How to Calculate Discounts, Sale Prices and Tax

Published 19 October 2026Guide for the Discount Calculator

Sale math looks easy until it is not: "50% off, then an extra 30% off" is not 80% off, and the difference between tax-inclusive and tax-exclusive prices changes every step after the first. Retail, payrolls, budgets and invoices all run on this arithmetic, and the mistakes are expensive in both directions.

This guide lays out the core operations - a single discount, stacked discounts, and tax applied before or after - with the one underlying fact that makes them all fall into place: every discount is multiplication by a remaining fraction.

One discount, one rule

A discount of d% leaves you paying (100 - d)% of the original price. That is the whole theory: 30% off means paying 70% - multiply the price by 0.70. The discounted price is original x (1 - d/100), and the amount saved is original x (d/100); the two always sum back to the original.

Working in fractions (0.70) rather than percentages (30%) is what makes everything stack cleanly - you multiply the remaining fractions, and no "adding percentages" happens anywhere.

Worked example

Original price:        80
30% discount:  80 x 0.70 = 56.00   (save 24.00)
Then 20% more:   56 x 0.80 = 44.80   (save 11.20)
Total saved:     35.20 of 80  ->  effective discount 44%
(not 50%: 0.70 x 0.80 = 0.56, i.e. you pay 56% of the original)

Stacked discounts are multiplications

"Extra X% off the sale price" is a chain: each discount multiplies the running total by its remaining fraction. The effective single discount is 1 minus the product of the fractions - never the sum of the percentages. Fifty percent off, then fifty percent off, is 0.5 x 0.5 = 0.25: you pay 25% of the original, a 75% total discount - not 100%. The second discount acts on the already-reduced price, and that is the entire story.

The practical consequence for shopping: a long chain of small "extra" discounts is worth less than it reads. A 10% base plus four "10% extra" steps leaves 0.9^5 = 59% of the original - a 41% total discount, not 50%.

Where tax sits in the calculation

Order matters, and conventions differ by region:

Tax-exclusive (typical US checkout): discount first, then tax on the discounted price. The discount saves you tax too - a 30% discount on a taxed price saves 30% of the tax as well.
Tax-inclusive (typical EU receipts): the printed price already contains VAT; discounts reduce the taxed price, and the VAT content of the discount is computed from the net.
The rule of thumb: always know whether the number you are holding is net or gross before you apply anything to it. "Add 20%" to a gross price and to a net price give different final totals.

Reading a receipt backwards

Just as often you need the reverse operation: given the final price and the discount, what was the original? Divide by the remaining fraction - a 56.00 price after 30% off implies an original of 56 / 0.70 = 80. For chains, divide by the product of the fractions. And if tax is involved, undo the last thing that was applied first: strip tax, then discount, in reverse order of how they were applied.

Frequently asked questions

Is 50% off then 50% off the same as 100% off?

No - the second 50% acts on the already-halved price, so you pay 25% of the original (a 75% total discount). Free would require the second discount to be 100%.

Does the discount apply before or after tax?

Where tax is added at checkout (tax-exclusive), the discount comes first and the tax is charged on the discounted amount - so you save tax as well. Where prices are tax-inclusive, the discount reduces the total and the VAT within it.

How do I find the original price from the sale price?

Divide the sale price by the fraction you paid: sale price / (1 - discount/100). A 70 price after a 30% discount came from 70 / 0.70 = 100.

How accurate is the mental math?

Good enough for decisions: round the fraction (30% off = pay 0.7), multiply, and check the order of size. For invoices and refunds, use exact arithmetic - the rounding differences add up.