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Finance & Business · pattern A, Numeric fields

Sales tax added, and backed out.

Enter a net price and rate for the tax and gross price, with the reverse calculation that recovers the net amount from a tax-inclusive figure.

Inputs

The formula used

tax = net × rate; net = gross ÷ (1 + rate)

The reverse calculation divides rather than subtracts. Taking the rate off a gross figure by subtraction is the classic error and always understates the net amount.

Tax

8.25

Gross price
108.25
Net from the gross figure
100.00
Tax within the gross figure
8.25
Tax as a share of the gross price
7.621 %
Wrong answer: subtracting the rate
99.32
Error that subtraction causes
0.68

Going backwards means dividing, not subtracting.

To recover the net price from a tax-inclusive figure you divide by 1 plus the rate. Subtracting the rate from the gross figure gives a different, smaller number, because the tax was calculated on the net rather than on the gross. At 20% the two answers differ by 4% of the price — enough to matter on any real invoice.

Questions about sales tax

Why does dividing work?
Because gross = net × (1 + rate). Reversing a multiplication requires division; there is no way around it.
Do rates vary within a country?
In the US considerably, by state, county and city. Rates also depend on the type of good, with food and medicine often exempt or reduced.
Is sales tax the same as VAT?
No. Sales tax is charged once at the final sale; VAT is charged at every stage with credits for tax already paid.

A calculator handles the arithmetic. It cannot teach you the method.

If the number is not the part you are stuck on, that is what the service is for — a specialist who explains the working, not just the answer.

These are coursework tools. Nothing here is financial advice, no figure accounts for tax rules in your jurisdiction, and no result should be relied on for a real borrowing or investment decision.