. Put it in a 120° downlight 2 m above a desk and the axis reads 63.7 lx while the average over the whole lit circle is 21.2 lx. The lumen is a total and the lux is a density; the geometry is the conversion factor and only you have it.

How do I convert candela to lumens?

Multiply by the solid angle of the beam in steradians: lm = cd × Ω, where Ω = 2π(1 − cos(θ/2)) and θ is the FULL apex angle of the cone. Halving the angle in the cosine is the step everybody drops, and dropping it multiplies a narrow beam’s flux by about four. A 1000 cd source in a 36° flood is 307.5 lm; the same 1000 cd radiating in all directions would be 12,566 lm.

Is 1 foot-candle 10 lux or 10.76 lux?

10.763910 lux, exactly, and the exactness is free: a foot-candle is one lumen per square foot, a foot is 0.3048 m by definition, so the factor is 1/0.3048². The rule of thumb that 1 fc ≈ 10 lx is 7% low, which matters when a specification is written in one unit and a meter reads the other.

Can I convert lumens to watts?

Not without knowing how efficient the lamp is, and not at all without knowing its colour. Lumens per watt — luminous efficacy — is a property of the particular lamp: roughly 14 lm/W for a mains incandescent, 60 for a compact fluorescent, 80 to 200 for an LED. That is a lamp-design question and the electronics section’s lumens-to-watts converter is where it lives. What this page can give you is the hard floor: divide lumens by 683 and you have the radiant power your light would need if every photon were at 555 nm, the peak of human sensitivity. Nothing can beat it.

What is the difference between lux and cd/m²?

Lux is light arriving at a surface; cd/m² is light leaving one, which is what your eye actually sees. They are connected only by what the surface does with the light. For a perfectly matte (Lambertian) surface, luminance = reflectance × illuminance ÷ π, which is the last three rows of the results. Point a light meter at a mirror and that relation fails completely, because a mirror is not Lambertian.

Why is there a π in the foot-lambert and the apostilb?

Because those units were built around matte surfaces. A perfectly diffusing surface receiving 1 lm/cm² emits with a luminance of 1/π cd/cm² — the π is the integral of the cosine over a hemisphere — and the lambert, apostilb and foot-lambert were each defined to make that come out as 1. So 1 fL is 3.4263 cd/m² and 1 asb is 0.3183 cd/m².

Related calculators

References

Bureau International des Poids et Mesures. The International System of Units (SI), 9th edition 2019, section 2.3.1. The candela is defined by fixing the luminous efficacy of monochromatic radiation of frequency 540 × 10¹² Hz at exactly 683 lm/W, which is why 683 is a definition and not a measurement. That frequency is 555.016 nm in vacuum; the V(λ) peak is at 555 nm, where the efficacy is 683.002 lm/W.
International Commission on Illumination. CIE spectral luminous efficiency for photopic vision, V(λ), 1 nm steps, from CIE 018:2019 The Basis of Physical Photometry (3rd ed.), Table 1; also ISO/CIE 23539. DOI 10.25039/CIE.DS.dktna2s3. This is the function that defines the lumen. The CIE data table is copyrighted and is not reproduced here: four values are quoted in the text and the rest is used only to compute. V(450) = 0.0380 and V(660) = 0.0610 were cross-checked against the table condensed from Wyszecki & Stiles in Mobley, Light and Water, chapter 2, Table 2.1.
Palmer JM. The SI System and SI Units for Radiometry and Photometry, Appendix I to Palmer & Grant, The Art of Radiometry (SPIE Press). Source for the phot (1 lm/cm² = 10⁴ lx), the nox (1 millilux), the stilb, the apostilb (1/π cd/m²), the lambert and the foot-lambert (1/π cd/ft²). Every factor on this page was then rebuilt from the exact foot of 0.3048 m rather than copied.
National Institute of Standards and Technology. NIST Handbook 44, Appendix C, General Tables of Units of Measurement. The international foot is 0.3048 m exactly, the US liquid gallon is 231 cubic inches exactly, the imperial gallon is 4.546 09 L exactly and the grain is 64.798 91 mg exactly. Every foot-, gallon- and grain-based factor on this page descends from those four.
ANSI C78.379, Electric Lamps — Classification of the Beam Patterns of Reflector Lamps. The named beam-spread classes (spot, narrow flood, flood, wide flood) come from this standard; it is copyrighted and is cited rather than reproduced. The angles in the dropdown are the ordinary trade labels and the page computes from the angle, not the name.