How to use the discount calculator
The page holds four small calculators. Each answers one shopping question, updates as you type and shows the working underneath so you can check it. Any currency works.
- Price after discount – enter the original price and the discount. Use Extra discount for offers such as “a further 10% off sale prices”, and Sales tax / VAT if tax is added at the till. You get the sale price, how much you save (as an amount and a percentage) and the price with tax.
- What percent off is it? – enter the original and the sale price to see the real discount. If the second price is higher, it tells you how much more expensive it is instead.
- Original price before the discount – work backwards from a sale price and the discount percentage.
- Add or remove tax – say whether your price already includes tax, and get the amount before tax, the tax itself and the amount after tax.
The formulas
- Sale price = original price × (1 − discount ÷ 100)
- Discount % = (original price − sale price) ÷ original price × 100
- Original price = sale price ÷ (1 − discount ÷ 100)
- Price with tax = price × (1 + tax rate ÷ 100), and price before tax = price with tax ÷ (1 + tax rate ÷ 100)
Worked examples
- Stacked discounts. A jacket costs 80, with 25% off and an extra 10% at the checkout: 80 × 0.75 × 0.9 = 54. You save 26, which is 32.5% – not 35%. With 20% VAT on top, you pay 64.80.
- Is it a real bargain? A price drops from 129.99 to 99.99. (129.99 − 99.99) ÷ 129.99 × 100 = 23.08% off, which sounds less impressive than “save 30”.
- Finding the original price. A tag says 64 after 20% off. The original was 64 ÷ 0.8 = 80, not 64 × 1.2 = 76.80.
- Taking VAT out. A price of 96 includes 20% VAT. Before tax it is 96 ÷ 1.2 = 80, so the tax is 16 – not 19.20, which is 20% of 96.
Why percentages don't simply add up
Each discount is a multiplication, and the second one applies to a price that is already reduced. Two discounts combine to 1 − (1 − first) × (1 − second): 20% and 10% make 28%, 30% and 20% make 44%, and 50% and 20% make 60%. Whenever you use the extra discount field, the calculator shows the combined percentage.
The same logic explains why a price that rises 25% and then falls 25% ends lower than it started (100 → 125 → 93.75), and why a 20% price cut needs a 25% rise to get back to where it was.
Multi-buy offers can be turned into percentages too. “Buy one, get the second half price” on two items of the same price is 25% off each; “buy two, get one free” is 33.33% off. That makes them easy to compare with a plain discount.
Sales tax and VAT
In the United States and Canada, shelf prices usually exclude sales tax, which is added at the register at a rate that depends on the state, province or city. In the UK, the EU and many other countries, consumer prices already include VAT; the “already includes tax” option shows the net price, which is useful for businesses that reclaim VAT. Because both are percentages, the order of discount and tax doesn't change the result: 80 with 25% off and then 20% tax is 72, exactly the same as adding the tax first.
Tips
- Compare deals by the final price, not by the size of the percentage. A smaller discount on a cheaper item can still be the better buy.
- “Up to 70% off” means only some items get the biggest reduction.
- A coupon worth a fixed amount, such as 10 off, isn't a percentage. Subtract it separately, then use What percent off is it? to see what it is worth as a percentage.
- For other percentage questions, such as a percentage change or what percent one number is of another, use the Percentage Calculator.
FAQ
Is 20% off plus an extra 10% the same as 30% off?
No, it is 28% off: 100 × 0.8 × 0.9 = 72.
Is the discount applied before or after tax?
Shops normally discount the price first and add tax to the reduced price. If both are percentages the total is the same either way; the order only matters with fixed-amount coupons or special tax rules.
Why must the discount be less than 100% when finding the original price?
At 100% off the sale price is zero, and no original price can be worked out from zero.
Why might my receipt differ by a cent?
Results are rounded to two decimal places. Shops may round the tax on each item separately, so a receipt can differ slightly from a calculation on the total.