There are two paragraphs, not one, and the second is the one nobody quotes. The IRS's own page splits them exactly the way the statute does:
Both run at 0.5 percent a month to a 25 percent ceiling. The (a)(3) branch is what applies after an examination adjustment or a notice proposing additional tax: the balance was never on the return, so there was no due date for it until the IRS demanded it. That $100,000 threshold is a fixed statutory amount. It looks like the kind of round number that would be indexed, and it is not; section 6651(j) indexes only the 60-day minimum filing penalty.
The base shrinks month by month, and the IRS's one-line version hides that. The IRS says the "unpaid tax is the total tax required to be shown on your return minus amounts paid through withholding, estimated tax payments and allowed refundable credits." Section 6651(b)(2) is more precise: the amount shown "shall, for purposes of computing the addition for any month, be reduced by the amount of any part of the tax which is paid on or before the beginning of such month and by the amount of any credit against the tax which may be claimed on the return." So the penalty is recomputed each month against a declining balance, and every partial payment reduces every future month's charge. Section 6651(b)(3) does the same job for the (a)(3) branch, reducing the amount stated in the notice and demand by any part of the tax "paid before the beginning of such month", though it carries no parallel reduction for claimable credits. Section 6651(c)(2) adds a small fairness rule: where the tax actually required to be shown is less than what the return showed, the lower figure is used.
An extension to file is not an extension to pay, and this is the most common misconception on the subject. Section 6651(a)(2) measures from the date prescribed for payment "determined with regard to any extension of time for payment", which is a different and much rarer thing than the automatic extension of time to file. An extended return stops the filing penalty and does nothing to the payment penalty. There is one important relief: Treasury Regulation section 301.6651-1(c)(3) presumes reasonable cause for the extension period where at least 90 percent of the tax shown on the return was paid by the original due date and the balance is remitted with the return. That safe harbor is covered in full, with a worked example, on the extension page.
The rate moves in both directions, and both moves are statutory.
Downward: section 6651(h), "Limitation on penalty on individual's failure to pay for months during period of installment agreement", provides that "In the case of an individual who files a return of tax on or before the due date for the return (including extensions), paragraphs (2) and (3) of subsection (a) shall each be applied by substituting '0.25' for '0.5' each place it appears ... for any month during which an installment agreement under section 6159 is in effect for the payment of such tax." Two conditions bind and one of them is easy to drop: the return must have been filed by its due date including extensions, and a section 6159 installment agreement must be in effect. A late-filed return does not get the reduced rate however faithfully the plan is paid. The statute conditions the relief on an agreement "under section 6159", and nothing published establishes that the IRS's fee-free 180-day short-term payment plan is one, so treat the reduction as belonging to a long-term installment agreement.
Upward: section 6651(d) substitutes "1 percent" for "0.5 percent" for each month beginning after the earlier of "the day 10 days after the date on which notice is given under section 6331(d)", the notice of intent to levy, or the day a jeopardy notice and demand for immediate payment is given. Note what triggers it. It is the notice, not the levy, and it is ten days after that notice rather than thirty, so the rate can double while the taxpayer still has time left in the 30-day window to request a hearing.
The interaction rule, and the floor inside it. Where both penalties apply in the same month, section 6651(c)(1) reduces the filing penalty by this one: "the amount of the addition under paragraph (1) of subsection (a) shall be reduced by the amount of the addition under paragraph (2) of subsection (a) for any month (or fraction thereof) to which an addition to tax applies under both paragraphs (1) and (2)." The IRS's own worked version is exact and worth quoting: "instead of a 5% failure to file penalty for the month, we would apply a 4.5% failure to file penalty and a 0.5% failure to pay penalty." So a return that is both late and unpaid costs 5 percent a month in total rather than 5.5. The same paragraph then adds a limit the IRS's page does not mention: in a case covered by the 60-day minimum, "the amount of the addition under paragraph (1) of subsection (a) shall not be reduced under the preceding sentence below the amount provided in such last sentence." The reduction can never take the filing penalty below the 60-day floor.
The two ceilings are reached at wildly different times, and that is the reason the advice runs the way it does. Both penalties cap at 25 percent, but at 5 percent a month the filing penalty gets there in five months and at 0.5 percent a month this one needs fifty. The IRS puts it plainly: "After 5 months the failure to file penalty will max out, but the failure to pay penalty continues." Anyone choosing between filing a return they cannot pay and not filing at all is choosing between a slow charge and a fast one.
No proration. The IRS states it directly: "We apply full monthly charges, even if you pay your tax in full before the month ends." The statute's words are "or fraction thereof", so a balance cleared on the second day of a month costs the same as one cleared on the last.
Reasonable cause here has a different content from reasonable cause for filing late. Treasury Regulation section 301.6651-1(c)(1) provides that a failure to pay is due to reasonable cause "to the extent that the taxpayer has made a satisfactory showing that he exercised ordinary business care and prudence in providing for payment of his tax liability and was nevertheless either unable to pay the tax or would suffer an undue hardship" if they paid on time. The regulation then illustrates the boundary bluntly: a taxpayer who "incurs lavish or extravagant living expenses" such that nothing is left for the tax, or who "invests funds in speculative or illiquid assets", has not exercised ordinary business care and prudence. The IRS's administrative relief for a clean three-year record also reaches this penalty, and is described on the failure to file page; under the automatic version the IRS says the failure to pay penalty "does not accrue and is not assessed on unpaid tax" at all.
A quiet asymmetry in section 6651(g). A substitute return the IRS prepares under section 6020(b) is disregarded for the filing penalty, but 6651(g)(2) provides that it "shall be treated as the return filed by the taxpayer for purposes of determining the amount of the addition under paragraphs (2) and (3)". So an IRS-prepared return does not stop the filing penalty and does start this one.
Interest is separate and runs on top. The IRS charges interest on penalties, at the rate it sets quarterly under section 6621, and adds the corollary that constrains any request for relief: "By law we cannot remove or reduce interest unless the penalty is removed or reduced."