Discount Calculator

A discount is one multiplication, but it is the multiplication people most reliably get backwards — usually by subtracting a percentage when they should be dividing, or by adding two discounts together. The calculator above does the arithmetic; this page covers the traps around it.

How it works

Enter the original price and the discount percentage. The tool reports two figures as you type:

• You save — the original price multiplied by the percentage, divided by 100.
• Final price — the original price minus that saving.

Both are rounded to two decimal places, because a price is a money amount and the third decimal is not spendable. The percentage is constrained to 0–100 and the price must not be negative; outside those ranges the tool shows a short message instead of a nonsense result. A 0% discount correctly returns the original price, and 100% correctly returns zero rather than an empty field.

The defaults are 80 and 25%, so the first thing you see is a worked example: save 20, pay 60.

The three mistakes

Discounts do not add. Two successive 10% reductions are not 20% off. The second is applied to the already-reduced price, so you pay 81% of the original — a 19% discount. Chain them by running the calculator twice, feeding the first final price in as the second original price, or multiply the remaining factors directly: 0.9 × 0.9 = 0.81. The same applies to a staff discount stacked on a sale price.

Reversing a discount means dividing, not adding the percentage back. If a jacket cost 68 after 15% off, the sale price is 85% of the original, so the original was 68 ÷ 0.85 = 80. Adding 15% to 68 gives 78.20, which is wrong, and wrong in the direction that understates the original price. The same asymmetry is why a 50% loss needs a 100% gain to recover.

Tax and discount are not commutative in every jurisdiction. Applying 20% VAT to a discounted price is not the same as discounting a VAT-inclusive price only if the discount is fixed-amount; for a percentage discount the two orders agree. Where they differ is rounding: each step rounds to the cent, and two roundings can land a cent apart from one. If an invoice total must reconcile exactly, apply the discount to the net amount and compute tax once, on the result.

Rounding and money

The tool rounds half-up to two decimals, which matches what most shoppers expect. Payment systems are stricter: amounts are transmitted as integers in the currency's minor unit, so 60.00 EUR travels as 6000 and there is no representation for 60.005 at all. That constraint is why the discount on a line item is normally computed and rounded per line, then summed, rather than computed on the order total — the two approaches can differ by a cent per line, and the ledger has to balance. Payment systems fundamentals covers minor units, currency exponents and why amounts are never floats in a real settlement flow, and card payments walks through how an authorised amount is captured and adjusted.

For a quick sanity check on the percentage itself — "68 is what percent of 80?" — the percentage calculator answers the question in the other direction, and the tip calculator does the same arithmetic with the sign flipped.