Tool · Units and conversions

Lumens to Watts Converter

How many watts are in a lumen? It depends on the spectrum: the converter goes between luminous flux and power for a single wavelength using the CIE luminous efficiency tables, for thermal light from a blackbody at any temperature, or for a lamp whose efficacy in lumens per watt is known, in daylight or night vision. Background: radiometry and photometry and visible light.

Convert

You have

Luminous flux (lm)

Lumens measure light as the eye weighs it; watts measure power. The conversion needs the spectrum, chosen below.

Light source

Spectrum

Wavelength (nm)

Temperature (K)

Luminous efficacy (lm/W)

Eye

For a lamp, the efficacy on its data sheet is lumens per electrical watt and already includes the losses of the lamp and its driver; the watts found are then electrical watts.

Presets

Readouts

Luminous efficacy of one wavelength

Blue: 683·V(λ), daylight. Dashed orange: 1700·V′(λ), night. At night the eye is more sensitive overall and its peak moves from 555 to 507 nm.

Efficacy of blackbody radiation

The efficacy of thermal light peaks near 6600 K, where it is 95.4 lm/W photopic; an incandescent filament near 2856 K manages about 16. Most of its output is infrared.

Learn with it

Two short experiments. Each one sets the inputs, says where to look, and asks for a prediction before it shows the result.

Checked against

These checks run in your browser on every load. The efficacies are compared with the CIE table values and with the SI definition of the candela.

Check	Expected	Computed	Tolerance

The expected values are 683·V(λ) with V from the CIE 1924 table, 1700·V′(λ) from the CIE 1951 table, and the definition K_cd = 683 lm/W at 540 THz (555.016 nm). The tolerance is the largest difference from Expected that still passes, relative to Expected or to 1, whichever is larger.

The model

Luminous flux is radiant power weighted by the eye’s spectral sensitivity,

Φ_{v} = K_{m} \int Φ_{e, λ} (λ) V (λ) d λ, K_{m} = 683 l m / W

where $V (λ)$ is the CIE photopic luminous efficiency, equal to 1 at 555 nm. The SI fixes the luminous efficacy of 540 THz radiation (555.016 nm) at exactly 683 lm/W in its definition of the candela. For one wavelength the efficacy is simply $683 V (λ)$ . For night vision the scotopic curve $V^{'} (λ)$ , peaking at 507 nm, is used with $K_{m}^{'} = 1700 l m / W$ . For a blackbody the calculator integrates the Planck spectrum against $V (λ)$ from 380 to 780 nm and divides by the total radiated power $σ T^{4}$ :

K (T) = \frac{683 \int_{380}^{780} M_{λ} (λ, T) V (λ) d λ}{σ T^{4}}

A lamp’s rated efficacy is lumens per electrical watt and already includes the conversion losses, so the watts found from it are electrical. The tables are the CIE 1924 photopic and CIE 1951 scotopic functions at 1 nm; mesopic vision, in between, is not modeled.

Worked example

A 5 mW green laser pointer at 532 nm, where $V = 0.8850$ , gives $683 \times 0.8850 \times 0.005 = 3.022 l m$ . A red pointer of the same power at 650 nm ( $V = 0.107$ ) gives 0.3654 lm, about 8.3 times less. A blackbody at 2856 K, close to an incandescent filament, has an efficacy of 16.45 lm/W, so 1000 lm needs 60.8 W of radiated power; at 5772 K the efficacy is 92.03 lm/W, still only 13.47 % of 683 lm/W.

Related: the wavelength to color converter uses the same tables, the Wien’s law calculator gives the blackbody peak, and the photon flux calculator counts photons instead of lumens.

References: Bureau International des Poids et Mesures, The International System of Units (SI), 9th ed. (2019), definition of the candela. CIE 018:2019, The Basis of Physical Photometry, 3rd ed. W. R. McCluney, Introduction to Radiometry and Photometry, 2nd ed., Artech House (2014).