Computing i0 in the Butler-Volmer equation: How to interpret Wikipedia and Wolfram Alpha So far, when using the Butler-Volmer equation, I had j0 given and could then just use I = A * j0 * [exp(...) - exp(...)], with A the electrode surface area.

Now I have a material from which I don't know j0 but just the rate constant. According to Wikipedia on exchange current density I can compute j0 as 



Wolfram-Alpha on Butler-Volmer equation however says:



In this equation, the expression F * k0 would correspond to the above j0. k0 is explicitly defined as the rate constant in m/s on that same page.

Is Wolfram-Alpha wrong by missing out the concentration? The F * k0 does not even result in the units of a current density, and the whole expression will not evaluate as a current.
k0 has units of frequency (1/time)
All concentrations are surface concentrations (mol/area)

Sometimes people use k0 with units length/time and volume concentrations (mol/volume)

On Wikipedia: Coxy stands for Ox concentration * at equilibrium *. Cred stands for Red concentration * at equilibrium *. It's for 1 electron. Multiply by n for n electrons. 

On Wolfram: [Ox] stands for Ox concentration at electrode, [Red] stands for Red concentration at the electrode. These concentrations are not necessarily at equilibrium.