Withdrawals from a pre-tax 401k are always subject to regular income tax. That could be 0, 12%, 22% or more depending on your other income, deductions and dependents.
If you are under age 59-1/2 there is an additional 10% penalty unless you qualify for a specific exception listed here. (See that IRAs and qualified workplace plans are listed differently, and some exceptions allowed for IRAs are not allowed for workplace plans.)
https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-exceptions-to-tax-o...
There is no exception for a general hardship. If you are still employed by the plan sponsor, you must show a hardship to make a withdrawal (and some plans do not allow any hardship withdrawals). But showing a hardship to permit a withdrawal is not the same thing as having an exception to the 10% penalty, they are different.
You will certainly owe more tax. How much, and how much it affects your refund, will depend on your overall income, how much you withdraw, any penalties or penalty exceptions, and how much tax you have withheld from the withdrawal. You can try this estimator.
https://www.irs.gov/individuals/tax-withholding-estimator
