You do not have to calculate exactly your estimated taxes. You just need to make an informed guesstimate. You estimate your marginal tax bracket and multiply it by the amount of the Roth conversion.
If you overestimate estimated taxes, you'll receive a refund. If you underestimate, you may have a penalty, but which will be much lower than if you didn't pay estimated tax.
Moreover, you won't have any penalty if estimated taxes (plus tax withholdings) are at least 90% of the current year's tax.
There is also a safe harbor amount of estimated taxes (for which there is no penalty) which is 100% of the previous year's tax (or 110% if your AGI is over $150,000 or over $75,000 if married filing separately).
Please read this IRS document for more information.