Discount Calculator — % Off, Sale Price, Original Price

Percentages do not add

Three modes: the sale price from an original and a percentage, the percentage from an original and a sale price, and the original from a sale price and a percentage. The third is the one almost nobody uses and the one that catches people out.

But start with the rule underneath all of it. A percentage is always a fraction of the current amount, never a fixed sum — and once that is clear, both of the errors below stop being surprising.

Stacked discounts

Take 20% off 100 and you have 80. Take a further 10% off that and the 10% applies to 80, not to 100 — so it is 8, leaving 72.00.

A single 30% discount would have left 70.00. The two are not the same, and the gap widens as the discounts get larger.

This is not a retailer trick, it is arithmetic — and knowing it helps you rather than them. "Extra 10% off sale prices" is genuinely worth less than it reads, because the second cut is measured against an already-reduced figure. Worth remembering when deciding whether a stacked offer justifies spending more to reach it.

Working backwards is division, not addition

Here is the same error seen from the other side, and it is the more consequential one.

To recover an original price from a sale price you cannot add the percentage back. Add 20% to 80 and you get 96, not 100 — because that 20% was calculated on 80, the smaller number.

You have to divide by the complement: 80 / 0.8 = 100, where 0.8 is 1 minus the 0.2 discount. Same for any figure — divide by one minus the discount as a decimal.

This matters in two practical places. Checking whether an advertised "was" price is consistent with the discount claimed: if a sign says 25% off and shows 80, the original should be 80 divided by 0.75, and a "was" price that does not match tells you something. And reconstructing a pre-discount figure for a receipt or an expense claim, where adding the percentage back gives a number that will not reconcile.

Tax

Applying tax before the discount and applying it after give different totals, so the order is not a detail. Tax is normally charged on the amount actually paid, which is the discounted price — but the rule varies by country and sometimes by product category, so check what applies where you are rather than assuming.

The tax field here applies to the discounted figure and shows the final total.

The reference price is doing most of the work

One honest note. A percentage off is only as meaningful as the price it is measured against, so a large discount on an inflated original can be worth less than a small one on a real price.

That is a fact about retail rather than a criticism of it, and the practical response is simply to look at both numbers. If the original looks higher than what you have seen the item sell for elsewhere, the percentage is describing a comparison that was chosen rather than found.

Everything runs in your browser. For percentage arithmetic that is not about prices — what share one number is of another, or converting between a decimal and a percentage — see the percentage calculator.