“Thirty percent off” is one of the simplest claims in retail, and one of the most misunderstood. Shoppers add discounts that should be multiplied, compute sales tax on the wrong price, and assume a 50% markdown returns a marked-up price to its original cost. The math underneath is only two short formulas — but every promotion you will ever meet is built out of them, stacked, reversed, and taxed. This guide states both formulas precisely, then works them through real numbers: a $240 jacket at 25% off, stacked coupons, sales tax applied correctly, and the classic markup trap that costs shoppers money. Check your own numbers against the percentage calculator as you go.
The two formulas, in plain words
A discount is a percentage of the original price. Convert the percentage to a decimal (divide by 100), then:
Discount amount: D = P × d
where P is the original price and d is the discount rate as a decimal (25% = 0.25). This is the number of dollars taken off.
Final sale price: S = P × (1 − d)
This is the number of dollars you actually pay. It skips the intermediate step: instead of subtracting the discount from the price, you multiply by the fraction that remains. At 25% off, you pay 75% of the price — one multiplication, one answer.
Both formulas always agree, because S = P − D = P − P×d = P × (1 − d). Use whichever is faster for the problem in front of you.
Worked example: the $240 jacket at 25% off
A jacket is priced at $240, marked 25% off.
Discount amount: D = 240 × 0.25 = $60
Sale price: S = 240 × (1 − 0.25) = 240 × 0.75 = $180
Check: 240 − 60 = 180. Both formulas agree.
Here is the same price at the most common discount levels, so the pattern is visible:
| Discount | You save | You pay |
|---|---|---|
| 10% | $24.00 | $216.00 |
| 15% | $36.00 | $204.00 |
| 20% | $48.00 | $192.00 |
| 25% | $60.00 | $180.00 |
| 30% | $72.00 | $168.00 |
| 40% | $96.00 | $144.00 |
| 50% | $120.00 | $120.00 |
The sale-price column is the useful one at the shelf: it is exactly (1 − d) of $240, and each row is computed the same way — 240 × 0.90, 240 × 0.85, and so on.
Stacked discounts: 30% off plus an extra 20% off is NOT 50% off
Retailers love stacking: “30% off, plus take an extra 20% off at checkout.” Most shoppers add 30 + 20 = 50 and expect half price. That is wrong. The second discount applies to the already-discounted price, not the original.
Worked example on a $100 item:
- After the first 30%: 100 × (1 − 0.30) = 100 × 0.70 = $70
- After the extra 20%: 70 × (1 − 0.20) = 70 × 0.80 = $56
Total saved: $44, which is a 44% effective discount — not 50%. The general rule for n stacked discounts:
S = P × (1 − d₁) × (1 − d₂) × … × (1 − dₙ)
Two observations fall out of this. First, the order does not matter: 30% then 20% gives 0.70 × 0.80 = 0.56, and 20% then 30% gives 0.80 × 0.70 = 0.56. Multiplication commutes, so whichever coupon is scanned first, you pay the same. Second, adding percentages overstates the deal — and retailers know it. An “extra 20% off” after 30% off only removes 20% of the remaining 70%, i.e., 14 percentage points of the original price.
Sales tax is charged on the discounted price
In the US, sales tax applies to what you actually pay — the post-discount price — not the original sticker. Worked example: the $180 jacket above, in a state with 7% sales tax.
Tax: 180 × 0.07 = $12.60
Total out of pocket: 180 + 12.60 = $192.60
The common error is computing tax on $240 (tax = $16.80, total = $196.80) — $4.20 too high. Whenever you estimate a final checkout total, the sequence is: discounts first, then tax. The combined formula is:
Final total = P × (1 − d₁) × (1 − d₂) × … × (1 + t)
where t is the tax rate as a decimal. On the jacket with the single 25% discount: 240 × 0.75 × 1.07 = $192.60.
The markup trap: 50% up, then 50% off, does not return to the start
A store buys a gadget for $100 wholesale, marks it up 50%, then clears it at 50% off. Is the clearance price $100 again? No.
- Markup: 100 × (1 + 0.50) = $150
- Clearance: 150 × (1 − 0.50) = 150 × 0.50 = $75
The store sells at $75 — $25 below its cost. The asymmetry: a percentage gain and an equal percentage loss do not cancel, because the loss applies to a larger base. This is the same math as stacked discounts in disguise. Whenever a retailer advertises a deep markdown off an “original” price, the question worth asking is what the item actually sold for before the promotion — the percentage calculator makes the two-way check quick.
Working backward: find the original price from the sale price
Ads sometimes give only the sale price and the discount: “Now $168 — save 30%.” To recover the original price, rearrange the sale-price formula:
P = S ÷ (1 − d)
Worked: S = 168, d = 0.30 → P = 168 ÷ 0.70 = $240. Check: 240 × 0.70 = 168. This also exposes inflated “was” prices: if the claimed original price doesn’t match the math, the discount is measured against a price the item rarely sold for.
Which deal is actually better?
Two stores sell similar sneakers. Store A: $89.99 at 25% off. Store B: $99.99 at 30% off. The bigger percentage does not automatically win.
- Store A: 89.99 × 0.75 = $67.49
- Store B: 99.99 × 0.70 = $69.99
Store A is cheaper by $2.50, even though its discount percentage is smaller. The percentage only tells half the story; the base price tells the other half. When comparing, compute both sale prices — one multiplication each — and compare the answers, not the headlines.
Mental-math shortcuts that are actually reliable
- 10% of anything: move the decimal one place left. 10% of $240 is $24.00.
- Any multiple of 10%: scale the 10% figure. 30% off $240 = 3 × $24 = $72.
- 50%, 25%, 20%: halve ($120), halve twice ($60), or divide by 5 ($48) — on $240 these are $120, $60, and $48 respectively.
- 15%: take 10% and add half again. 10% of $240 is $24; half is $12; total $36.
- 5%: take 10% and halve it. 5% of $240 = $12.
For a stacked discount, estimate sequentially: 30% off $100 is $70 (10% is $10, times 3 is $30, off $100), then 20% off $70 is $56 (10% is $7, times 2 is $14, off $70). The register should show $56 — close enough to catch a scanning error on the spot.
How to check your own numbers
Enter the original price and the discount percentage into the percentage calculator: the “X% of Y” mode gives the discount amount, and subtracting it from the price gives the sale price — or compute the sale price directly as price × (1 − d). For stacked coupons, run the calculator once per discount on the running total. Compare the register’s sale price to your calculation before paying; a mismatch of more than a few cents usually means a coupon didn’t scan.
Frequently asked questions
Does the order of stacked coupons change the final price?
No. Each discount multiplies the running total by (1 − d), and multiplication order does not change the result. On a $100 item, 30% then 20% gives 100 × 0.70 × 0.80 = $56, and 20% then 30% gives 100 × 0.80 × 0.70 = $56. The only thing that can change the total is an exclusion — a coupon marked “not valid on sale items” that the register rejects.
Is sales tax charged before or after the discount?
After, in every US state: tax is computed on the amount you actually pay. On the worked $240 jacket at 25% off with 7% tax, the correct total is 240 × 0.75 × 1.07 = $192.60. Manufacturer’s coupons and instant rebates can occasionally be taxed differently at the register (a manufacturer’s coupon may be treated as a form of payment rather than a price reduction), but store discounts and percent-off coupons always reduce the taxable price first.
Why do “up to 50% off” sales feel disappointing?
Because “up to” describes the maximum discount on something in the sale — usually a small clearance subset. The store is advertising the best-case row of the table, not the typical one. A second effect: 50% off an inflated “was” price can be worse than 30% off a fair one, as the sneakers comparison shows. Judge the sale price in dollars against what the item sold for last week, not the advertised percentage.
How do I reverse-engineer a discount from two prices?
If an item was $240 and is now $168, the discount is (240 − 168) ÷ 240 = 72 ÷ 240 = 0.30, or 30%. The general form: d = (P − S) ÷ P. This is the same calculation retailers use when they print “Save 30%” on the tag — and it is worth recomputing whenever the claimed percentage seems too generous.
Can a discount ever exceed 100%?
A true discount of more than 100% would mean the store pays you to take the item — it doesn’t happen as a percentage-off price. What does happen: rebates and cash-back offers stacked on a deep discount can push your net cost below zero in rare promotional cases (e.g., a $5 item with a $6 rebate app offer). Those are rebates, not discounts — the register price never goes negative; the extra value arrives after purchase.
What is the difference between a discount and a rebate?
A discount reduces the price you pay at the register — the sale-price formula S = P × (1 − d) describes it exactly. A rebate is money returned after the purchase, usually by mail or app, and it does not change the register total or (typically) the taxable amount. A “$200 item, 25% off plus $20 mail-in rebate” costs $150 at checkout, with $20 arriving weeks later. Always separate the two when comparing deals.
verified_user Editorial Guidelines
Written by real humans with real-world experience. Our content at CalcaTools prioritizes factual accuracy, usability, and your privacy. We continuously review our articles to ensure they meet modern E-E-A-T (Experience, Expertise, Authoritativeness, and Trustworthiness) standards.