TaxWedge

Guides

The arithmetic, explained

Six things about UK pay that are true, computable, and almost never shown. Every figure in these is generated from the same engine as the tables — including the ones inside sentences.

  • 6 guides

    What these guides are for

    The calculators on this site answer a question about a number. These guides answer the questions behind the number — why the system produces the shape it does, which of its quirks are deliberate and which are accidents of two rules overlapping, and what any of it means for a decision you are actually making.

    Each one is built on the same engine as the calculators, so the figures in the prose are computed rather than quoted, and they update when a threshold moves. Where a guide states a rule rather than a number, the government page it comes from is listed on sources with the date it was read.

    Where to start

    If you read one, read the difference between your marginal and effective rate. Almost every other idea on this site depends on that distinction, and it is the one most commonly collapsed — including by people who know the tax system well. The effective rate describes what you have paid; the marginal rate decides what the next pound is worth, and they routinely differ by twenty points on the same payslip.

    After that, the two guides that describe rates nobody legislated: the £100,000 trap, where withdrawing the personal allowance taxes the same pound twice and produces a 60% band that appears in no rate table, and Scotland against the rest of the UK, where two independent sets of thresholds fail to line up and open a window in which further pay is taxed more heavily than it is twenty thousand pounds higher.

    The wedge is the site's organising idea and the reason for its name: of everything an employer spends to employ you, what share reaches you. The remaining two are practical — salary sacrifice, which is the one lever that reliably beats the system rather than merely describing it, and student loan repayment, which is not a tax and behaves exactly like one for every purpose that matters.

    Each one is checkable

    Every computed figure in a guide comes from the same engine as the calculators, and every rule it relies on is listed on sources with the government page it came from and the date that page was read. Where a guide is simplifying, it says so in the text.

    Why there are six rather than sixty

    A guide is only worth writing where the arithmetic on this site actually changes what someone would conclude. There is no shortage of UK tax topics; there is a shortage of ones where a computed marginal rate overturns the received explanation. These six are the ones where it does, and the list will grow slowly and only for that reason.

    Guides, not advice

    Nothing here is tax advice, and the distinction is not a formality: advice is given by someone who knows your circumstances and takes responsibility for the conclusion, and neither applies. These are explanations of how a published system behaves, with the arithmetic shown so you can disagree with it. For a decision that matters, check the figures against HMRC's own estimator or an accountant who has seen your papers.

    How to read a figure in one of these

    Every computed figure in a guide carries the tax year it belongs to, because a tax figure without a year is not a fact. The thresholds move on 6 April and occasionally in-year, and because every page is generated from one parameter file, a change regenerates the whole site rather than being patched into individual pages — there is no mechanism by which one guide could be left quoting last year's allowance while the calculators use this year's.

    Where a guide quotes a band boundary, that boundary was discovered by the engine rather than typed: the rate on the next pound is computed across the income range, the points where it changes are bracketed, and each bracket is bisected to the nearest pound. The result is then checked against the published statutory thresholds and the build fails if they disagree. That is why a threshold in a guide and a threshold in a table are always the same number.

    What they assume, and what they do not

    All of them assume a single employment taxed through PAYE on a standard tax code, with employment income only. None of them models benefits in kind, a second job, dividend or savings income, self assessment, or the benefit tapers — Universal Credit in particular produces marginal rates well above anything discussed here, and modelling it needs household circumstances a salary box cannot ask for. Where a guide is simplifying, it says so in the text rather than in a footnote.

  • Updated when the rates change

These are not explainers of things you could read on GOV.UK. Each exists because there is a question people demonstrably ask, and an answer that requires arithmetic nobody publishes.

The editorial rule is narrow, and worth stating because it decides what is not here. A guide gets written when the site can compute the answer from published rates — the shape of a marginal curve, what a rise is worth in the hand, what a pension contribution costs per pound of pot, how two tax regimes diverge at a given salary. It does not get written when the honest answer depends on circumstances the site cannot see. That is why there is a guide on what student loan repayment does to your marginal rate and none on whether to clear the loan early: the first is arithmetic, the second needs your interest rate, your thirty-year earnings path and your write-off date, and getting any of those wrong reverses the answer.

Every figure inside these pages — including the ones inside sentences — is generated at build time from the same engine as the tables. Numbers typed into prose are the part of a site that goes stale first and most quietly, because nothing fails when a threshold moves and a paragraph does not.

If you read one

Read the £100,000 trap if you earn near six figures or expect to. It is the most expensive thing in UK personal tax that almost nobody is told about until it has already happened to them — and the response to it, a pension contribution made inside the band, is worth more there than anywhere else in the system.

Read the wedge if you have ever negotiated a salary. It is the number your employer is actually deciding about, and it runs about ten points above the one on your payslip.