Calculate RMSE based on R squared and vice versa

Question

If for example I have the value of RMSE can I calculate the $R^2$? And vice versa if I have the value of $R^2$ can I calculate the value of RMSE?

I have all predictions, dataset, training set, and test set.

Answer 1

$$ R^2 = 1 - \dfrac{(RMSE)^2} { \sigma^2_y } $$

(Use the “population” variance calculation for $\sigma^2_y$.)

You have to have the denominator term in order to convert between $R^2$ and $RMSE$, but once you do, it’s just simple algebra.