Methodology

The principle: compute, cite, date

Every number on this site is produced by a deterministic engine from constants that carry three things: the document they were read from, the URL of that document, and the date someone read it. There are 105 such constants across federal, withholding, deduction limits, 51 state rule sets, 3,672 local jurisdictions, labour rules and price indices, and the sources page lists all of them with a CSV export. Nothing is typed into a page by hand: a salary figure in a sentence is the engine's output for the inputs the sentence names, so that when a constant changes, every sentence that depends on it changes with it. The AI layer, where a page offers it, receives the computed figures and is prevented from producing any number of its own; that boundary is described below. And the site publishes what it does not model, on the calculator itself and on this page, because a calculator that is silent about its limits is asking to be trusted rather than checked.

The date matters as much as the document. Tax figures change every January, some mid-year, and the most common failure across the calculators compared on this site is not a wrong formula but a right formula fed last year's constants. Each page shows the figures it used and when they were checked; the changelog records every change to a constant with the reason; and the sidebar's data-status card is computed from the constants themselves, so it cannot be forgotten.

Federal income tax: the annual computation

The annual federal income tax that drives the «refund or owed» figure is computed as the Internal Revenue Code describes it: gross wages minus pre-tax deductions gives adjusted income; minus the standard deduction ($16,100 single, $32,200 joint, $24,150 head of household in 2026, from IRS Rev. Proc. 2025-32, § 3.14) or itemised deductions gives taxable income; the seven brackets for the filing status (IRS Rev. Proc. 2025-32, § 3.01, Tables 1-4) give the tax; credits reduce it. The brackets are stored with the cumulative tax at each threshold as printed in the Revenue Procedure, which lets the tests check the engine's bracket arithmetic against the IRS's own figures rather than against a formula. Additional standard deduction amounts for age and blindness, the $2,200 child tax credit and its refundable part, and the 2026 deductions from Public Law 119-21 for overtime premium (up to $12,500), tips (up to $25,000), seniors and car-loan interest are applied here, at the annual level, because that is where the law applies them.

Federal withholding: Publication 15-T, derived

Per-paycheck federal withholding follows the percentage method for automated payroll systems in Publication 15-T: annualise the period's taxable wages; add W-4 step 4(a) other income; subtract step 4(b) deductions; subtract the step 1 allowance ($12,900 joint, $8,600 otherwise, halved when box 2(c) is checked); look the result up in the table for the filing status (the standard table or the step 2 checkbox table); divide the tentative annual amount by the pay periods; subtract step 3 credits per period, not below zero; add step 4(c). A pre-2020 W-4 on file is computed by the older method with the allowance value the publication gives.

The tables themselves are marked «derived» rather than «verified», and the distinction is deliberate. Publication 15-T's tables are the brackets and standard deduction rearranged: the zero-rate band at the bottom of each table plus the step 1 allowance equals the standard deduction, and the bands above it are the brackets. This site builds the tables from the verified 2026 brackets and deduction by that rule (IRS Publication 15-T (2026), Section 1 — Percentage Method Tables for Automated Payroll Systems; Form W-4 (2026)), and the tests confirm the derived tables reproduce the published ones for the standard and checkbox cases. Saying «derived» tells the reader exactly how much to trust them: as much as the brackets and the rule, no more.

Supplemental wages — bonuses, commissions, severance, vacation payouts — are withheld at the flat 22% when paid separately (37% above $1,000,000 in the year) or by the aggregate method when combined with regular wages, exactly as Treas. Reg. § 31.3402(g)-1 allows the employer to choose; the bonus pages show both.

Social Security and Medicare

Social Security is 6.2% of FICA wages up to the $184,500 wage base (SSA, Contribution and Benefit Base 2026; IRS Topic no. 751); Medicare 1.45% with no cap; the Additional Medicare Tax 0.9% above $200,000 of year-to-date wages regardless of status, as employers must withhold it, with the statutory thresholds by status applied to the annual figure. FICA wages are gross minus Section 125 deductions and not minus retirement deferrals, which is the single most common configuration error in payroll and the first line the stub checker tests. Year-to-date wages entered in the calculator move the cap to the right paycheck. Self-employment tax on the self-employed page applies both halves to 92.35% of net earnings and deducts half from income, per IRC §§ 1401–1402 and 164(f).

The 51 states: rules, verification, publication

Each state has a rule set: the system (9 states with no wage tax, 13 with a flat rate, 29 with brackets), the brackets by status and the rule for joint filers (doubled, same, or a custom schedule), the standard deduction, the personal exemption and whether it is a deduction or a credit, whether the state has local wage taxes, and a public note. Each rule set carries the revenue department's document and the date it was read, and a verification status: «primary» when read from the state's own publication, «compiled» when taken from a secondary source and pending the primary. 40 of 51 are primary today.

The verification log below records, state by state, what was checked, against which document, and what came out. 21 match; 12 did not match the compiled figure and were corrected (Arizona, California, Georgia, Oregon, New Jersey, Massachusetts, Maryland, Ohio, South Carolina, Mississippi, Hawaii, Louisiana); 1 are waiting for the state to publish its 2026 figures; 1 could not be read automatically and are being read by hand. 37 of the entries record a rule the compiled source omitted — a credit given as a flat amount rather than a deduction, a joint schedule that does not double, a deduction that phases out — and those findings feed the engine's backlog. State withholding on each paycheck is the annual state tax divided by the pay periods, which reproduces the state's percentage-method tables for the standard case and differs from them where a state's tables build in a credit differently; the state page says so where it does.

Local wage taxes

The local layer covers 3,672 jurisdictions in 7 states: every Pennsylvania municipality and school district from the DCED register (resident, non-resident and local services tax); Ohio municipalities and school districts with their credits; every Indiana county; every Maryland county with the non-resident rate; the Michigan cities with a tax; New York City's resident schedule; and 12 named cities elsewhere (Philadelphia, Louisville, Kansas City and others). Each applies the state's own rule for residents and non-residents. Cities whose charge could not be verified against a primary source — Yonkers, Birmingham, St. Louis, Kansas City, Denver, Wilmington, Newark, Charleston — are described on their pages with the source and are not applied by the engine, which is the honest treatment of a figure that has not been checked.

What is not modelled

State disability and paid family leave contributions (California, New York, New Jersey, Rhode Island, Hawaii, Washington, Massachusetts, Colorado, Oregon, Connecticut), which appear as separate lines on the stub. US territories. The alternative minimum tax. Itemised deductions beyond the amount entered. Credits other than the child tax credit and those entered on the W-4. The earned income credit at the paycheck level. Employer-side taxes outside the payroll calculator. State-specific supplemental rates where a state publishes one (the state line on a bonus uses the annual rule). Reciprocity agreements between states for cross-border commuters. Each of these is named on the calculator's «not covered» list where it matters, and the list shrinks as items are built and verified; nothing is added to the engine before its source is in the table.

How the engines are tested

The test suite checks the federal engine against the cumulative tax figures printed in the Revenue Procedure at every bracket threshold for every status; the withholding engine against the published Publication 15-T tables for the standard and checkbox cases and against worked examples from the publication; FICA against the cap and the Additional Medicare threshold; and the state engines against the examples each state publishes in its withholding guide where it publishes any. The paycheck engine is tested for the invariant that net equals gross minus every line to the cent after rounding, for the Social Security cap landing on the right paycheck given year-to-date wages, and for the supplemental methods. Tests run on every change; a change that alters a published figure without a changelog entry fails.

The data pipeline

Documents are read — the Revenue Procedure, the SSA notice, each state's withholding guide, each local register — and the figures are typed into constants with the document, URL and date beside them. Tests run against the documents' own examples. The engine computes; the pages render the engine's output; the sitemap and the data-status card are generated from the same constants. Every page carries the figures it used and their dates. Readers report discrepancies through the form on each page; reports are checked against the source; corrections are published with the date and the cause. The changelog is the audit trail of the whole loop. The Paycheck Reality Index closes it from the other side: anonymous submissions of real stubs against the computed figure, aggregated by state and salary band and published once a cell has thirty of them, so that the site's accuracy is measured by its readers rather than asserted by its author.

The AI boundary

The «Explain my paycheck» button sends the computed figures — gross, each tax, the marginal and effective rates, the deduction used, the caveats — to a language model with instructions to explain them in plain English. It receives nothing you typed except those figures, and no identifying data. Its reply is checked before it is shown: any number in the reply that is not one of the figures it was given, or a rounding of one, causes the reply to be discarded. The model cannot compute, cannot look anything up, and cannot change a figure; it can only describe what the engine produced. Requests are cached by rounded profile, rate-limited by address, and capped per month; when the cap is reached the explanation pauses and every number on the page is unaffected. The model is a commodity provider chosen for cost; its identity does not matter because it is never a source.

Reproducing any figure

Pick a parameter in the tool above and it shows the value the engine uses, the document it was read from, the date and the status. For a whole paycheck, the API returns the same engine's output with the sources in the response, and the walkthrough on the withholding guide prints every intermediate number of the federal computation. $75,000 in California, biweekly, single, no deductions: gross $2,884.62, federal $295.00, Social Security $178.85, Medicare $41.83, state $106.71, net $2,262.23 — reproducible from Rev. Proc. 2025-32, Publication 15-T and the California Employment Development Department's 2026 guide.

Corrections and the changelog

Anything wrong is corrected in the data, not in the prose, so that every page that depended on the figure changes at once; the correction is listed on the corrections page with the date, the page, what was wrong, what the source says and who reported it (anonymously unless they ask otherwise). Changes to constants for any other reason — a new year, a mid-year law, a newly verified state — go to the changelog with the reason. Neither list is ever pruned. The site covers 1,533 pages from one engine, which is the only way a correction can reach all of them the same day.