The variance of $\hat \beta_j$ can be written as
$Var(\hat \beta_j) = \frac{\sigma^2}{\sum (x_{i,j} - \bar x_j)^2} \times \frac{1}{1-R^2_j}$
where $R^2_j$ is the [[coefficient of determination]] for $x_j$ regressed on all other predictors in the model.
The second term is known as the variance inflation factor (VIF) for predictor $x_j$.
$VIF_j = \frac{1}{1-R^2_j}$
If VIF is less than 5, [[multicollinearity]] is not considered a problem. VIF over 10 is evidence of multicollinearity.