How this instrument works
A percent-off sign is a single multiplication wearing a costume. Taking 25% off does not mean subtracting 25 from anything — it means keeping 75% of what was on the tag, so the answer is the ticket figure multiplied by 0.75. Written once and for all: sale = p × (1 − d ⁄ 100). The bracket is the fraction still owed, which is why a 40% sign and a 0.60 multiplier are the same instruction to a till.
The saving is the other half of the same split, saved = p × d ⁄ 100, and the two always add back to what was on the tag. That identity is the fastest sanity check on a shop floor: if the reduced figure and the saving do not sum to the ticket, one of them was mistyped. It also explains why stacked offers disappoint — 20% off followed by another 20% off keeps 0.8 × 0.8 = 0.64 of the original, a 36% reduction rather than 40%.
Rounding happens after the multiplication and only at the end, to the nearest cent. A $59.99 jacket at 30% off works out at exactly $41.993, which a till prints as $41.99 with an $18.00 saving — a penny of drift that is normal and legal. This sheet shows the unrounded product to two decimals so you can see precisely where that penny went.
- Type the figure from the tag into ORIGINAL PRICE, $ — the amount before anything is taken off.
- Set DISCOUNT, % to the advertised percentage: 25 for a quarter off, 33.3 for a third, 70 for the clearance rail.
- Read SALE PRICE for what you hand over, and YOU SAVE for what stays in your pocket.
- Confirm the two readouts add back to the ticket figure. If they do not, a digit slipped in the entry.
Worked example — the $80 jacket at 25% off
A jacket is ticketed at $80 and the rail says 25% off. The multiplier is 1 − 25 ⁄ 100 = 0.75, so you hand over 80 × 0.75 = $60.00. The saving is 80 × 25 ⁄ 100 = $20.00, and $60.00 plus $20.00 lands back on $80 exactly — the check that catches almost every slip.
Quarter-off tags are worth doing in your head: a quarter of 80 is 20, so 80 becomes 60. The shortcut breaks on the second markdown. Take another 25% off that $60 and you pay $45.00, a total saving of $35.00 against the original tag — 43.75% off, not the 50% that two signs seem to promise.
Questions
How do I work out 25% off in my head?
Take a quarter away. A quarter of $80 is $20, so you pay $60. The same trick scales to almost any sign: 10% is the number with its decimal point moved one place left, 20% is that doubled, and 5% is half of the 10%. Most shop-floor percentages are assembled from those three pieces — 35% off an $80 tag is 10 + 10 + 10 + 5, which comes to $28 saved and $52 paid.
Do two 20% discounts add up to 40% off?
No — they compound to 36%. The second markdown applies to the already-reduced figure, so the item keeps 0.8 of 0.8, or 0.64 of the original. On a $50 tag that is $32.00 paid and $18.00 saved, not the $30 and $20 a naive sum suggests. To model a stacked offer on this sheet, run it once, then feed the result back in as the new starting figure and apply the second percentage.
How do I find the original price from the sale price?
Divide instead of multiplying: p = sale ⁄ (1 − d ⁄ 100). A coat bought for $63 at 30% off was ticketed at 63 ⁄ 0.70 = $90.00. The common error is adding 30% back onto $63, which returns $81.90 — wrong because the percentage was taken from the larger number, so it has to be undone against the larger number too.
Is sales tax applied before or after the discount?
After. Tax is charged on the amount actually paid, so the markdown comes off first and the rate applies to the reduced figure. An $80 jacket at 25% off with 8% tax rings up as 60 × 1.08 = $64.80. Manufacturer coupons are the exception in several states, where tax may be assessed on the pre-coupon amount because the maker reimburses the store; the receipt is the authority on which rule your state uses.
Can a discount be more than 100%?
Not meaningfully. At 100% the bracket falls to zero, the item is free, and the saving equals the whole tag; beyond that the shop would be paying you to carry the goods away. The DISCOUNT, % field is capped at 100 for that reason. Figures above 100% do turn up in trade pricing as markups, but a markup is measured against cost, which is a different quantity from the tag a customer sees.
References
- FTC — Guides Against Deceptive Pricing, 16 CFR Part 233
- FTC — advertising and marketing guidance for businesses
- NIST Office of Weights and Measures — price verification
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.