Discount Calculator
Two discounts do not add. Thirty per cent off, then a further twenty off the reduced price, is 44% off — not 50.
You pay
$67.20
- You pay
- $67.20
- You save
- $52.80
- Effective discount
- 44.00%
- After the first
- $84.00
- Two discounts do not add. 30% and then a further 20% is 44.0% off, not 50% — because the second one comes off the already reduced price.
- A quick check on any single discount: 20% off means paying 80% of the price, so multiply by 0.8. It is faster than working out the saving and subtracting it.
- Compare against the price before the sale rather than the ticket price. A "was" price that was never really charged makes any discount look larger than it is.
About stacked discounts
A single discount is straightforward: 30% off $120 leaves $84. The quick way to do it in your head is to work out what you pay rather than what you save — 30% off means paying 70%, so multiply by 0.7.
Stacking is where it goes wrong. "An extra 20% off sale prices" applies to the already-reduced figure, so the second discount is 20% of $84 rather than of $120. You pay $67.20 and the effective discount is 44%, not the 50% that adding them suggests.
The gap widens as the discounts grow. 50% and then a further 50% is 75% off, not 100% — which it obviously cannot be, since that would mean free. That impossibility is the quickest way to see that discounts multiply rather than add.
The other thing to check is what the discount is measured against. A "was" price that was never really charged makes any percentage look larger than it is, and in most places there are rules about how long a price has to have been genuinely charged before it can be advertised as a reduction. Comparing against what the thing normally sells for is more useful than comparing against the ticket.
What it works out
- Price after a discount
- A second discount applied to the reduced price
- The effective total discount
- What you save in money
The formula
Final = Price × (1 − First) × (1 − Second)
Multiplication rather than addition, and that is the whole point.
$120 × 0.7 is $84 after the first discount. $84 × 0.8 is $67.20 after the second. You saved $52.80, which against $120 is 44%.
Adding 30 and 20 would give 50%, or $60 — $7.20 less than you actually pay. The reason is that the second 20% applies to $84, not to $120, so it is worth $16.80 rather than $24.
The shortcut for combining them: multiply the "you pay" fractions. 0.7 × 0.8 = 0.56, so you pay 56% and save 44%. That works for any number of stacked discounts and is far quicker than doing them one at a time.
It also makes the ceiling obvious. However many discounts you stack, multiplying fractions below one never reaches zero, which is why 50% and another 50% is 75% off and not free.
- Price
- Before any reduction. Check it is a price genuinely charged.
- First
- The headline discount.
- Second
- Applied to the reduced price, which is why the two do not add.
A worked example
A $120 item at 30% off, with a further 20% off the sale price.
That works out to $67.20 .
- You pay
- $67.20
- You save
- $52.80
- Effective discount
- 44.00%
- After the first
- $84.00
Questions
How do I calculate a discount?
Multiply by what you pay rather than what you save. 30% off means paying 70%, so $120 × 0.7 = $84. It is quicker than working out the saving and subtracting it.
Do stacked discounts add together?
No, they multiply. 30% and then a further 20% is 44% off, not 50, because the second applies to the already-reduced price. Multiply the fractions you pay — 0.7 × 0.8 = 0.56 — and you have it in one step.
What is 50% off and another 50% off?
75% off, not free. Half of a half is a quarter, so you pay 25%. This is the clearest demonstration that discounts multiply rather than add.
Is a bigger discount always a better deal?
Only against a real reference price. A 70% discount from an inflated "was" price can leave you paying more than a 20% discount elsewhere. Compare final prices, not percentages.
How do I work out the original price from a sale price?
Divide by what you paid as a fraction. $84 after 30% off is $84 ÷ 0.7, which is $120. Adding 30% back to $84 gives $109.20 and is wrong — the classic reverse-percentage mistake.
Which order should discounts be applied in?
It makes no difference to the final price — multiplication is commutative, so 30 then 20 gives the same as 20 then 30. It can matter for tax and for coupon terms, which is a rules question rather than an arithmetic one.