Home › Guides › Discount Math: Percentage Off and Sale Prices
Everyday mathSale signs are designed to short-circuit your math. "70% off!" "Extra 20% off sale!" "Was $199, now $129!" — each format nudges you toward a different (and usually wrong) mental calculation.
This guide teaches the discount formula once, then arms you against every retail trick: stacked discounts, inflated "was" prices, and the art of reversing a discount to find the original price.
Try it yourself: Check any sale price instantly — including stacked discounts and the original price. Percentage Calculator →
The one discount formula
Sale price = original × (1 − discount ÷ 100)
Example: 30% off an $80 jacket: $80 × (1 − 0.30) = $80 × 0.70 = $56. You save $24.
The mental shortcut: compute 10% (move the decimal: $8), then scale — 30% is 3 × $8 = $24 off. For 15%, take 10% plus half ($8 + $4 = $12 off). Two anchor calculations handle almost every sale.
Stacked discounts do NOT add
"Extra 20% off already-reduced items" — if the item is already 30% off, is that 50% off? No. Discounts multiply, they do not add:
$100 → 30% off → $70 → extra 20% off → $70 × 0.80 = $56. Total discount: 44%, not 50%. Each discount applies to the already-reduced price.
The general rule: convert each discount to its "keep" multiplier (30% off → 0.70) and multiply them: 0.70 × 0.80 = 0.56, so you pay 56%. Three stacked discounts of 20/15/10%: 0.80 × 0.85 × 0.90 = 0.612 — you pay 61.2%, saving 38.8%.
"Was $199" — the inflated anchor
Retailers know the first number you see anchors your sense of value. Common plays:
- Inflated "was" prices — the item never meaningfully sold at $199; the "discount" is fictional.
- "Up to 70% off" — one token item is 70% off; most are 15–20%.
- Charm pricing after discount — $129.99 feels much cheaper than $130, though it is one cent.
Defense: check the price history (many shopping tools show it) and compare against competitors' current prices, not the store's claimed "was."
Reverse: find the original price
Paid $56 after 30% off and want the original? Divide by the keep-multiplier:
Original = sale price ÷ (1 − discount ÷ 100)
$56 ÷ 0.70 = $80. This is handy for checking whether a claimed "was" price was real — and for computing discounts from receipt totals when the percentage is not printed.
When a discount is actually a deal
A discount is only a deal if you would have bought the item anyway at near that price. The tests:
- The history test: was it selling at the "original" price recently? If yes, the discount is real.
- The competitor test: is the sale price actually below what rivals charge today — not below their inflated list prices?
- The need test: 50% off something you would not buy at full price is not saving — it is spending with a coupon.
- The total test: add shipping, taxes and "required accessories" before comparing. A 30%-off deal with $20 shipping often loses to a 10%-off deal with free shipping.
The savviest shoppers do the math before the sale: keep a short list of things you genuinely need with their normal prices noted. When a sale hits, you will know in seconds whether it is real.
Frequently asked questions
Multiply the price by 0.80 (which is 1 − 0.20). A $65 item at 20% off: $65 × 0.80 = $52. Mentally: 10% of $65 is $6.50, double it for 20% ($13 off), subtract: $65 − $13 = $52.
No — they equal 28% off. The first discount applies to the full price, the second to the reduced price: 0.80 × 0.90 = 0.72, so you pay 72% and save 28%. Stacked discounts always total less than their sum.
Divide the sale price by (1 − discount as a decimal). Paid $42 after 30% off? $42 ÷ 0.70 = $60 original. This also lets you verify whether a store's claimed "was" price is genuine.
Disclaimer: Calculator content is for education and everyday use. Results are arithmetic estimates — for tax, payroll or contractual matters, confirm with the relevant authority or a qualified professional.