Home/Calculators/Discount & tax calculator
CalculatorDiscount & Tax Calculator
Work out a final price after a discount and a tax, in whichever order your receipt actually applies them, or convert a "buy X get Y free" offer into the plain percentage discount it really is.
Final price
—
Order does not matter — mathematically
Applying a discount then a tax, or a tax then a discount, produces the same price. Multiplication does not care which order you multiply in: P × (1 − d) × (1 + t) is exactly the same value as P × (1 + t) × (1 − d), because (1 − d) and (1 + t) are just two numbers being multiplied together, in either order, against P.
…but rounding at each step can make them differ by a cent
Real tills round to the nearest cent after every step, not just at the end. That extra rounding is not part of the mathematics above, so it can break the equality. Take a price of 1.01, a 5% discount and 10% tax:
| Order | Step 1 | Step 2 | Final |
|---|---|---|---|
| Discount, then tax | 1.01 × 0.95 = 0.9595 → 0.96 | 0.96 × 1.10 = 1.056 → 1.06 | 1.06 |
| Tax, then discount | 1.01 × 1.10 = 1.111 → 1.11 | 1.11 × 0.95 = 1.0545 → 1.05 | 1.05 |
A one-cent gap on a single low-value item, caused entirely by where the rounding happened to fall. It rarely survives past a few pence on everyday prices, but on a large order made of many small lines, or on a system that rounds at every stage of a multi-step price build, the gaps can accumulate into something worth reconciling. The "round after each step" checkbox above reproduces this behaviour so you can see when it applies to your own numbers.
"Buy 2, get 1 free" is 33.3% off, not 50%
The intuition trips people up because it feels like "one of three is free," which sounds like a third off — and it is, but it is easy to instead compare the free item to what you paid for and land on 50%. The correct comparison is the free item against the total items you walk away with, not against what you paid for.
| Offer | Items paid for | Items free | Real discount |
|---|---|---|---|
| Buy 1, get 1 free | 1 | 1 | 50.0% |
| Buy 2, get 1 free | 2 | 1 | 33.3% |
| Buy 3, get 1 free | 3 | 1 | 25.0% |
| Buy 3, get 2 free | 3 | 2 | 40.0% |
| Buy 4, get 1 free | 4 | 1 | 20.0% |
The formula is Y ÷ (X + Y): free items divided by the total items in the deal. "Buy 1 get 1 free" really is 50% off because the free item is exactly half of what you take home — that one happens to match intuition. The others do not, which is why retailers reach for "buy 2 get 1 free" far more often than an equivalent "33% off" sign.
Questions people ask
Does tax apply to the pre-discount or post-discount price?
This depends on local tax rules, not on mathematics — some jurisdictions tax the discounted price, others tax the original price before a coupon is applied. Check which applies to you; the calculator will compute either order correctly once you know which one you need.
Why is my receipt's final total a cent different from this calculator?
Almost always intermediate rounding, exactly as shown above. Turn on the rounding checkbox to match how a real till accumulates cents at each step rather than only at the end.
Can I use a negative discount to model a surcharge instead?
Yes. A negative value in the discount field increases the price rather than reducing it, which works for modelling a service fee or surcharge applied the same way a discount would be.