What a discount percentage is measured against

A reduction is always a share of a price that existed first. The one-line arithmetic is easy; what causes trouble is the reference point. “Twenty per cent off” means twenty per cent of the ticket price, not of the price you were hoping to pay, and “an extra twenty per cent” in a shop window means twenty per cent of what is left, not forty off the original. This page computes the straightforward single-stage case and shows both halves of it: how much you saved and what you pay.

The formula

saved = price × discount ÷ 100

final price = price − saved

The discount field accepts 0 to 95 per cent with quick-pick buttons at 10, 20, 30, 50 and 70, and the currency selector governs display only — it applies no conversion. The 95 per cent ceiling is deliberate in the sense that the field stops short of 100, so a completely free item cannot be entered here.

Numbers to check

The defaults. 199 at 20 per cent: the saving is 199 × 0.20 = 39.80, and the final price is 199 − 39.80 = 159.20.

A half-price sale. 240 at 50 per cent: saved 120.00, final 120.00.

Two discounts, not one. 199 with 20 per cent applied twice is not 40 per cent off. The first stage gives 159.20; a second 20 per cent stage takes 31.84 more and leaves 127.36. The overall reduction is 71.64 on 199, or 36 per cent — because the second reduction was charged against the already-reduced figure. Multiplying the surviving fractions gives the same answer directly: 0.8 × 0.8 = 0.64, so you pay 64 per cent of the original.

Working backwards. If something costs 159.20 after 20 per cent came off, dividing by 0.8 recovers 199.00. Dividing by 1.2 or subtracting 39.80 would both be wrong.

Where discounts mislead

• Stacked reductions compound downward, not additively. 50 per cent off followed by another 50 per cent off leaves a quarter of the original price, not zero. This is why “take an extra half off” on an already discount-sale item is a much smaller concession than it sounds, and why the page must be run once per stage, feeding each result into the next.
• Discount is not margin. If you buy at 60 and sell at 100, your gross margin is 40. Discounting 40 per cent takes the price to exactly 60 — the whole margin, gone. A discount equal to your margin percentage is not a 40 per cent loss of profit, it is a total loss of it. Anything beyond that sells below cost.
• The original price may be invented. A ticket price inflated shortly before a sale makes the percentage technically true and commercially meaningless. Track the price you would actually have paid before.
• Tax and shipping sit outside the percentage. A 20 per cent saving on a 199 item is 39.80, but sales tax applies to 159.20 and delivery is unaffected, so the reduction in what leaves your account is smaller than the headline.
• Round numbers hide the total. Buying three discounted items to “save” 40 each spends 477.60 to avoid spending 597. A saving is only a saving if the purchase was going to happen anyway.
• Percentage caps cut off the extremes. The field cannot express 100 per cent off, so bundle deals and free-with-purchase offers need to be handled by hand.
• Rounding to a psychological price. Retailers often take 20 per cent off and then round down to 159 or 158.99. The tool reports the exact arithmetic, so expect the till to differ by a cent or two.

Common questions

How do I work out the price when I only know the saving?

Divide the saving by the discount rate. Saving 39.80 at 20 per cent means the original was 39.80 ÷ 0.20 = 199.00.

What is the difference between a discount and a markdown taken at the till?

None arithmetically; both are subtractions from a listed price. The distinction is commercial, and it matters for returns: some shops refund the price paid and others the current selling price, so keeping the receipt is what protects the difference.

How do I compare two offers — 30 per cent off, or buy two get one free?

Convert both to the fraction of the original you actually pay. Thirty per cent off leaves 0.70 per item. Three for two leaves 0.667 per item, because you pay for two of the three. The second is the better deal by about 3.3 per cent, provided you needed three.

Why does my result differ slightly from the shop's?

Almost always mid-calculation rounding. The page keeps full precision and rounds once when displaying, while a till may round the saving to the nearest cent first and then subtract.

Which other pages use this arithmetic?

The Percentage page covers the same formula without the retail framing and can compute a rise as easily as a fall, and the Tip page is the identical operation in the opposite direction, adding a percentage to a base instead of removing one.