How to convert magnitudes to bolometric luminosity?

• If we know a star's magnitudes from several bands(say u,g,r,i,z,J,H,k) and the star's distance, how to calculate Lbol?

Let's suppose the star has a black body spectrum. Is there any manual about the calculation? It's better to have a lot of technical details.

Are you looking for something more complicated than find a bolometric correction?

@Rob yes, these objects are cool and bright in infrared, but I know their magnitudes from 2MASS and WISE, and even Sloan. Convert magnitudes to flux and fit using a blackbody model is enough?

They are certainly not blackbodies. You would need to fit with proper stellar models.

@Rob If we know magnitudes and stellar type, how to calculate Lbol?

@Rob Do you know any table like this (https://sites.uni.edu/morgans/astro/course/Notes/section2/spectraltemps.html)? Perhaps a table is a more direct way for me, but spectral types are sort of sparse especially for cool objects in this table.

@Rob A table(especially for cool objects) does not appear in that question.

I have added a reference to a relevant table for cool objects.

• Quoting from Wikipedia,

The bolometric magnitude Mbol, takes into account electromagnetic
radiation at all wavelengths. It includes those unobserved due to
instrumental pass-band, the Earth's atmospheric absorption, and
extinction by interstellar dust. It is defined based on the luminosity
of the stars. In the case of stars with few observations, it must be
computed assuming an effective temperature. Classically, the
difference in bolometric magnitude is related to the luminosity ratio
according to:

$M_{bol,*} - M_{bol,sun} = -2.5log_{10}(\frac{L_*}{L_{sun}})$

In August 2015, the International Astronomical Union passed Resolution
B2[7] defining the zero points of the absolute and apparent bolometric
magnitude scales in SI units for power (watts) and irradiance (W/m2),
respectively. Although bolometric magnitudes had been used by
the absolute magnitude-luminosity scales presented in various
astronomical references, and no international standardization. This
led to systematic differences in bolometric corrections scales, which
when combined with incorrect assumed absolute bolometric magnitudes
for the Sun could lead to systematic errors in estimated stellar
luminosities (and stellar properties calculated which rely on stellar
luminosity, such as radii, ages, and so on).

[leading to the accepted definition of]
$M_{bol} = -2.5log_{10}(L_*) + 71.1974...$ , where the constant term is the zero-point luminosity $L_0$ .

Dunno if this helps, other than that you have to determine the spectral luminosity of the star in question.