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IRA and 401(k) accounts allow you to save without paying taxes first. You pay the taxes when you withdraw money from these accounts.
If you want an amount (X), and you have no other funds with which to pay the taxes (T0) on this amount, you need to withdraw not X, but X+T0. But then you also need the funds to pay the taxes (T1) on the taxes (T0), and the taxes (T2) on those taxes (T1), and so on.
Plus, if you are under 59.5, there is an additional tax penalty (P) of 10% of the complete withdrawal.
So if you want X, you need to withdraw Y, where Y = X + T + P, and P (the penalty) is either 0 or 10% of Y, and T is the taxes on Y.
This web page uses the 2020 Tax Tables to compute Y, given the amount you want to withdraw and the base income that you have without the withdrawal. It also needs to know your filing status, and whether or not there is a penalty (are you under 59.5?). It computes the tax strictly from the tax tables, so it does not handle deductions or exemptions, or AMT, or capital gains, or phasing out of various credits and deductions. All that is rolled into your base income.
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