# Difference between luminosity, luminous flux, and radiant flux?

I've looked this up, and was wondering the differences between them. Luminosity is the total energy emitted by a source, in watts. However, I'm confused about luminous flux and radiant flux. Since radiant flux is the total energy emitted by an object, would that make luminosity the same as radiant flux? Then how does luminous flux relate to luminosity? Is luminous flux just radiant flux, but only showing the visible light? And this website, https://www.ifa.hawaii.edu/~barnes/ASTR110L_S03/inversesquare.html, says lumens are a unit of luminosity, but how if lumens are candela times steradians?

• Recommend closing because this is a physics question, and further shows a significant lack of research. These terms are all well-defined. Feb 13 '17 at 16:18
• I think this is a perfectly valid question. While these concepts are technically physics related, they're most prominently used in astronomy. Furthermore, just because they're well-defined, does not mean OP finds it easy to understand them. General relativity is well defined but I'd still expect anyone new to the material to struggle in understand it. Feb 13 '17 at 18:52
• General relativity would also be off topic here, I think. Feb 14 '17 at 8:36
• This is a valid question, because it involves confusion between terms and measurements in astronomy, radiometry, and photometry (as opposed to photometry). These fields use some of the same words (e.g., "flux") in different ways, so the confusion is understandable. Apr 21 '19 at 8:56

Photometric units can often seem complex at first sight.

Luminosity

Luminosity refers to the total energy released by an object per unit time. This quantity is dimensionally equivalent to power, and is therefore measured in joules per second, or watts $(\mathrm{W})$. Another common unit is the solar luminosity $\mathrm{L}_{\odot} = 3.846 \times 10^{26}$ $\mathrm{W}$.

Luminous Intensity

Luminous intensity refers to the wavelength-weighted power emitted by a source in a particular direction. Wavelength-weighted is important here. Because the human eye is more sensitive to some wavelengths than others, this weighting is designed to set a standard for perception. This is set at $555$ $\mathrm{nm}$, the wavelength to which the human eye is most sensitive. This unit is called the candela $(\mathrm{cd})$, and is equivalent to a source emitting at $555$ $\mathrm{nm}$ with a power of $\frac{1}{683}$ $\mathrm{W}\cdot \mathrm{sr}^{-1}$. Essentially this is taking into account the fact that concentrating the same amount of light into a smaller solid angle will cause it to appear brighter. Finding the luminous intensity of a source with multiple wavelengths is a little more complicated. Let us define the following:

$I_v$ is the luminous intensity in candelas,

$I_e$ is the radiant intensity in watts per steradian, and

$\bar{y}(\lambda)$ is the standard luminosity function, which does the wavelength-weighting.

Then we can define the luminosity intensity of a multi-wavelength source to be:

$I_v = 683 \int_{0}^{\infty} \bar{y}(\lambda) \cdot \frac{dI_e(\lambda)}{d\lambda}d\lambda$

Luminous Flux

The luminous flux is equivalent to the total wavelength-weighted power emitted by a source. It is similar to luminosity. It is measured in the lumen $\mathrm{lm}$, which is equivalent to the candela-steradian $(\mathrm{cd}\cdot\mathrm{sr})$. One can imagine this as the human-useful amount of light emitted by a source.

The radiometric units are the same, except they refer to the true emitted power, with no wavelength-weighting.

In astronomy, luminosity is exactly as you've defined it.

In radiometry, the usual term for this is radiant flux. So, yes, they are the same thing.

Luminous flux, however, is different. It is a term from "photometry", which is the measurement of light *as perceived by the human eye" (I put it in scare quotes because in astronomy, the word "photometry" usually means measurement of light without any reference to human perceptions, and is sometimes casually used to refer to imaging or analysis of images). It is analogous to luminosity/radiant flux, but not the same thing, because it involves weighting the energy of the light by how well or poorly the human eye can sense it. (See the linked Wikipedia article for more details.)

Imagine a radio source that doesn't emit any visible light. An astronomer would say it has a luminosity of (say) $$X$$ watts. From a radiometric perspective, it has a radiant flux of exactly the same amount. But it would have a luminous flux of zero, since the human eye can't detect radio photons.

this website ... says lumens are a unit of luminosity, but how if lumens are candela times steradians?

Technically, that website isn't really correct, since it's casually equating luminosity (or radiant flux) with luminous flux.