How to Work Out Sales Tax From a Total

You have a receipt for $107.50 and you know it includes sales tax. You need the pre-tax figure for an expense claim. The receipt doesn’t break it out.

The instinct is to take 7% off. That’s wrong, and it’s wrong in a direction that costs you money every time.

Why subtracting the percentage doesn’t work

Tax was added to the pre-tax price, not to the total. So the percentage you’re trying to remove was calculated against a smaller number than the one you’re holding.

Take $107.50 at 7.5%:

Check the correct one: $100.00 × 0.075 = $7.50, and $100.00 + $7.50 = $107.50. It reconciles. The other doesn’t — $99.44 plus 7.5% is $106.90, which isn’t your receipt.

The gap is small on one coffee and material on a quarter of expenses.

The formula

For a rate written as a percentage:

• Pre-tax = total ÷ (1 + rate ÷ 100)
• Tax = total − pre-tax

At 8.25%, divide by 1.0825. At 20%, divide by 1.2. The divisor is never “1 minus the rate” — that’s the same mistake wearing a different hat.

The harder version: you don’t know the rate

This is the common case and it’s the one nobody’s calculator handles. You have a total and a tax amount, and you want to know what rate was applied — because you’re checking whether a vendor charged you correctly, or reconstructing which jurisdiction a purchase happened in.

Rate = tax ÷ (total − tax) × 100. Straightforward, except that receipts are rounded, and rounding destroys the exactness.

A receipt showing $12.99 tax on a $171.42 total is consistent with a range of rates, not one. The tax figure was rounded to the cent, so anything that rounds to $12.99 is possible. That range can easily be wide enough to contain two real, adjacent tax rates — 6.3% and 6.35%, say.

So the honest answer isn’t a single number. It’s the band the receipt actually proves, plus the recognisable rate inside it. Our Reverse Sales Tax Calculator does that: it solves for the rate, reports the band, and tells you when more than one plausible rate fits — rather than picking one and sounding confident about it.

Why “the tidiest rate” beats “the fewest decimals”

When several rates fit, you need a rule for which to suggest. The obvious rule — fewest decimal places — picks 8.24% over 8.25%, because both have two. But 8.25% is a real rate and 8.24% isn’t.

The better rule is roundness. Real rates land on quarters, eighths and tenths of a percent, because they’re built by stacking state, county and city components that are themselves round numbers. A rate that’s a clean multiple of 0.25 is far likelier than a neighbour that isn’t.

Stacked rates

In much of the US the rate on a receipt is several rates added together — state, county, city, sometimes a transit or stadium district. A 9.5% total might be 6.25% state, 2.25% county and 1% city.

For working backwards from a total, the components don’t matter. Add them up and divide by 1 + the sum. They start mattering when you need to apportion the tax you paid back to each jurisdiction, which is a bookkeeping requirement in some places and a nuisance everywhere.

Rounding, and why your total is a cent out

Two conventions exist and they disagree:

• Per line item. Tax is calculated and rounded on each line, then summed.
• Per invoice. The lines are summed, then tax is calculated once and rounded once.

On a long invoice these differ by a few cents. Neither is wrong; they’re different conventions, and the one your accounting software uses may not be the one your vendor used. If a reconstructed total is a cent or two off, that’s usually the cause — not an error in the arithmetic.

The short version

Divide by 1 + the rate. Never subtract the percentage from the total. If you’re solving for an unknown rate, remember the receipt was rounded, so the answer is a range — and the round number inside that range is almost certainly the real one.