Lumens to Watts Converter (Luminous Efficacy)
Lumens to Watts Converter (Luminous Efficacy)
Lumens to watts and back through luminous efficacy, with typical figures for incandescent, halogen, CFL and LED — plus lumens to candela to lux for a beam angle you give, and the old-bulb equivalent people actually want.
Lumens, watts, candela and lux
800 lm from an LED lamp at 100 lm/W, in a 120° beam, 2 m away
Efficacy, solid angle and the inverse-square law
Ω = 2π(1 − cos(θ/2)) Iv = Φv ÷ Ω Ev = Iv ÷ d² D = 2d·tan(θ/2)
- Φv
- luminous flux, in lumens (lm)
- P
- electrical input power, in watts (W)
- ηv
- luminous efficacy of the source, lm/W
- θ
- full beam angle of the cone
- Ω
- solid angle of that cone, in steradians (sr). The whole sphere is 4π sr
- Iv
- luminous intensity, in candela (cd) — 1 cd = 1 lm/sr
- Ev
- illuminance on the surface, in lux (lx) — 1 lx = 1 lm/m²
Worked example
800 lm from an LED lamp at 100 lm/W, in a 120° beam, 2 m away
Input power: P = 800 ÷ 100 = 8 W
The same 800 lm from a 230 V incandescent at 13.8 lm/W would need 58 W — the “9 W LED ≈ 60 W bulb” line, arrived at rather than asserted
Solid angle: Ω = 2π(1 − cos 60°) = 2π × 0.5 = π = 3.142 sr
Intensity: I = 800 ÷ 3.142 = 254.6 cd
Illuminance at 2 m: E = 254.65 ÷ 2² = 63.66 lx, over a lit circle 2 × 2 × tan 60° = 6.93 m across
Lumens, and the watts each kind of lamp needs for them
| Light output | Incandescent, 230 V (13.8 lm/W) | Halogen (19.8 lm/W) | CFL (60 lm/W) | LED (100 lm/W) |
|---|---|---|---|---|
| 250 lm | 18.1 W | 12.6 W | 4.2 W | 2.5 W |
| 450 lm | 32.6 W | 22.7 W | 7.5 W | 4.5 W |
| 800 lm | 58.0 W | 40.4 W | 13.3 W | 8.0 W |
| 1,100 lm | 79.7 W | 55.6 W | 18.3 W | 11.0 W |
| 1,600 lm | 115.9 W | 80.8 W | 26.7 W | 16.0 W |
| 2,600 lm | 188.4 W | 131.3 W | 43.3 W | 26.0 W |
Beam angle, solid angle and what it does to the intensity
| Beam angle θ | Solid angle Ω = 2π(1 − cos(θ/2)) | Intensity of an 800 lm lamp | Lux at 2 m |
|---|---|---|---|
| 15° | 0.054 sr | 14.88 kcd | 3.721 klx |
| 30° | 0.214 sr | 3.737 kcd | 934.2 lx |
| 60° | 0.842 sr | 950.4 cd | 237.6 lx |
| 90° | 1.840 sr | 434.7 cd | 108.7 lx |
| 120° | 3.142 sr | 254.6 cd | 63.66 lx |
| 180° | 6.283 sr | 127.3 cd | 31.83 lx |
| 360° | 12.566 sr | 63.66 cd | 15.92 lx |
Watts do not measure light
A watt is a rate of energy use. A lumen is a quantity of light, weighted by how well the eye sees each wavelength. Nothing connects them except the lamp in between, and the number that describes that lamp is its luminous efficacy in lumens per watt. That is the whole conversion: watts to lumens is a multiplication by efficacy, lumens to watts a division. Everything else on this page is geometry.
Why the old habit persists. For most of a century every household lamp was a tungsten filament, so watts were a usable proxy for brightness — all the lamps on the shelf converted power to light equally badly. A 100 W bulb at 230 V manages 13.8 lm/W and turns about 2% of its input into visible light; the rest is heat. An LED retrofit at 100 lm/W is more than seven times better, so the proxy broke, and packaging has printed lumens ever since. When someone says a 9 W LED replaces a 60 W bulb they mean it makes about the same light: 800 lm, which needs 58 W of incandescent and 8 W of LED.
Lumens, candela and lux are three different questions. Lumens are the total light a lamp puts out in every direction it emits. Candela is how much of it goes one way — lumens per steradian — and depends entirely on how tightly the beam is focused. Lux is how much lands on a surface, lumens per square metre, and falls with the square of distance because the same cone covers four times the area at twice the range. A torch and a bare bulb can emit the same lumens and differ a hundredfold in candela.
Where the solid angle comes from. A cone of half-angle θ/2 cuts a cap off a sphere of radius r. Integrating the surface element r² sinφ dφ dψ over φ from 0 to θ/2 and ψ over the full turn gives a cap area of 2πr²(1 − cos(θ/2)); the solid angle is that area divided by r², so Ω = 2π(1 − cos(θ/2)). Two sanity checks fall straight out: θ = 180° gives a hemisphere, 2π sr, and θ = 360° gives the whole sphere, 4π = 12.566 sr. At the page default of 120°, cos 60° = 0.5 exactly, so Ω = π = 3.142 sr.
The caveats worth keeping. The efficacy of a real lamp depends on its colour temperature, its driver and its temperature; the list here gives class typicals and says so. A luminaire’s efficacy is lower than its bare lamp’s, because the fitting absorbs light. And a single beam angle is a simplification — real sources have a distribution, and the quoted angle is usually where the intensity has fallen to half. For how many fittings a room needs, use the room lighting lux calculator; for the resistors behind an LED array, the LED array calculator; for what the lamps cost to run, the electricity consumption calculator.
Frequently asked questions
How many watts is 800 lumens?
It depends entirely on the lamp. 8 W of LED at 100 lm/W, 13.3 W of CFL at 60 lm/W, 40.4 W of halogen, or 58 W of a 230 V incandescent. Watts are what goes in; lumens are what comes out.
What LED wattage replaces a 60 W bulb?
A 60 W incandescent at 230 V makes roughly 800 lm, and 800 lm from an LED at 100 lm/W is 8 W. That is where the familiar “9 W LED for a 60 W bulb” comes from; the exact answer depends on the efficacy of the lamp you buy, which its energy label gives.
How do I convert lumens to lux?
Lux is lumens per square metre on the surface, so you need the geometry. Divide the lumens by the beam’s solid angle Ω = 2π(1 − cos(θ/2)) to get candela, then divide by the square of the distance in metres. 800 lm in a 120° beam is 254.6 cd, and 63.66 lx at 2 m.
What is luminous efficacy?
Lumens of light out per watt of power in. It is the only thing linking the two units, and it spans more than twenty to one: about 10 lm/W for a small incandescent, 20 for halogen, 46–75 for compact fluorescent, and 75–217 for LED lamps.
Is a higher candela figure better than a higher lumen figure?
They answer different questions. Candela says how concentrated the beam is, lumens how much light there is in total. A narrow torch beam has high candela and modest lumens; a room lamp is the other way round. For lighting a room you want lumens; for throwing light a long way you want candela.
Related calculators
References
- Wikipedia, Luminous efficacy — luminous efficacy of a source, lm/W, with the overall luminous efficiency alongside: tungsten incandescent 40 W / 100 W at 230 V, 10.4 and 13.8 lm/W; 100 W at 120 V, 17.5 lm/W; tungsten halogen 100–500 W at 230 V, 16.7–19.8 lm/W; compact fluorescent 9–32 W with ballast, 46–75 lm/W; LED lamp 5–16 W at 230 V, 75–217 lm/W. Retrieved 24 September 2026.
- BS EN 12464-1, Light and lighting — Lighting of work places, Part 1: Indoor work places: maintained illuminance Eₘ. Values quoted here as reproduced by TECHLUMEN, Lighting standards guide (corridors 100 lx, staircases 150 lx, classrooms and retail sales areas 300 lx, offices, meeting rooms and food-service kitchens 500 lx, fine workshop tasks 500–1,000 lx) and by Fagerhult, Standard EN 12464-1 in brief (500 lx for a normal office workplace).
- Bureau International des Poids et Mesures. The International System of Units (SI Brochure), 9th ed., 2019. The candela as a base unit (683 lm/W at 540 THz), and the coherent derived units lumen (lm = cd·sr) and lux (lx = lm/m²).