Personal finance
Discount calculator
Price and discount, even several in a row: see the final price, what you save and why 30% + 20% is not 50%. Or start from the final price and find the discount.
How to work out a discount
A discount is the price times the percentage: 30% of 120 is 120 × 0.30 = 36, so the final price is 84. Quicker still: the sale price is the price times (1 − discount), that is 120 × 0.70.
With two discounts in a row, the second applies to the already discounted price. On 120, 30% takes it to 84 and a further 20% to 67.20: the overall discount is 44%, not 50%. In general the effective discount is 1 − (1 − d₁)(1 − d₂).
To find the percentage from two prices, divide the saving by the original price: from 80 to 60 you save 20, that is 20/80 = 25%. Mind sales tax: a shop discount usually applies to the price including tax.
Common mistakes
- Adding stacked discounts: 30% + 20% is 44%, not 50%.
- Working out the percentage on the final price instead of the original one.
- Thinking a 25% increase undoes a 25% discount: 100 → 75 → 93.75.
Frequently asked questions
How do you take 20% off a price?
Multiply the price by 0.80: 50 with 20% off becomes 40. The saving is 50 × 0.20 = 10.
What is 50% off plus another 20%?
60%: after 50% half the price is left, and 20% of that half is another 10% of the full price.
How do I find the price before the discount?
Divide the final price by (1 − discount): 72 after 20% off comes from 72 / 0.80 = 90.
How this calculation works
For each discount dᵢ the price becomes P · (1 − dᵢ/100), applied one after another. The effective discount is (original price − final price) / original price × 100. In the reverse calculation the percentage is (P − F) / P × 100.