Personal savings allowance calculator — methodology

The calculation, in order

1. Hand the other income and the interest to the income tax engine together, as one taxpayer. The personal allowance is deducted first, allocated across income types in whichever way produces the lowest bill.
2. The starting rate band, reduced pound for pound by non-savings taxable income.
3. The personal savings allowance, whose tier is decided by the band that total taxable income reaches — interest included.
4. Interest above both, at the ordinary rates.
5. Ask again with the “unused” allowance actually received, and subtract. That is what the spare allowance costs.
6. Locate the pound that steps the allowance down, and price it and the pound before it.

starting rate band = max(0, £band − non-savings taxable income)
allowance tier     = f(total taxable income)          ← interest is INSIDE this

cost of "unused"   = tax(interest + unused) − tax(interest)
value of allowance = tax(interest + unused + allowance) − tax(interest + unused)

next £100          = tax(interest + £100) − tax(interest)   ← on SAVINGS income

There is no tax arithmetic on this page. Every figure is a difference between two engine answers, or a units conversion over one of the engine’s own thresholds.

Why an unused allowance is not headroom

The engine reports the allowance as a row with available, used and remaining, and the obvious caption for remaining is “tax-free interest still available”. That caption is the trap, and the reason is circular in a way that is easy to miss: the interest is part of what decides how large the allowance is.

On £50,000 of salary the row shows £1,000.00 available and nothing used. Receive exactly that much interest and total taxable income crosses into the band above, the allowance halves to £500.00, and the bill goes up by £146.00. The advertised £1,000.00 of free interest costs £146.00.

Part of that is not even charged on the interest. The law permits the personal allowance to be allocated across income types in whichever way produces the lowest bill, so adding the interest changes the allocation and drags some of the reader’s salary into a more expensive place. The tax on the interest’s own bands is £92.00; the interest cost £146.00. Both figures are shown on the calculator, named, because either alone is misleading.

The rule this produces is stated as a rule rather than as a preference, and it is asserted by this page’s test suite: no allowance figure appears anywhere on the page or in its CSV export without the measured cost of using it beside it.

The allowance steps; it does not taper

The personal allowance tapers — 50p of allowance per £1 of income, smoothly, across a long stretch. The personal savings allowance does nothing of the kind. It has three values and moves between them in one step, on total taxable income.

A step in an allowance is a step in a bill, because the part that disappears moves out of a nil-rate band and into a taxed one retrospectively, for the whole year. So the pound of income that crosses a boundary is charged with the entire consequence of crossing it. At £48,000 of other income, that pound costs £0.40 where the pound before it costs £0.20.

The engine’s own marginalRate cannot show this, and is not wrong not to. It reports the rate on the next pound at the reader’s current income — correct, right up until they are standing on the crossing pound. A calculator that reports only a marginal rate tells the truth and misses the cliff completely.

Why the cliff is found by bisection rather than by arithmetic

The allowance steps at thresholds expressed in taxable income, and the reader has gross income. Converting between the two is a closed-form inversion of gross ↦ gross − personalAllowance(gross), and it carries a residual of about a pound: the statute rounds the surviving personal allowance up to a whole pound inside the taper, so the true function is a staircase and the inversion is its centre line.

A pound of error is nothing on a threshold-distance figure and everything here, because the thing being located is a pound — and the two pounds either side of it differ by a factor of hundreds. So the conversion is used for the tier table, where a figure “roughly this much gross income” is what a reader wants, and the cliff itself is located by asking the engine which pound actually changes the allowance.

Bisection needs no estimate at all: the allowance is non-increasing in income, so halving the interval is exact. It costs about twenty engine calls and has no window to size and no failure mode in which the page confidently denies that a step exists.

/savings-calculator locates the same crossing by a different route — a closed-form estimate with a small search window, backed by a bisection it has never needed — which is right there, because that page already holds the inversion machinery. Two implementations of one figure must agree, and that is checked rather than trusted: this page’s test suite sweeps a range of incomes and asserts the two report the same crossing.

The starting rate for savings, which is not an allowance

It is a band of £5,000.00 charged at 0.00%, sitting immediately above the personal allowance and below the personal savings allowance in the stack. Two things about it are almost always got wrong:

• It is withdrawn pound for pound by non-savings taxable income above the personal allowance — not by half, not gradually. It is gone entirely once that income reaches £17,570, which is to say it is gone for almost everybody with a salary. Writing that lists it beside the personal savings allowance as though both were generally available describes a taxpayer who mostly does not exist.
• It is a nil-rate band, not a deduction. Interest inside it still occupies space in the schedule, so it still pushes interest above it further up. That distinction is invisible until the reader is near a threshold, and then it decides the answer.

Why the next pound of interest is measured rather than read off

computeTaxPosition reports a marginal rate, and it probes earned income: it adds a pound to earnedIncome and differences. That is the right question on a salary page and the wrong one here. The reader wants to know what the next pound of interest costs, and the two figures differ whenever any of the starting rate band or the personal savings allowance is left — which is exactly the condition this page is about.

So the interest figure is its own forward difference on savingsIncome, and the engine’s marginal rate appears on the page only where it is labelled as the rate on earned income — beside the cliff, where the contrast between the two is the point.

Rates, thresholds and allowances

Savings interest is not devolved. The tiers are decided on UK-wide bands wherever the reader lives, so a Scottish intermediate-rate taxpayer is a UK basic-rate taxpayer for this purpose — the one place on this site where the region a reader selects changes half the answer and not the other half.

Sources

• gov.uk — Tax on savings interestThe personal savings allowance by band, the starting rate for savings and its pound-for-pound withdrawal, and what counts as savings interest.
• gov.uk — Income Tax rates and Personal AllowancesThe bands the allowance tiers are decided against, and the personal allowance that sits underneath everything on this page.
• gov.uk — Income tax rates and allowances: current and pastThe published figures behind the rates table below, including the personal allowance taper.
• gov.uk — Change to tax rates for property, savings and dividend income (technical note)The separate rate schedule for savings income taking effect on 6 April 2027, which is after every tax year this calculator offers. The allowance and the starting rate are unchanged by it.

Five things this calculation does not model, stated here rather than buried

• The savings rate schedule taking effect on 6 April 2027. From that date savings income is charged on its own rates in England, Wales and Northern Ireland rather than on the earned schedule. The personal savings allowance and the starting rate for savings are unchanged by it, so everything on this page about how the shelter works still holds — but the rates above the shelter move. Every tax year offered here precedes it, and the new figures are deliberately not written into this page, because a page whose whole claim is that its numbers come from a verified rules file must not carry a number that does not.
• Dividends. They count towards the total taxable income that decides the allowance tier and have an allowance and rates of their own. A reader with dividends may be in a lower tier than this page reports.
• When interest is paid. It is taxed in the year it is credited, not the year it accrued, so a fixed-rate bond paying at maturity can land several years’ interest in one — the commonest way an ordinary saver ends up on the wrong side of a step.
• How the money is held. Interest on a joint account is normally split between the holders and each has their own allowance; ISA interest is outside the income tax system entirely and counts towards nothing here; children’s accounts and trusts have rules of their own.
• Collection, and everything that is not income tax on interest. A basic-rate taxpayer with modest interest usually pays through a change to a tax code rather than a bill. Nothing here about student loan repayments, the High Income Child Benefit Charge, or what savings income does to a means-tested benefit.