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Lets assume I have a source and receive $8 \times 10^{-20}$ ${\rm Wm}^{-2}$ in (400-750) nm filter. How do you convert this received flux to the unit Jansky, is there a formula? (Ultimately, I want to express this flux in magnitude AB.)

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    $\begingroup$ Just check the Wikipedia page for the Jansky: en.wikipedia.org/wiki/Jansky $\endgroup$ – Phiteros Dec 19 '16 at 19:00
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    $\begingroup$ Your source has a given flux in [energy/time], but Jansky is a measure of flux density in [energy/time/frequency bin] or, equivalently, [energy/time/wavelength bin]. Have a look at the link given by Phiteros, and the answer to the question Conversion of magnitudes to Jansky and MAGPHYS, which I think is so close to your question that I'm actually voting to close yours as a duplicate. $\endgroup$ – pela Dec 20 '16 at 8:52