If you don't have money out-of-pocket to pay taxes, you need to withdraw beyond the conversion amount, and this results in more taxes, and also a penalty (penalty only for people below 59-1/2). Then, you need to withdraw more, and this leads to more taxes, and penalty. So how to compute this?
As an example, I worked out the OP's info. See if I am correct.
Suppose you want to have $50K in income by Roth conversion, and have no other sources of income.
For a married couple filing jointly, you are allowed a standard deduction of $25,100. This means your taxable income is $24,900. The Fed tax on this $24,900 is $2,590.
You will also have to pay a state income tax. Let's say that your state tax is $645, for a combined tax of $2590+$500 = $3235.
Case 1) $50,000 withdrawal, $50,000 conversion, $2,590 Fed tax, $645 state tax, $0 penalty -> Need $3,235 out of pocket
If you don't have this $3235 cash you will have to bump up the $50,000 to have extra for taxes. But then, the additional $3,235 is now income to be taxed, plus the 10% penalty.
Case 2) $53,235 withdrawal, $50,000 conversion, $2,978 Fed tax, $729 state tax, $324 penalty -> Need $796 out of pocket ($2,978 + $729 + $324 - $3,235) .
Let's bump the additional $3,235 to $3,235 + $796 = $4,031.
Case 3) $54,031 withdrawal, $50,000 conversion, $3,074 Fed tax, $749 state tax, $403 penalty -> Need $195 out of pocket ($3,074 + $749 + $403 - $4,031).
As you can see, increasing the withdrawal to pay for tax leads to more taxes and penalty. However, the amount ouf-of-pocket keeps getting smaller and smaller. If you keep the iteration, eventually it will converge.
A quicker way to compute this is to recognize that it is a geometric series. Each $1 you withdraw above the $50,000 for conversion costs you 12% for Fed tax, 2.6% for state tax (I use AZ tax here), and 10% for penalty. For each $1 that you withdraw, you only have 75.4c left. In order to obtain the original $1, you will need to withdraw 1/0.754 = 1.326. For the original amount of $3,235 that you do not have out-of-pocket, you will need to withdraw $4,290.
Let's check it out.
Case Final) $54,290 withdrawal, $50,000 goes to Roth, $3,105 Fed tax, $756 state tax, $429 penalty. No money out of pocket.
Conclusion: It takes $54,290 of withdrawal to convert $50,000, because your total tax+penalty is $4,290. Your ACA income is $54,290.
The net effective rate of the conversion is 7.9%. That's excellent because you make use of your standard deduction when your income is low. Wait till you draw SS or pension or IRA. Your tax rate will be much higher.