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Income tax here is calculated in two steps. First, taxable income = gross income - deductions, where the deduction is either the standard amount for your country and filing status or an itemised figure you enter. Second, that taxable income is sliced across the brackets, and each slice is taxed at its own rate rather than the whole amount being taxed at the top rate reached. The slices are added together to give the income tax figure.

Any additional contributions you switch on are computed separately on their own thresholds. UK National Insurance Class 1, for example, applies 8 per cent between 12,570 and 50,270 and 2 per cent above that. Total tax is income tax plus those additions, and take-home pay = gross income - total tax.

Two rates are then reported. The effective rate is total tax / gross income x 100. The marginal rate is the rate applied to your last unit of income.

For VAT and sales tax: adding tax gives total = net x (1 + r), while extracting tax from an inclusive price gives net = gross / (1 + r), with the tax being the difference.

Take the custom bracket mode with three bands: 0 per cent up to 10,000, 20 per cent from 10,000 to 40,000, and 40 per cent above 40,000. Enter a gross income of 60,000 and a deduction of 5,000.

Taxable income is 60,000 - 5,000 = 55,000. The first 10,000 is taxed at 0 per cent, giving nothing. The next 30,000, covering the band from 10,000 to 40,000, is taxed at 20 per cent, giving 6,000. The remaining 15,000 above 40,000 is taxed at 40 per cent, giving another 6,000. Total income tax is 12,000.

The effective rate is 12,000 / 60,000 x 100 = 20 per cent, even though the marginal rate is 40 per cent. Take-home pay is 48,000, which is 4,000 a month against a monthly gross of 5,000.

Now switch to the sales tax mode. A price of 250 that already includes 20 per cent VAT breaks down as 250 / 1.20 = 208.33 net, with 41.67 of VAT. Entering 208.33 as a pre-tax price and adding 20 per cent returns the same 250 total, confirming the two directions agree.

The single most useful output is the gap between the effective and marginal rates. In the example above they are 20 and 40 per cent, which explains why the widespread fear of a pay rise pushing you into a higher bracket is misplaced. Only the income above the threshold is taxed at the higher rate; everything below keeps its original treatment, so a raise always leaves you with more after tax.

Treat the figure as an estimate. Bracket thresholds, standard deductions and contribution rates change every tax year, and the calculator cannot know your full circumstances. It does not model state or provincial income tax, local taxes, tax credits, pension relief, student loan repayments, salary sacrifice arrangements, dividend or capital gains rates, or the many allowances that taper at higher incomes. In the United States in particular, state income tax can add several percentage points that are absent here.

Use it to sanity-check a payslip, compare two job offers, or see the effect of a salary change. For filing, a refund claim or any decision with money at stake, confirm the numbers against your tax authority or an accountant. Nothing here is tax advice.