Key takeaways
- Sale price = original price × (1 − discount ÷ 100). 20% off 250 is 200.
- Two discounts multiply: 20% then 10% off is 28% off in total, not 30%.
- To find the original price, divide the sale price by (1 − discount): 45 after 25% off was 60.
- A percentage discount and VAT can be applied in either order; a fixed-amount coupon cannot.
On this page
The four everyday calculations
| Question | Formula | Example |
|---|---|---|
| What is the sale price? | price × (1 − d) | 250 with 20% off = 250 × 0.8 = 200 |
| How much do I save? | price × d | 250 × 0.2 = 50 |
| What percentage is the discount? | (old − new) ÷ old × 100 | 80 down to 60 = 20 ÷ 80 = 25% |
| What was the original price? | sale price ÷ (1 − d) | 45 after 25% off = 45 ÷ 0.75 = 60 |
Here d is the discount as a decimal: 20% is 0.2. The discount calculator works out the sale price, the saving and the total discount, including an extra discount and tax.
Stacked discounts are not added together
"20% off, plus an extra 10% at the till" applies the second discount to the already reduced price:
250 × 0.8 = 200, then 200 × 0.9 = 180. That is 70 off, or 28%, not 30%. The total is always 1 − (1 − d1) × (1 − d2). Two 50% discounts make 75% off, not "free".
The original-price trap
A common slip is to add the percentage back: "45 after 25% off, so 45 + 25% = 56.25". That is wrong because the 25% was taken from the larger, original price. Dividing gives the right answer: 45 ÷ 0.75 = 60, and 25% of 60 is indeed 15.
Discounts and VAT
For a percentage discount, the order does not matter: 200 with 10% off and then 5% VAT is 200 × 0.9 × 1.05 = 189, and adding VAT first gives the same 189. A fixed coupon is different: taking 20 off before VAT gives (200 − 20) × 1.05 = 189, while taking 20 off after VAT gives 210 − 20 = 190. Check the terms if the difference matters, and see our reverse VAT guide to split a VAT-inclusive total.
For sellers: what a discount does to your margin
A 20% discount can cut far more than 20% of your profit. If you sell for 100 and the item costs you 60, your profit is 40. At 20% off you sell for 80 and keep 20: half your profit is gone. The profit margin calculator shows the margin at any price, and our article on margin vs markup explains the difference. For any other percentage question, there is the percentage calculator.
Fact-checked against the sources above. We test every tool we mention. Editorial policy.
