How do you calculate the volatility contribution of individual assets in a portfolio?

You can calculate a Portfolio Covariance Matrix like this one below.

This Covariance matrix represents a Portfolio with Stocks and ETFs. The diagonal in the matrix that is highlighted are the calculated Variances of each security in the Portfolio. The Variance shows how far each security is from the mean and the Square Root of the Variance (SQRT) is the Volatility. The other outputs are the Covariances which show the degree in which two assets move together.

This is a good way to see the contribution each security has to the overall portfolio but when actually calculating the Portfolio Volatility you need to use the entire Covariance matrix, the security weightings, and matrix math to calculate the Portfolio Variance and Volatility.

Cheers.