Stockholders' equity does not include dividends. Stockholders' equity is the value left over -- or in some cases the debt -- when liabilities are deducted from assets. On financial statements, the "Stockholders' Equity" section appears as the third section on the balance sheet. Dividends appear under "Financing Activities" on the cash flow statement and also on the income statement.
The basic equation for stockholders' equity is assets minus liabilities. Stockholders' equity is therefore the surplus value that a company generates, above the retail value of its assets. The surplus value is attributed to stockholders as the owners of the company and therefore the owners of the company's profits. Dividends are not part of stockholders' equity because they are defined once they are paid out; stockholders' equity stays with the company.
The accounting within the "Stockholders' Equity" section is notoriously boring. The section details the change in stock that the company holds or issued and notes the profits that it put back into the company, labeled "Reinvested Capital." While reinvested capital and dividends are both uses for cash profits, dividends do not appear in stockholder equity accounting.
Dividends are an act, as opposed to a thing that the company holds or an obligation it has. A company decides to distribute some of its profits to stockholders; when the company parcels out the profits, the profits become dividends. The full value of the dividends is then transferred from the company to its shareholders.
Dividends pop up in two places in companies' financial statements. Dividends first appear on the income statement, where companies list the dividend amount for each share for the quarter. The total value of dividends appears in the third section of the cash flow statement, where it is listed as an activity that takes an amount of cash out of the company.