Lumens (lm) to candela (cd) calculator and how to calculate.

## Lumens to candela calculator

Enter the luminous flux in lumens, apex angle in degrees and press the *Calculate* button to get the luminous intensity in candela:

Candela to lumens calculator »

### Lumens to candela calculation

For uniform, isotropic light source, the luminous intensity *I*_{v} in candela (cd) is equal
to the luminous flux Φ_{v }in lumens (lm),

divided by the solid angle *Ω* in steradians (sr):

*I*_{v(cd)} = *Φ*_{v(lm)} / *Ω*_{(sr)}

The solid angle *Ω* in steradians (sr) is equal to 2 times pi times 1 minus cosine of half the
cone apex angle *θ* in degrees (º):

*Ω*_{(sr)} = 2π(1 - cos(*θ*/2))

The luminous intensity *I*_{v} in candela (cd) is equal to the luminous flux Φ_{v }in lumens (lm),

divided by 2 times pi times 1 minus cosine of half the apex angle *θ* in degrees (º):

*I*_{v(cd)} = *Φ*_{v(lm)} / ( 2π(1 - cos(*θ*/2)) )

So

candela = lumens / ( 2π(1 - cos(degrees/2)) )

Or

cd = lm / ( 2π(1 - cos(º/2)) )

### Candela definition

The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10^{12} Hz, Kcd, to be 683 when expressed in the unit lm W^{–1}, which is equal to cd sr W^{–1}, or cd sr kg^{–1} m^{–2} s^{3}, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.

The candela (/kænˈdɛlə/ or /kænˈdiːlə/; symbol: cd) is the base unit of luminous intensity in the International System of Units (SI); that is, luminous power per unit solid angle emitted by a point light source in a particular direction. Luminous intensity is analogous to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the standard luminosity function (a model of the sensitivity of the human eye to different wavelengths). A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.

The word candela is Latin for candle. The old name "candle" is still sometimes used, as in foot-candle and the modern definition of candlepower.

### Lumen definition

The lumen (symbol: lm) is the SI derived unit of luminous flux, a measure of the total quantity of visible light emitted by a source per unit of time. Luminous flux differs from power (radiant flux) in that radiant flux includes all electromagnetic waves emitted, while luminous flux is weighted according to a model (a "luminosity function") of the human eye's sensitivity to various wavelengths. Lumens are related to lux in that one lux is one lumen per square metre.

If a light source emits one candela of luminous intensity uniformly across a solid angle of one steradian, the total luminous flux emitted into that angle is one lumen (1 cd·1 sr = 1 lm). Alternatively, an isotropic one-candela light-source emits a total luminous flux of exactly 4π lumens. If the source were partly covered by an ideal absorbing hemisphere, that system would radiate half as much luminous flux—only 2π lumens. The luminous intensity would still be one candela in those directions that are not obscured.

The lumen can be thought of casually as a measure of the total amount of visible light in some defined beam or angle, or emitted from some source. The number of candelas or lumens from a source also depends on its spectrum, via the nominal response of the human eye as represented in the luminosity function.

The difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread. A flux of 1000 lumens, concentrated into an area of one square metre, lights up that square metre with an illuminance of 1000 lux. The same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Mathematically, 1 lx = 1 lm/m^{2}.

A source radiating a power of one watt of light in the color for which the eye is most efficient (a wavelength of 555 nm, in the green region of the optical spectrum) has luminous flux of 683 lumens. So a lumen represents at least 1/683 watts of visible light power, depending on the spectral distribution.

Lumens to candela calculation »

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