Do capital gains and dividends get added on top of my regular income for bracket purposes?

They are stacked on top of your ordinary income but taxed on a separate rate schedule. First your wages and other ordinary income fill up the ordinary brackets. Then long-term capital gains and qualified dividends sit on top and are taxed at the preferential 0%, 15%, or 20% long-term rates, based on where your total income lands, per the IRS. So ordinary income can push your gains into a higher capital-gains rate, but the gains themselves do not push your wages into a higher ordinary bracket. Short-term gains, by contrast, are taxed as ordinary income. This stacking is why a low-income year can be a great time to realize gains at the 0% rate. See the Capital Gains tool at wealthserene.com/tools/capital-gains.