# Going from normal to Log-normal implied volatility

Let's denote the Implied normal volatility (Bachelier) as $$\bar{v}$$, and the implied log-normal (Black Scholes) as $$v$$.

When everything else is known (spot, strike, maturity, rates etc) how can you go from $$\bar{v}$$ to $$v$$ and vice versa?

The math suggests that there must be a simple formula you can just plug but unfortunately I cannot find that formula. Of course I know that I can derive it myself, but I am just interested in the result. So the answer does not have to include the proof derivation.