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Converting units is simple if you simply work with the units as algebraic symbols. Thus start with the equalities $$1\textrm{ cal}=4.18\text{ J},$$ $$1\text{ day}=24\times60\times60\text{ s}=86,400\text{ s, and}$$ $$1\text{ cm}=0.01\text{ m}$$ and just plug the numbers in: $$1\text{ cal cm}^{-2}\text{ day}^{-1} =\frac{4.18\text{ J}}{(0.01\text{ m})^2 \times ... 0 Genie already stated the definition of brilliance: Number of photons per second per mm2 per rad2 per 0.1% bandwidth. Of the parameters you have listed, you are missing the divergence of the beam (needed to get rid of the "per rad2" in the formula for brilliance). However, I see at the APS link given that for each beamline, the APS provides pure flux ... 1 I am not sure about this, but I think a “measure equation” is something astronomers seem to like a lot:$$ \frac\Gamma H \approx \left( \frac T{1.6\cdot 10^{10} \, \mathrm K} \right)^3 $$Or for absolute, relative magnitude and distance (although I am sure I mixed something up):$$ m - M = 5 - 5 \log\left(\frac{R}{10 \, \mathrm{pc}}\right) $$So equations ... 2 There were historically several systems of units (ancestors to modern SI, CGS electric, CGS magnetic, CGS Gaussian, CGS by Heaviside), and the ultimate choice in favour of Gaussian CGS was made when Special Relativity has united electric and magnetic fields into one electromagnetic field tensor. Only in Gaussian (and Heavisidian) versions, these fields take ... 5 The natural way to write it in this notation is$$F = q(E + \beta \times B)$$where \beta is the velocity measured in natural units - the velocity as a fraction of the speed of light. In the CGS system, we instead write \beta = \frac{v}{c} and the equation becomes$$F = q(E + \frac{v}{c} \times B) That's not silly enough, though, so we go really ...