How the cross-border maths works

The full method behind the Retire Abroad comparison and the data study — what is taxed where, how the treaty credit really behaves, and which simplifications the model makes. Written so you can check it rather than trust it.

The shape of the calculation

Income is simulated month by month, not projected with an annual formula. Each month the model draws the requested amounts from each account, works out the tax due on that year's income, applies healthcare cost, and grows the remaining balances. Phase figures are the average of the months inside them.

Phases are cut at the ages where the arithmetic genuinely changes — 65 (Medicare replaces marketplace insurance), the Social Security claim age, 73 (Required Minimum Distributions begin, on the IRS Uniform Lifetime Table) and 80. Putting a boundary on the claim age matters: it means Social Security never starts halfway through a phase, so every phase is either wholly before or wholly after it.

Brackets, deductions, thresholds and healthcare costs are inflated per phase, so a bracket ceiling at 80 is not the ceiling that applies at 60.

What each country taxes

United States

Federal brackets of 10 / 12 / 22 / 24% applied to taxable income after the standard deduction and the senior add-on. Social Security is taxed the IRS way — through the provisional-income test, so only a portion becomes taxable rather than all or none. Long-term capital gains on brokerage withdrawals are handled separately from ordinary income, and the Net Investment Income Tax applies above its threshold. State income tax is a flat rate you set; the published comparisons set it to zero.

United Kingdom

The personal allowance, then basic (20%), higher (40%) and additional (45%) bands. Two details that are easy to miss and are modelled here:

The personal-allowance taper — £1 of allowance is lost for every £2 of income above roughly £100,000, so there is an effective marginal spike in that band.
Treaty Article 17: US Social Security is not taxable by the UK. What the UK does tax is 401(k) withdrawals, the UK State Pension, equity gains and any part-time earnings.

Canada

Federal brackets applied after the basic personal amount, plus a provincial rate. Unlike the UK, there is no treaty carve-out for US Social Security in this model — it is taxed as income along with the full 401(k) withdrawal, which is why Canada carries the heaviest tax burden in every published comparison.

Australia

The tax-free threshold, then 19 / 32.5 / 37 / 45% (the Stage 3 rates), reduced by the Low Income Tax Offset — $700 below $37,500, tapering to zero at $66,667. The Medicare Levy of 2% is then added on income above the levy threshold. Superannuation withdrawals after 60 are tax-free and are excluded from assessable income.

The Foreign Tax Credit: you pay the higher bill, not the sum

This is the part most write-ups get wrong, so it is worth stating precisely. For a US citizen resident in the UK the model computes both liabilities and then credits one against the other:

credit = min(UK tax, US tax) → US tax payable = US tax − credit

The credit cannot exceed the US liability. Work the algebra through and the total falls out as max(UK tax, US tax) — you pay whichever of the two bills is larger, and never both.

That single line explains something that otherwise looks like a coincidence. In the data study, the UK resident's tax bill is higher than the American's before Social Security starts — $632 against $367 a month — and then, from 67, the two become identical to the dollar at $361, $377 and $359 across the remaining phases. Nothing has been rounded or fudged. Once Social Security lands, the UK's own liability drops below the US one, the credit can no longer absorb all of it, and the total settles at the US figure.

The practical consequence: after Social Security starts, moving between the US and the UK stops being a tax decision. Whatever difference remains is healthcare.

Healthcare

For a US resident this is modelled in two regimes. Before 65: ACA marketplace premiums, including the 400%-of-federal-poverty-level subsidy cliff and the 250% FPL Silver cost-sharing-reduction band — both driven by MAGI, so a withdrawal decision can move the premium. From 65: Medicare Part B and Part D, plus IRMAA surcharges, which use a two-year income lookback — the surcharge you pay at 67 is set by your income at 65.

For the UK, Canadian and Australian columns the model applies no direct healthcare premium, on the assumption that the public system covers a resident.

This assumption does more work than any other in the model. In the published base case it is worth $312–$486 a month, and from age 67 it is the entire remaining gap between the US and the UK. Anything that changes it — private cover, an insurance condition attached to a visa, a surcharge for recent arrivals — moves the answer directly. Treat it as the first thing to challenge, not a footnote.

Simplifications, stated plainly

Every model simplifies. These are the ones that could change a conclusion, so they belong on the page rather than in a disclaimer:

Known asymmetry: US tax abroad

The UK column applies both liabilities and the treaty credit. The Canadian and Australian columns apply local tax only — no US layer — even though a US citizen abroad still has US filing obligations.

Where local tax is higher than the US figure, this makes no difference, because the credit result would be the local bill anyway. That is the case throughout the published comparisons at $900k and above.

Below roughly $600k it can matter. At that level Australian tax falls to about $70/month against a US figure near $95, so the Australian column understates by around $25/month. Small, but real — and it flatters Australia at the lower end. We have checked that it does not overturn the published finding: Australia still leads at $600k after allowing for it.

The rest

No local social-security entitlements — no CPP, OAS, Age Pension or UK State Pension accrual. The comparison holds the same savings against different tax systems; it is not a comparison of different working lives.
No currency risk. Everything is priced in US dollars. For destinations where cost arbitrage is the whole proposition, this matters a great deal.
Nominal dollars in the published tables, not inflation-adjusted — though inflation is applied to brackets and thresholds inside the model.
State income tax set to zero in published comparisons, which flatters the US column.
Nothing about visas, residency tests or domicile. Whether you may live somewhere is a separate question from what it would cost.
No destination-country model for other currencies. The planner supports Philippine peso, Thai baht and euro as display currencies with US federal tax only — no local tax model. They are deliberately excluded from these comparisons, because a column showing near-zero tax and zero healthcare would top the table for the wrong reasons.

How it is checked

The engine ships with a golden-master self-test: fixed fixture plans re-run on every build and diffed against known-good values, so silent calculation drift shows up immediately rather than in a customer's plan. Coverage spans all four tax regimes, Social Security claim-age splits, RMDs, NIIT, ACA, early retirement, Roth conversions, pensions and lump sums.

The free comparison tool and the data study run that same engine — not a simplified re-implementation — and the study's generator refuses to produce output unless it first reproduces a twenty-value cross-check against the paid planner, and unless the engine's own identity (net = gross − tax − healthcare) holds for every country in every phase.

That second check is not decoration. It is what caught a real error: the tool had been reporting a UK resident's income tax as $0, because the field it displayed held only the US federal component — which the treaty credit had reduced to nothing. The net income figures were correct throughout; the breakdown row was not. It is fixed, and the check now makes that class of mistake impossible to ship quietly.

See it applied

Read the worked comparison, or put your own numbers through the same engine — free, no sign-up, no email.

The data study → Try the comparison tool →

This is an educational model, not financial, tax or legal advice, and not a personalised recommendation. Cross-border tax is genuinely complicated — treaty position, domicile and residency tests can all change the answer for an individual. Talk to a qualified cross-border adviser before acting on any of it.