It is possible. the income tax calculation is on your total income including wages and Business. The standard deduction could bring your income tax to zero.
The profit from your business then goes through a second tier of taxes. That is the se tax. You already took your deductions against the business, there is no other standard deduction.
The self-employment tax rate is 15.3%. That rate is the sum of 12.4% for Social Security and 2.9% for Medicare.
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