Most people’s payslip is a monthly mystery they’ve agreed not to investigate. Gross at the top, a smaller number at the bottom, and between them a set of deductions taken on faith. Which means most people can’t answer basic questions about their own money: what does a £2,000 raise actually pay? What does upping the pension really cost per month?

A payslip is arithmetic, the arithmetic is banded, and banded arithmetic is exactly what Excel is for. One evening builds a model that answers those questions for good.

Honesty first: rates and thresholds change at Budgets, and this guide deliberately teaches the machine, not this year’s numbers — build with the current figures from gov.uk beside you. Personal quirks (student loans, benefits in kind, Scottish bands, tax codes that aren’t standard) are extra rows on the same skeleton.

The machine: marginal bands

The single most misunderstood fact in UK money: tax bands are marginal. Crossing into the 40% band does not tax your whole salary at 40% — it taxes the slice above the threshold at 40%. Nobody has ever been made poorer by a raise (the folk belief to the contrary has cost people real money in refused overtime).

Marginal maths in Excel is a small stack of MAX slices. With named cells for the thresholds and rates (names, always):

taxable   = MAX(0, salary - allowance)
basic_tax = MIN(taxable, basic_width) * basic_rate
higher_tax= MAX(0, taxable - basic_width) * higher_rate

…and so on if a band above applies. Each line is one slice of income meeting one rate — readable, checkable, and exactly how the real calculation works. National Insurance is the same machine with its own thresholds and rates: build it as a second small block, not by copying the tax block and hoping.

one salary, three slices — each taxed at ITS OWN rate 0% 20% 40% allowance basic band the slice above crossing a line taxes the NEW SLICE only — a raise is never a pay cut; the folk belief has refused real overtime
The bar fills left to right; each segment pays only its own rate. Marginal bands in one picture — the fact that untangles every payslip question.

Assemble the payslip

With both blocks built, the payslip is four rows:

pension    = salary * pension_pct
take_home  = salary - pension - income_tax - ni
monthly    = take_home / 12

Order matters, and it’s where the model starts paying rent: pension contributions (salary-sacrifice or net-pay arrangements) come out before the tax maths sees your income. Which produces the model’s first revelation: raise your pension by £100/month and take-home falls by only £60–72 — the state quietly funds the rest. That number — your number, at your marginal rate — is the strongest argument in the countdown model’s favour, and most people have never seen it calculated.

Then interrogate it, the way you now interrogate everything:

  • The raise question. salary +£2,000 → watch monthly. At the basic rate roughly £113/month arrives; higher rate, ~£97. Real numbers end both the cynicism (“hardly worth it” — it is) and the fantasy (“£166 a month!” — it isn’t).
  • The cliff edges. The one place “will a raise cost me?” has substance isn’t the bands — it’s withdrawal tapers around specific thresholds (personal allowance taper, child benefit clawback, childcare eligibility). If your salary sits near one, model your specific situation — this is also where professional advice earns its fee.
  • The reconciliation. Put your actual payslip beside the model. Within a rounding whisker? You understand your pay. A gap? Now you know what question to ask payroll — by name, with a number.

The general lesson is the one this whole field-notes series keeps landing on: systems that take your money arrive looking like faits accomplis, and a small model turns them back into arithmetic you can question. The payslip is the one you receive twelve times a year — decode it once, and every Budget-day headline for the rest of your life is just new numbers for cells you already own.