How this instrument works
Each markdown acts on whatever price survived the one before it, never on the original ticket. Taking 50% off leaves half; taking another 50% off that half leaves a quarter. So stacked cuts multiply rather than add — arithmetic with the same shape as compound growth, sign flipped — and that is why a rack marked 50% off with an extra 50% at the till never means free.
The second readout answers what shoppers actually want to know: which single percentage would have produced this price in one step. It is one minus the product of the two surviving fractions. Because multiplication commutes, the sequence a cashier rings the reductions in changes nothing about the total, though store policy often insists on one order and forbids the other.
Two limits are worth naming. This sheet works on the ticket price alone: sales tax is charged afterwards, usually on the reduced amount, and shipping, handling and restocking fees sit outside it entirely. It also assumes the second cut lands on the already-reduced price. A handful of promotions instead take both percentages off the original ticket, which makes them genuinely additive — read the fine print before trusting either arithmetic.
- Put the ticket price into Original price, $ — before tax, before any reduction.
- Enter the rack or storewide markdown as First discount, %.
- Enter the coupon, loyalty rate or extra cut as Second discount, % — the one applied to the already-reduced figure.
- Read You pay for the register total on that item.
- Check Effective single discount, % to see the one percentage that matches, and compare it against a rival's flat offer.
Worked example — half off, then half off again
A jacket rings up at $100. The rack says 50% off, and a register coupon takes another 50% off that reduced figure. First cut: 100 × 0.5 = $50. Second cut: 50 × 0.5 = $25. You pay $25 — not nothing.
That pair is worth an effective single discount of 75%, because a quarter of the price survives and three quarters has gone. Anyone adding 50 and 50 to reach 100 walks to the till expecting a free jacket; the shortfall is exactly a quarter of the ticket, at every price, every time.
Questions
Why isn't 50% off twice the same as free?
Because the second cut applies to the already-halved figure, not the original ticket. Half of $100 is $50; half of $50 is $25. A quarter always survives two 50% reductions, whatever the starting price. Adding percentages only works when both come off the same base, which stacked retail promotions almost never do.
Does the order of the two reductions matter?
Not to your total — multiplication commutes, so 20% then 10% and 10% then 20% both land on $72 from $100. Sequence matters only to store policy and to rules about which coupon may be applied to which price. If a cashier insists on an order, your receipt should come out identical either way; if it doesn't, one reduction is being computed on a different base than you assume.
What single percentage matches 20% plus an extra 10%?
28%, not 30%. Eighty percent of the price survives the first cut and ninety percent of that survives the second: 0.8 × 0.9 = 0.72, so 72% of the ticket remains and 28% has gone. The gap between the naive sum and the true figure widens as the percentages grow — 40 and 25 give 55, not 65.
Is sales tax included in You pay?
No. This sheet works on the ticket price only. Across most US states tax is charged on the discounted amount, so it is applied after both cuts and added on top of the figure shown here. Shipping, handling, restocking fees and any minimum-spend threshold for free delivery also sit outside this calculation.
My store took both percentages off the original ticket — why does my total differ?
A few promotions do exactly that, and it is a different arithmetic: two reductions drawn from the same base really do add. Both taken from $100 gives $100 − $50 − $50 = nothing, whereas this instrument returns $25. Look for wording like 'off the original ticket' versus 'off already-reduced prices'. Only the second phrase describes the multiplicative case modelled here.
Which pair of cuts beats a straight 60% off?
Any pair whose surviving fractions multiply below 0.40. Fifty then twenty leaves 0.5 × 0.8 = 0.40, exactly matching. Fifty then twenty-five leaves 0.375, an effective 62.5%. Enter candidates as First discount, % and Second discount, % and read Effective single discount, % to line them up against a flat offer directly.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.