How this calculator works
A spherical star with effective temperature T emits the same total power as a blackbody of its radius at that temperature. Effective temperature is defined by this total-power relationship even when the spectrum is not a perfect blackbody. Absolute bolometric magnitude uses the exact IAU B2 luminosity zero point, not a rounded solar magnitude. The distance modulus assumes no extinction and a nearby Euclidean geometry. Visual-band magnitudes require bolometric corrections before use here.
Formula
L = 4 pi R^2 sigma T^4; M_bol = -2.5 log10(L/3.0128e28 W); m_bol-M_bol = 5 log10(d/(10 pc)). L_sun_nom = 3.828e26 W; R_sun_nom = 695700000 m.
Worked example
A source with absolute bolometric magnitude 0 has luminosity exactly 3.0128e28 W. If its apparent bolometric magnitude is 5, its distance is 100 pc.
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Frequently asked questions
Can I enter visual magnitude?
Convert it to bolometric magnitude first. Visual brightness omits radiation outside that filter.
Are nominal solar radius and luminosity measurements?
They are exact conversion constants fixed by IAU 2015 B3. The physical Sun varies.
Does dust change the distance result?
Yes. Uncorrected extinction makes a source appear fainter and causes the simple distance modulus to overestimate distance.