Is retained earnings part of owner's equity?

Yes. Retained earnings is part of equity. It is the profit the business has earned over the years and kept: past years' net income added up, less what was paid out to the owners.

On a small business balance sheet, equity usually has a few lines: money the owners put in, money they took out (draws or distributions, often in their own account), retained earnings from past years and this year's net income. Together they make total equity, which many owners call owner's equity. Sole proprietors sometimes see it all as one owner's capital line. Same idea, different label.

Retained earnings is not cash. A business can show large retained earnings and a thin bank balance, because the profit went into equipment, debt payments or draws.

Switchbooks works this out for you. Under Equity on the Balance Sheet, this year's profit shows as Net Income and earlier years' profit as Retained Earnings, with no year-end closing entry to book. Draws stay in their own account.