About · Methodology
Calculators built from first principles, not affiliate templates.
Most UK tax and pension calculators online are point-estimate toys with affiliate links bolted on. BracketMath is built differently — every figure on this site comes from explicit HMRC-published rates, peer-reviewed return models, and bounded numerical optimisation. The maths is the product.
What BracketMath is
BracketMath is an independent UK project building rigorous tax and pension calculators from first principles. It exists because most free UK calculators online are point-estimate toys with affiliate links bolted on: they quietly use naive rule-of-thumb heuristics for salary–dividend splits, ignore sequence-of-returns risk in retirement projections, and skip the interaction effects between corporation tax, the Personal Allowance taper, dividend allowance, and employer's NI that actually determine the optimal answer for UK contractors and Ltd Co directors.
Every calculator here is transparent by design. The methodology section below documents the exact formulas, the data sources, the assumptions, and the limitations — so you (or your accountant) can verify the numbers rather than trust a black box.
Methodology — the short version
Tax calculations
All income tax, National Insurance (Class 1, 2, 4), corporation tax (including the £50,000–£250,000 marginal relief formula), and dividend tax computations use the published HMRC rates and thresholds for the UK tax year 2026/27. The Personal Allowance taper above £100,000 and the High Income Child Benefit Charge are modelled exactly, not approximated. Scotland and Wales income tax variants are supported where the underlying calculator is sensitive to region.
Joint optimisation
The Salary–Dividend Split Optimiser does not optimise salary or dividends or pension contributions in isolation — it searches the joint space of all three using bounded numerical optimisation, accounting for the interaction effects between corporation tax, the Employment Allowance, employer's NI, the dividend allowance, and the £100k Personal Allowance taper. The optimum is often £500–£3,000 a year better than rule-of-thumb advice.
Monte Carlo & retirement modelling
Pension and retirement calculators use block-bootstrap resampling of historical UK equity (1900–2024, Dimson-Marsh-Staunton total return) and gilt returns. Block bootstrapping preserves the autocorrelation and volatility clustering that naive monthly resampling destroys — the difference matters most in sequence-of-returns risk, which dominates outcomes in early retirement. Each calculation runs 10,000 simulated paths and reports the 5th, 25th, 50th, 75th, and 95th percentiles of pot value and the probability of capital exhaustion before age 95.
What this site is not
This site is not financial advice. It does not know your full personal circumstances, your employer's pension scheme, your other investments, your tax residency complications, or your appetite for risk. Every calculation is a model — useful for thinking, not a substitute for a regulated adviser when the stakes are large. See the full disclaimer.
Updates
Tax bands and thresholds change every April. BracketMath is updated each tax year to reflect the new figures, with a changelog noting which calculators changed and why. If HMRC publishes a mid-year change (rare, but it happens), affected calculators are updated within 14 days of the announcement.
Contact
Spotted a bug in a calculation? Have a calculator request? Email [email protected].