Shops are good at making two offers look like more than they are. "20% off everything, plus an extra 10% at the till" sounds like 30%. "Buy 2, get 1 free" sounds like a third off whatever you buy. A bigger pack sounds cheaper per gram. Sometimes they are; often they are not. This article works through each case with real numbers from our discount and unit price calculator.
Stacked discounts multiply
A discount of 20% means you pay 80% of the price. A second discount of 10%, applied at the till, means you pay 90% of what is left. Together you pay 0.80 × 0.90 = 0.72 of the original price.
On a jacket priced at 100:
| Step | Price before | Off | Price after |
|---|---|---|---|
| 20% off | 100.00 | 20.00 | 80.00 |
| extra 10% off | 80.00 | 8.00 | 72.00 |
You save 28, a 28% discount, not 30%. The general rule for discounts a and b is 1 − (1 − a)(1 − b). The gap grows with the size of the discounts: 50% plus 50% is 75% off, not free.
Two consequences:
- The order of percentage discounts does not matter. 10% then 20% is 0.9 × 0.8 = 0.72, the same.
- The order does matter once a fixed amount is involved. A 10% discount and a 5-off voucher on 100: percentage first gives 90, then 85. Voucher first gives 95, then 10% of 95 is 9.50, leaving 85.50. If you can choose, use the percentage first; if the shop decides, check which order it applies.
Buy X get Y: count what you actually take
"Buy 2, get 1 free" on items costing 30 means three items for 60: 20 each, 33.33% off, but only for complete groups of three. The calculator works from the quantity you want:
- 3 items: 60 in total, 20 each.
- 7 items: two complete offers (6 items for 120) plus one at full price, 150, or 21.43 each: 28.57% off overall.
- 2 items: no free item at all, 60, 0% off.
"Buy one, get the second half price" is 25% off a pair (30 + 15 = 45 for two) and nothing off one item. An offer is only a discount on what you would have bought anyway; taking an extra item you did not need to "unlock" it is spending, not saving.
Tax: dividing, not subtracting
Adding 10% tax to a net price of 100 gives 110. Going back, the common mistake is to take 10% of 110 (11) and get 99. The tax was calculated on the net price, so it is 1/11 of the gross price: 110 ÷ 1.1 = 100 before tax, 10 of tax. With 8% included in a price of 100, the net price is 100 ÷ 1.08 = 92.59 and the tax 7.41.
Discounts and percentage taxes are both multiplications, so whether a 20% discount is applied before or after a 10% tax makes no difference to the final price (100 × 0.8 × 1.1 = 100 × 1.1 × 0.8 = 88). It does matter for a fixed-amount voucher and for how the receipt shows the tax.
Unit prices: per 100 g, per 100 ml, per piece
The honest way to compare packs is price per unit of quantity. Two packs of the same coffee:
- 500 g for 45,000: 45,000 ÷ 500 × 100 = 9,000 per 100 g.
- 1 kg for 85,000: 85,000 ÷ 1,000 × 100 = 8,500 per 100 g.
The big pack is cheaper per gram; the small one costs 500 ÷ 8,500 = 5.88% more for the same amount of coffee. Bigger is not always cheaper, though, and promotions on small packs regularly reverse the result, which is why a calculation beats a rule of thumb.
Multipacks need the total quantity: a 6-pack of 330 ml cans for 60,000 is 1,980 ml, so 60,000 ÷ 1,980 × 100 = 3,030.30 per 100 ml; a 1.5 l bottle of the same drink for 30,000 is 2,000 per 100 ml. Imperial units convert exactly (1 oz = 28.349523125 g, 1 lb = 453.59237 g, so 16 oz is exactly one pound). The calculator refuses to compare grams with millilitres, because that needs the product's density.
Common mistakes
- Adding percentages. 20% + 10% is 28% off; 30% + 20% is 44%; 50% + 50% is 75%.
- Ignoring the order with vouchers. A fixed amount before a percentage saves less than after it.
- Counting a multi-buy offer on items you would not have bought.
- Subtracting the tax rate from a tax-inclusive price. Divide by (1 + rate) instead.
- Comparing pack prices instead of unit prices, or comparing a unit price "per 100 g" on one shelf label with "per kg" on another. Convert both to the same base.
- Forgetting the drained weight. For tinned food in liquid, compare the drained weight if the label gives it.
For other percentage questions (what percent of, percentage change, reverse percentages), the percentage calculator shows the formula for each.