"40% off" looks simple on a price tag until you're standing in a store trying to do the math in your head, or building a shopping cart that needs to show it automatically. Here's every version of the discount calculation you'll actually run into.
Finding the Sale Price
Sale Price = Original Price − (Original Price × Discount% ÷ 100)
A $80 jacket at 25% off: 80 − (80 × 25 ÷ 100) = 80 − 20 = $60.
There is a one-step shortcut: if you take 25% off, you pay the remaining 75%. So Sale Price = Original × (1 − Discount% ÷ 100), and the jacket is 80 × 0.75 = $60. This version is easier to type into a phone calculator and becomes essential once discounts start stacking.
Quick Reference: Common Discounts on a $60 Item
| Discount | You save | You pay |
|---|---|---|
| 10% | $6.00 | $54.00 |
| 15% | $9.00 | $51.00 |
| 20% | $12.00 | $48.00 |
| 25% | $15.00 | $45.00 |
| 30% | $18.00 | $42.00 |
| 40% | $24.00 | $36.00 |
| 50% | $30.00 | $30.00 |
| 70% | $42.00 | $18.00 |
Finding the Discount Percentage
Sometimes you know the before and after price and want the percentage itself — useful for comparing whether a "sale" is actually a good deal.
Discount% = ((Original − Sale) ÷ Original) × 100
A $200 item now selling for $150: ((200−150)÷200)×100 = 25%.
This is also how you compare two differently worded offers. Is "$15 off a $60 purchase" better than "20% off"? Convert the fixed amount into a percentage: 15 ÷ 60 × 100 = 25%. The $15 coupon wins on a $60 basket. On a $100 basket, though, $15 off is only 15%, so the 20% offer would be better — fixed-amount coupons are worth more, in percentage terms, on smaller purchases.
Working Backward From the Sale Price
If you only know the discounted price and the percentage off, and need the original price:
Original Price = Sale Price ÷ (1 − Discount% ÷ 100)
A jacket on sale for $60 at 25% off: 60 ÷ (1 − 0.25) = 60 ÷ 0.75 = $80.
A tempting but wrong shortcut is to add 25% back on to the sale price. That gives 60 × 1.25 = $75, not $80, because the 25% was taken from the original price, not from $60. To undo a discount you always divide by the "keep" fraction rather than adding the same percentage back.
Stacking Two Discounts
This is where most mental math breaks down: two discounts don't add together. "25% off, plus an extra 10% off" is not 35% off — the second discount applies to the already-reduced price, not the original.
$100 item: 25% off brings it to $75. Then 10% off that: 75 − 7.50 = $67.50. The combined discount is actually 32.5%, not 35% — a smaller saving than it sounds like.
A Quick Sanity Check
A useful shortcut: multiply the "keep" percentages instead of adding the discounts. Keeping 75% and then 90% of that is 0.75 × 0.90 = 0.675, meaning you pay 67.5% of the original — which matches the $67.50 above.
The same method works for any combination:
| Stacked offer | Multiply the "keep" parts | Real total discount |
|---|---|---|
| 20% + 10% | 0.80 × 0.90 = 0.72 | 28% (not 30%) |
| 25% + 10% | 0.75 × 0.90 = 0.675 | 32.5% (not 35%) |
| 50% + 20% | 0.50 × 0.80 = 0.40 | 60% (not 70%) |
| 50% + 50% | 0.50 × 0.50 = 0.25 | 75% (not 100%) |
| 50% + 20% + 10% | 0.50 × 0.80 × 0.90 = 0.36 | 64% (not 80%) |
For percentage discounts, the order does not matter — multiplication gives the same answer either way. A fixed-amount coupon is different. On a $100 item, 20% off and then $10 off gives 80 − 10 = $70, but $10 off first and then 20% off gives 90 × 0.80 = $72. If a store lets you choose, apply the percentage discount first.
Discounts and Sales Tax
Where sales tax is added at the till, it is normally charged on the price you actually pay. The $80 jacket at 25% off costs $60; with 8% tax, the total is 60 × 1.08 = $64.80. Because both are percentages, you get the same total if you calculate the other way round: 80 × 1.08 × 0.75 = $64.80. Tax rules for coupons and rebates vary by country and state, so check the receipt if the exact amount matters.
Multi-Buy Deals as Percentages
"Buy one, get one" style offers are easier to compare once you convert them into a discount on everything you buy:
- Buy one, get one free: you pay for 1 item out of 2, which is 50% off each — but only if you actually wanted two.
- Buy one, get one half price: you pay for 1.5 items out of 2, so
0.5 ÷ 2 = 25%off overall. - Buy two, get one free: you pay for 2 items out of 3, a saving of
1 ÷ 3 ≈ 33.3%.
When the items have different prices, the free one is usually the cheapest, so the real saving is lower than these figures.
Discount vs. Markup
Retailers raising a price and later discounting it can leave you worse off than you expect. A $40 item marked up 50% becomes $60; a "50% off" sale then brings it to $30 — not back to $40. Percentages are always calculated on the current price, so equal-sized rises and falls do not cancel out. You can explore that effect in more detail in Percentage Increase and Decrease Formula & Examples.
Mental Math Tips at the Shelf
- Work in 10% blocks: 30% off $70 is three lots of $7, so you save $21 and pay $49.
- Halve for 50%, quarter for 25%: 25% off $48 saves $12, leaving $36.
- Round first, adjust after: 20% off $39.99 is close to 20% off $40, so expect to pay about $32.
Common Mistakes
- Adding stacked discounts together instead of multiplying the remaining fractions.
- Reversing a discount by adding the same percentage back on.
- Dividing the saving by the sale price instead of the original price when working out the discount percentage.
- Reading "up to 70% off" as "70% off" — usually only a few items carry the top discount.
Skip the mental math entirely with our Percentage Calculator — it handles all three directions of this calculation. For the general formulas behind every example here, see How to Calculate Percentage: Formula and Examples.
Frequently Asked Questions
How do I calculate a discount in Excel or Google Sheets?
With the original price in A2 and the discount in B2 formatted as a percentage (for example 25%), the sale price is =A2*(1-B2). To find the discount percentage from two prices, use =(A2-C2)/A2 where C2 is the sale price, and format the result as a percentage.
What is the difference between markup and margin?
Both describe profit, but against different bases. If an item costs a shop $50 and sells for $80, the $30 profit is a 60% markup (30 ÷ 50) but a 37.5% margin (30 ÷ 80). A discount is measured against the selling price, so a 37.5% discount would remove the entire profit.
Is a discount percentage the same as a percentage decrease?
Yes. A discount is a percentage decrease from the original price, using the original price as the base. That is why the formula matches the general percentage change formula, just reported as a positive "off" figure.
Should I round the sale price up or down?
Calculate with full precision, then round to the nearest cent at the end. Shops can have their own rounding rules at the till, so a one-cent difference from your own calculation is normal.
Try it yourself: next time you see a sale sign, estimate the price with the 10% method, then confirm it in the Percentage Calculator. Comparing two shops' prices rather than a before-and-after? The Percentage Difference Calculator is the right tool for that.