Pension calculator — methodology

Step one: relief is a subtraction, and it has to be

Tax relief is not a figure anybody computes directly. It is the difference between two tax positions — the taxpayer with the contribution and the taxpayer without — so that is exactly how it is worked out:

relief claimed = income tax without the contribution
               − income tax with the contribution
relief at source = gross contribution × the basic rate  (relief at source only)
total relief     = relief at source + relief claimed

The shortcut this replaces — contribution × marginal rate — is a second income tax engine, and a wrong one. It gets the £100,000 taper wrong, it gets a contribution that straddles a threshold wrong, and it gets Scotland wrong twice over. Doing it as a subtraction also means this page cannot disagree with any other calculator on the site, because it is the other calculators.

The two mechanisms, and which of them moves a band

Relief at source — SIPPs, personal pensions and many workplace schemes. You pay out of income that has already been taxed and the scheme reclaims the basic rate from HMRC, so £80 handed over becomes £100 of pension. Relief above the basic rate is not paid to the scheme. It is delivered by moving the top of the basic rate band up by the whole gross contribution, along with every rate limit above it:

basic rate limit → basic rate limit + gross contribution
every limit above it moves by the same amount
nothing below it moves

That last line is the one that is invisible in the ordinary case and wrong by a whole percentage point in another. In Scotland the starter-rate ceiling sits below the Scottish basic rate limit and stays where it is; extending every threshold instead would hand a Scottish intermediate-rate taxpayer 2% of extra relief where gov.uk publishes 1%.

A net pay arrangement — most occupational schemes. The employer deducts the contribution before operating PAYE, so taxable earnings are lower and relief lands at the marginal rate automatically. No band moves, because nothing needs to: the income never enters the higher band in the first place.

Neither reduces National Insurance. A net pay contribution is still your earnings for NIC purposes even though it never reaches your bank account, and this is the single most common thing to get wrong about it. Salary sacrifice is the mechanism that does reduce it, because it reduces gross pay itself — a different calculation, on the salary sacrifice calculator. Worth knowing for later: from 6 April 2029 only the first £2,000 a year of pension salary sacrifice keeps that National Insurance exemption, with income tax relief unaffected. That date is beyond every tax year this calculator offers.

Why the most valuable pension contribution in the country is made just above £100,000

Above £100,000 the personal allowance is withdrawn at £1 for every £2 of income, and it is gone entirely by £125,140. A pension contribution is deducted from the income that withdrawal is measured against, so a contribution in that window does two things at once: it moves income down a band and it restores allowance that was being taxed.

relief rate inside the taper = band rate × 1.5

Every figure in these two tables is measured by the same function the calculator runs, on 2026/27 rates, with a £1,000 contribution through relief at source. Nothing in them is typed.

Read the rate column rather than the income column: it does not run in order. Relief in the taper window is worth more than relief at the very top rate, which is the opposite of what almost everybody assumes and is the single most useful thing on this page.

Step two: two limits, and they are not the same limit

The relief limit (FA 2004 s.190) caps what may be relieved: the greater of 100% of your relevant UK earnings and £3,600 a year. Contribute beyond it and the excess simply attracts nothing.

The annual allowance caps tax-privileged saving. Exceed it and the contribution is relieved in full and then charged back through an annual allowance charge at your marginal rate — a separate liability, on a separate part of a self assessment return. A calculator that shows one of these and calls it “the limit” will tell somebody the wrong thing about the same pound.

pension input   = your gross contribution + your employer's contribution
available       = annual allowance + carry forward available
excess          = max(0, pension input − available)

The employer’s contribution is in that first line, and this is the part most often missing. It gets no relief through your tax return — it was never your income — but it is pension input in full, and on a generous scheme it is the larger of the two figures. It also raises adjusted income, which is one of the two tests below.

The taper, and the two income measures it is decided on

For high earners the annual allowance is reduced. The taper only bites when both measures are above their limits — testing adjusted income alone is the classic error, and it over-taxes people with a modest salary and a generous employer.

threshold income = salary − your contribution
adjusted income  = salary + your employer's contribution

if threshold income > £200,000 and adjusted income > £260,000:
    reduction = (adjusted income − £260,000) ÷ 2, rounded down to a whole £1
    allowance = max(£10,000, £60,000 − reduction)

Both derivations are worth checking against the statute rather than taken on trust, and the symmetry is not obvious. Threshold income is net income less any relief-at-source contribution; under a net pay arrangement the contribution never entered net income, so the same subtraction applies. Adjusted income is net income plus employer contributions, plus any member contribution relieved through net pay added back; under relief at source there is nothing to add back. One formula each, whichever mechanism you picked.

What the derivation does not include, stated rather than hidden: the statutory definitions carry add-backs this page does not collect — income other than the salary entered, salary sacrifice arrangements made after 8 July 2015 (added back to threshold income), and certain lump sum death benefits. Anyone with other taxable income has higher figures than the ones shown.

Two reporting details that follow from the arithmetic. The reduction is rounded down to a whole pound, so somebody £1 over both limits is technically inside the taper and has lost nothing — the page says the allowance is untouched rather than announcing a taper that took nothing. And where the money purchase annual allowance applies, no allowance has been tapered away at all: it is a separate flat cap rather than a reduction, so the page presents that case differently instead of reporting a loss of nil.

Carry forward, and the four conditions on it

Unused annual allowance from the three previous tax years can be brought forward. It is never presented here as spare capacity you have, because four things have to be true before any of it is reachable:

• Three years, and no further. The oldest of them drops out of reach at the end of this tax year.
• This year’s allowance is used first, and the carried-forward amounts are used oldest first after it.
• You must have been a member of a registered pension scheme in each of those years — a condition nothing on this page can check, and the one most likely to be missing for somebody who has just started saving.
• Relief is still capped at your relevant UK earnings. A large carried forward balance does not let anyone contribute more than they earn and get relief on it.

It is therefore off until it is asked for. Three prior-year boxes sitting at £0 would assert that nothing went into a pension for three years, which is the largest carried-forward figure the system can produce — three whole allowances — and it would be asserted on behalf of every reader who never touched the field. The neutral default belongs on the feature rather than on the boxes.

Carry forward cannot be set against the money purchase annual allowance. So when the page is told that a pot has been flexibly accessed, the carried-forward figure is nil — and the three prior years are still shown, with the reason, rather than the block silently disappearing.

The allowance was not the same in all three years — it stepped from £40,000 to £60,000 at 2023/24 — so each year is read against its own figure. Applying the current year’s allowance to all three would over-state the carried-forward amount by £20,000 for anybody whose window still reaches back that far, which is enough to trigger a charge. The allowance for a prior year in which you were tapered was lower still, and this page does not collect that; the figure shown is therefore the standard one and can be too high for a member who was tapered then.

Step three: the pot, period by period

The projection runs in periods — a month, a quarter or a year, whichever you pay in on — and every step is integer pence. In each period: apply the period’s growth, deduct the platform charge, then add the contribution.

balance ← balance × (1 + periodic rate)
balance ← balance − charges
balance ← balance + contribution

Every row satisfies opening + paid in + growth − charges = closing exactly, in whole pence, so the headline cannot disagree with the schedule it was read off. Contributions land at the end of each period, which is stated rather than assumed: a contribution paid at the start of a period earns one extra period of growth, every period, for the whole term. The difference is (1 + p) at the periodic rate, not the annual one, and the investment calculator is where a reader can see what the choice is worth on their own figures.

The annual contribution is divided into equal instalments and rounded to the penny, and both contributions escalate once a year rather than once a period — each year’s figure is computed from the base rather than from last year’s already-rounded one, so twenty-five years of rounding cannot drift.

Today’s money is a change of units, and never a second projection

The real-terms figures are the finished schedule deflated once, at the end:

today's money = nominal ÷ (1 + inflation)^years

The inflation assumption never moves the projection. It is not a lower growth rate and the two are not the same thing. Deflating inside the loop would produce a table whose growth column was neither the real return nor the nominal one and whose rows still had to add up; deflating once keeps the schedule checkable and makes the real-terms figure exactly what it claims to be — the same pot, priced in today’s pounds.

The other half of the same question is a separate field, and it is a separate field on purpose. An income or contribution that rises with prices is real money changing hands, so it changes the schedule; a restatement in today’s money is not. Conflating the two would mean ticking “show me today’s money” silently changed what was being paid in.

The tax figures are deliberately not deflated. Income tax is charged in the pounds of the year it falls in, against thresholds published for that year, and this calculator has rules files for the years it offers and no others — restating a future tax bill in today’s money would imply a view about future thresholds that nobody has.

Step four: the tax on what comes out

Normally 25.00% of a defined contribution pot can be taken free of income tax. The rest is taxed as earned income in the year it is withdrawn, which is the fact most pension calculators skip: it is added to your other income and taxed at whatever rate that income has already taken you to, rather than starting again at the personal allowance.

tax-free cash  = pot × tax-free rate
taxable income = other retirement income + pension income taken
income tax     = computeTaxPosition(taxable income, region, tax year)
tax caused by
the pension    = income tax with it − income tax without it

The last line is a measurement rather than a rate applied to the withdrawal, and it has to be: the income frequently spans two or three bands. No National Insurance is charged on a pension withdrawal, at any age.

There is no State Pension amount anywhere in this calculator. It is not one of the figures in tax-core’s rules files and it is not covered by the verification below, so typing one in would put an unchecked statutory figure inside a verified stamp’s blast radius. The “other retirement income” field defaults to zero and is where yours goes. It is also the field that most changes the answer: the State Pension alone uses most of a personal allowance before a private pension pays a penny.

What this page deliberately does not compute

• How long the pot lasts. Decumulation depends on the order returns arrive in after money starts coming out, which matters far more than the average once a pot is being drawn on. It has its own engine work and its own page: the pension drawdown calculator reports the year an income would first fall short and the largest level income a pot pays for a whole term. A second version of that answer here would be a near-duplicate rather than a second opinion.
• What a pot buys as a guaranteed income. The annuity calculator prices that from a rate you have been quoted.
• Salary sacrifice, which is a reduction in gross pay rather than a contribution, and therefore a National Insurance question as much as an income tax one. It is on the salary sacrifice calculator.
• How much to contribute. That is advice, and this site does not give it. This page prices a contribution you have chosen.

Rates and allowances

Income tax thresholds are taxable income, after allowances. The Scottish bands apply to a pension contribution and to a pension withdrawal alike, because both are measured against earned income and income tax on it is devolved.

Sources

• gov.uk — Tax on your private pension contributionsFor the relief mechanisms, the limit on relievable contributions and the annual allowance.
• gov.uk — Pension schemes rates and allowancesFor the annual allowance, its taper and the money purchase annual allowance. The lump sum allowance is published here too and is deliberately not modelled — see the limits section below.
• gov.uk — Income tax rates and allowances: current and pastRelief is the difference between two income tax positions, and a pension withdrawal is taxed as earned income, so the ordinary bands and the personal allowance taper govern both ends of this page.
• gov.uk — Tax when you get a pension
• gov.scot — Scottish income tax rates and bandsIncome tax is devolved, so a Scottish taxpayer gets a different amount of relief on the same contribution and meets a different set of bands on the way out.

The verification, and the parts of this page it covers

That stamp covers the tax calculations only — the relief, the allowances and the income tax on the way out. It is a check on the published rates, thresholds and allowances in the rules files, and it does not reach the projection at all: there is no published figure in the growth rate, the charge, the inflation assumption or the term for anyone to check, which is why the note above says the projection makes an arithmetic claim and no other.

The bounds on the input fields, and why they are not round numbers

• Growth is floored at -99%, not −100%. The projection engine rejects an annual rate of exactly −1 — a total loss is not a growth assumption — and the field’s clamp is inclusive, so a floor of −100 would be an unhandled error reachable by typing a minus sign. The contribution increase is floored at -99% for the same validator, and inflation at -50% because the deflation divides by (1 + inflation).
• The charge is capped at 5% a year. A platform fee is refused above a periodic rate of 1 — more than 1,200% a year at monthly periods — because above that a bigger pot ends the period smaller and the arithmetic runs backwards.
• An empty field means zero, not the bottom of the range. Clearing the growth box asserts no growth, which is what “I have not told you a growth rate” means. It does not assert the -99% at the floor.
• A net pay contribution is capped at the salary, and the page says when it has been. A deduction from pay cannot exceed the pay, and the tax engine refuses the input rather than clamping it — deliberately, because a form with two independently typed boxes is exactly where a confident wrong answer does the most damage.

Limits that change the answer, stated here rather than buried

• The lump sum allowance is not applied. The tax-free 25.00% is a verified figure; the cash cap on it is not in the tax engine’s schema at all. On a pot large enough for the cap to bite, this page shows more tax-free cash than could actually be taken, and therefore too little tax.
• The annual allowance charge is reported, not computed. The excess is shown; the charge on it falls at your marginal rate on top of your other income, and no published source settles the stacking cleanly enough to build on.
• One flat allowance. A member who has triggered the money purchase annual allowance and also accrues a defined benefit pension really has two limits — the money purchase cap on contributions and a separate alternative annual allowance on the defined benefit accrual, which can itself be tapered. Nothing on this page models defined benefit accrual.
• One income, treated as everything. The salary entered is used as the whole of your taxable income and as your relevant UK earnings. Those coincide for an employee and diverge for anybody with rental profit, dividends or savings interest — and they diverge completely for a pensioner, whose relevant earnings can be nil while their taxable income is substantial.
• One tax year’s rules, applied at both ends. The contribution and the eventual withdrawal are both priced on the tax year selected, because nobody knows what the bands will be in twenty-five years — the calculator offers the tax years it has rules files for and no others.
• Emergency tax on a first withdrawal is not modelled. Providers commonly operate a month-1 code on a first flexible payment, taxing it as though it were the first of twelve identical payments. Far too much comes off and it is reclaimed afterwards. This page shows the tax-year position.