How the sale price is calculated
A discount of d percent leaves you paying 100 − d percent of the price, so the calculator multiplies the original price by (1 − d / 100). The You save figure is the original price minus that final price. If you tick Add a second discount, a second percentage is applied to the already reduced price, not to the original:
final = price × (1 − d1 / 100) × (1 − d2 / 100)
Results display with up to two decimal places. Each percentage field is limited to 0 to 100.
The Find the original price button reverses the calculation: you enter the sale price you paid and the discount, and it divides by (1 − d / 100) to show the original price. A discount of 100% cannot be reversed, so that case shows a message.
Worked examples
A 25% discount on 80 is 80 × 0.75 = 60, so you save 20. For stacking, 20% off then a further 10% off 100 gives 100 × 0.8 × 0.9 = 72. Two stacked discounts of 20% and 10% are worth 28% in total, not 30%, because the second one applies to a smaller number.
| Price 100 | Final price | Effective discount |
|---|---|---|
| 50% then 50% | 25.00 | 75% |
| 20% then 10% | 72.00 | 28% |
| 30% then 20% | 56.00 | 44% |
| 10% then 10% | 81.00 | 19% |
The order of the two does not matter. 10% then 20% gives the same 72 as 20% then 10%, since multiplication is commutative.
Common mistakes
- Adding percentages. "Extra 20% off already-reduced items" never means 20% off the original. Adding 50% and 50% would mean a free item, which is why the stacked result is 25, not 0.
- Working backwards. If an item is 60 after a 25% discount, the original was 60 ÷ 0.75 = 80, not 60 × 1.25 = 75. Dividing by
(1 − d / 100)is the reverse step, and the Find the original price mode does it for you: enter 60 and 25%. - Tax timing. In most places the sales tax or GST is added after the discount, so the taxed amount is lower. See the sales tax calculator to add it to the final price.
- Percent off versus amount off. A flat coupon such as 10 off is not a percentage. To compare it with a percentage deal, express it as 10 ÷ price × 100.
To find the percentage from two known prices, use the change panel in the percentage calculator. Retailers who need the opposite view, the margin left after discounting, can use the profit margin calculator.