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This site describes solve-engine 2.44.0, the version npm installs.

Payroll & take-home

Package: PAYROLL_PACKAGE. Registered by createEngine(); for a slimmer engine, register it explicitly (see choosing packages).

Take-home pay is what actually reaches your account after a salary has had income tax and National Insurance taken off. Reading a payslip, or working out what a raise is really worth, means running those bands, which is exactly the fiddly arithmetic a calculator should do. Write the salary and ask for it after tax.

£50,000 after tax // £39,519.60
take home on £30,000 // £25,119.60
£120,000 after tax // £76,157.40

The word salary may sit before after tax, as it is often said, with the same answer:

£50,000 salary after tax // £39,519.60

A salary kept in a variable reads the same. A variable named salary is the variable, not the word before the phrase, so the two spellings do not collide: the word is dropped only when it follows an amount.

salary = £50,000 // £50,000.00
salary after tax // £39,519.60
salary per month after tax // £3,293.30

per month after tax gives the monthly take-home rather than the annual, and monthly after tax is the same question in one word:

£60,000 salary per month after tax // £3,779.78
£50,000 monthly after tax // £3,293.30

The salary has to be in pounds, because these bands are British. A salary in another currency, or a bare number that names no currency at all, is refused rather than answered: the bands would produce a confident figure about a country they say nothing about. What to write instead is on the line below.

A salary is what someone is paid, so it is never below zero. A negative one is refused by every form on this page rather than answered, since the bands charge nothing below their thresholds and would hand the amount straight back as a take-home no one has. A salary of zero is a year unpaid, and its take-home is nothing:

-£50,000 after tax // a salary is what someone is paid, so it cannot be below zero: write the pay as zero or more, such as £50,000
£0 after tax // £0.00

Income tax in Scotland is set by the Scottish Parliament, so a Scottish taxpayer pays it through six bands rather than three: starter 19%, basic 20%, intermediate 21%, higher 42%, advanced 45% and top 48%. National Insurance is the same across the UK. Write in Scotland after the salary or the after tax phrase:

take home on £50,000 in Scotland // £38,023.55
£50,000 after tax in Scotland // £38,023.55
£50,000 per month after tax in Scotland // £3,168.63
£120,000 after tax in Scotland // £71,357.35

in England, in Wales and in Northern Ireland name the bands used when no place is written, so they give the same answer as the plain line.

£50,000 after tax in Wales // £39,519.60

A student loan is repaid through the payroll: a share of pay above a yearly threshold is taken before the rest reaches your account. Each loan belongs to a plan, set by where and when the course started, and each plan has its own threshold. Name the plan after with:

£50,000 after tax with plan 2 student loan // £37,664.25
£50,000 after tax with plan 1 student loan // £37,440.60
£50,000 after tax with postgraduate loan // £37,779.60
£50,000 after tax with plan 2 student loan and postgraduate loan // £35,924.25

The plans are Plan 1 (£26,900 in 2026/27), Plan 2 (£29,385), Plan 4, the Scottish plan (£33,795), and Plan 5, first repaid in April 2026 (£25,000), each at 9% of pay above the threshold; the postgraduate loan is 6% above £21,000, and is repaid alongside an undergraduate plan. The word student may be left out, as in with plan 2 loan. A salary at or below the threshold repays nothing.

A loan with no plan named is refused rather than guessed, since the plans differ by thousands of pounds of threshold:

£50,000 after tax with student loan // a student loan needs its plan: write "with plan 1 student loan" (or plan 2, plan 4 or plan 5), or "with postgraduate loan"

A workplace pension is often paid from salary before income tax is worked out, so a contribution lowers the tax as well as the take-home. Write the contribution as a percentage of the salary, after with:

take home on £50,000 with 5% pension // £37,519.60
£50,000 after tax in Scotland with plan 4 student loan and 5% pension // £35,115.10

The contribution is taken the way a net pay arrangement takes it: out of gross pay before income tax, so the tax is charged on what is left (and the personal allowance tapers on that smaller figure too), while National Insurance and a student loan are still worked out on the full salary. The percentage is of the whole salary.

Several clauses can follow one another, joined by and or each with its own with, in any order. Each kind is written once: one place, one pension (the total of every contribution), and one undergraduate plan. Two undergraduate plans together share a single threshold under rules this does not model, so that line is refused and names the plan to write:

£50,000 after tax with plan 1 student loan and plan 2 student loan // Plan 1 and Plan 2 together share one threshold, which is not covered: name the plan with the lower threshold

Everywhere the bands do not reach, state the rate instead. Nothing about this form is national, so it works on any currency and on a bare number.

£50,000 after 20% tax // £40,000.00
$50,000 after 20% tax // $40,000.00
50000 after 20% tax // 40,000

It is the same take-home question with the arithmetic stated rather than looked up, which is what anyone outside the UK needs, and what anyone on a flat rate, a contractor rate or a rate they are modelling needs too.

hourly for is a plainer sum: the gross salary as an hourly rate, on a full-time year of 1,920 hours (a 40-hour week across 48 weeks), before any tax. No bands are involved, so it takes any currency.

hourly for 45000 // 23.44
hourly for $45,000 // $23.44

after tax takes the whole sum written before it as the salary, so a pay rise added to a salary is taxed together with it. A comparison is not part of the salary: in £50,000 after tax > £30,000 the take-home is compared with £30,000, and a check reads the two sides the same way.

£50,000 + £2,000 after tax // £40,717.40
£50,000 after tax > £30,000 // true
check £50,000 after tax > £30,000 // ✓
check £30,000 < £50,000 per month after tax // check failed: £30,000.00 is not less than £3,293.30

The same holds for per month after tax and for a rate you state (after 20% tax).

The bands are the full HMRC figures for England, Wales and Northern Ireland, tax year 2026/27: the £12,570 personal allowance, tapered away £1 for every £2 earned over £100,000; income tax at 20%, 40% and 45%; and employee National Insurance at 8% between £12,570 and £50,270, then 2% above. The Scottish bands for the same year run from £12,571 (starter), £16,538 (basic), £29,527 (intermediate), £43,663 (higher) and £75,001 (advanced), with the top rate above £125,140. The student loan thresholds are the Student Loans Company’s for the same year.

A tax year has to be chosen, because take-home depends on one. Solve uses the latest year it ships figures for, and that is a fixed table rather than a year read off today’s date: a new tax year the package has no figures for would otherwise be answered with the previous year’s, silently. The England, Wales and Northern Ireland figures above are unchanged across 2024/25, 2025/26 and 2026/27, so a salary answers the same in all three there; Scotland’s lower bands and the student loan thresholds move each year, and the package carries a table for each year beside its neighbours.

The boundary: the figures cover an employee on the standard tax code. A different code, and self-employment (where National Insurance is charged differently), are not covered, and neither are pensions taken by relief at source or by salary sacrifice, which change the answer in other ways (a salary sacrifice lowers National Insurance too). A rate that is not shipped is not assumed: that is the same boundary the tax rule draws, and the same one the pound requirement above draws. after 20% tax is the form for every case the tables do not describe, and it takes no place or clause, since its rate is already stated. Any set of income tax bands can also be written as a table and applied with banded rates.