How to calculate a discount
A discount is just a percentage taken off a price, and it takes one short step. Here is how to find the sale price and the amount you save, how to reverse a discount to the original price, why two discounts never simply add, and how to tell a real deal from a fake one.
Enter the original price and the discount to see the final price and how much you save.
A discount is simply a percentage taken off a price, and working it out takes one short step. Here is the part most shoppers miss: 20% off plus an extra 10% at the till is not 30% off. This guide shows how to find the sale price and the amount you save, how to reverse a discount to work out the original price, how to get the discount percentage from two prices, why two stacked discounts never simply add up, how sales tax fits in, and how to tell a genuine saving from marketing. The numbers here are currency-neutral: use whatever currency you like, the method does not change.
How to calculate a discount and the sale price
There are two numbers you usually want: how much you save, and what you actually pay. Both come straight from the percentage.
Amount saved = original price × (discount ÷ 100)
Sale price = original price − amount saved
Worked example: an 80 item at 25% off. The saving is 80 × (25 ÷ 100) = 80 × 0.25 = 20. The sale price is 80 − 20 = 60. There is an even faster one-step version: if 25% comes off, you pay the other 75%, so sale price = 80 × 0.75 = 60. In general, sale price = original × (1 − discount ÷ 100), which skips the separate subtraction.
Discount examples: 15%, 30% and 50% off
- 30% off 45.99. You pay 70%: 45.99 × 0.70 = 32.19, a saving of 13.80.
- 15% off 120. Saving 120 × 0.15 = 18, so you pay 102.
- Half price (50% off) 37. 37 × 0.50 = 18.50, so you pay 18.50.
The quick mental trick for 10% is to move the decimal one place (10% of 120 is 12). Build other percentages from that: 20% is double 10%, 5% is half of 10%, 25% is a quarter, so 35% off is 10% + 10% + 10% + 5%.
How to reverse a discount to the original price
Sometimes you know the sale price and want the original, for example to check a "was" price or to add a discount back for a refund. You cannot just add the percentage back on, because the percentage was taken off the larger original, not the smaller sale price. Instead, divide by what you paid as a decimal.
Original price = sale price ÷ (1 − discount ÷ 100)
If you paid 60 after 25% off, you paid 75% of the original, so the original was 60 ÷ 0.75 = 80. This is also why adding a percentage and then removing the same percentage does not return the start: 100 plus 20% is 120, but 20% off 120 is 96, not 100, because the second 20% is a bigger amount.
How to find the discount percentage from two prices
If you know the original and the sale price and want the percentage off, divide the saving by the original:
Discount % = (original − sale) ÷ original × 100
A coat that dropped from 80 to 60 is (80 − 60) ÷ 80 × 100 = 25% off. This is the formula to reach for when a tag shows both a "was" and a "now" price but not the percentage, and it is the same check you use later to test whether a "30% off" claim is honest.
Why stacked discounts never simply add up
This is the mistake people make most often. "20% off, then an extra 10% at the till" is not 30% off. Each discount applies to whatever price is left after the one before, so they multiply rather than add. Start at 100: take 20% off to get 80, then take 10% off that 80 to get 72. You paid 72, so the real discount is 28%, not 30%. The order does not matter (10% then 20% also lands on 72), but the total is always a little less than the two added together.
The shortcut is to multiply the "what you pay" fractions: 0.80 × 0.90 = 0.72, so you pay 72% and save 28%. As a formula, combined discount = 1 − (1 − d1)(1 − d2), so 20% and 10% give 1 − 0.8 × 0.9 = 0.28, that is 28%. Add a third offer and it keeps multiplying: 20%, 10% and 5% give 0.8 × 0.9 × 0.95 = 0.684, so 31.6% off, not 35%. The stacked discount calculator does this for you, but the rule is simple: when offers stack, multiply, never add.
Where sales tax and VAT fit in
A discount and a sales tax or VAT are two separate steps. The common case is that the discount comes off first and tax is charged on the reduced price. For 100 at 20% off with 15% tax: discount to 80, then add 15% tax to reach 92. Reversing the order gives the same 92 (100 × 1.15 = 115, then 115 × 0.80 = 92), because both steps are simple multiplications of the same base. What really changes the total is what the tax is charged on: some places tax the full pre-discount price when the reduction comes from a manufacturer coupon rather than a store markdown. Rules vary by country, so the receipt is the source of truth. If you need the tax step on its own, a VAT or sales-tax tool handles it; this guide sticks to the discount itself.
Is a discount actually a good deal?
The maths tells you the saving, not whether the deal is good. First, judge the final price, not the size of the "off" number: a big percentage off a price that was raised just beforehand is not a real saving. If the "was" price was never actually charged, the discount is fictional. You can test it with the formula above: a jacket marked "was 200, now 140, 30% off" that really sold at 150 last month is only (150 − 140) ÷ 150 × 100 = 6.7% off against its true recent price. Second, for groceries and bulk buys, a discount on a large pack can still cost more per unit than a smaller pack at full price, so compare the unit price, not the sticker. And spending 70 on something you did not plan to buy is a 70 loss, however large the "30% off" sticker looks.
Common discount calculation mistakes
- Adding stacked discounts. 20% then 10% is 28% off, not 30%. Multiply the pay-fractions (0.8 × 0.9), do not add the percentages.
- Reversing by adding the percentage back. Paid 60 after 25% off is not 60 + 25%; it is 60 ÷ 0.75 = 80, because the discount came off the bigger number.
- Percent off versus percent of. "25% off" means you pay 75%. Multiplying by 0.25 gives the saving, not the price; multiply by 0.75 for the price.
- Judging the deal by the percentage. A large discount on an inflated or unwanted item is not a saving. Look at the final price and the unit price.
Once you have the method, a discount is a one-step calculation: multiply by the pay-fraction for the price, or by the discount for the saving. If percentages themselves feel shaky, our guide on how to work out a percentage covers the basics first. When you want it instant, the free discount calculator gives the sale price and saving from any percentage, the stacked discount calculator handles two offers at once without the adding trap, and the percentage calculator covers the wider percentage questions.
Frequently asked questions
How do I calculate a discount?
Multiply the original price by the discount as a decimal to get the amount saved, then subtract it. For 25% off 80: 80 × 0.25 = 20 saved, so the sale price is 60. Faster, multiply by what you pay: 25% off means you pay 75%, so 80 × 0.75 = 60 in one step.
How do I find the original price before a discount?
Divide the sale price by what you paid as a decimal. If you paid 60 after 25% off, you paid 75% of the original, so the original was 60 ÷ 0.75 = 80. You cannot just add the percentage back, because it was taken off the larger original price.
Is 20% off then 10% off the same as 30% off?
No. Each discount applies to the price left after the previous one, so they multiply rather than add. Starting at 100: 20% off gives 80, then 10% off that gives 72. You pay 72, a real discount of 28%, not 30%. Multiply the pay-fractions (0.8 × 0.9 = 0.72) to combine stacked offers.
Does a discount apply before or after tax?
Usually the discount comes off first and sales tax or VAT is charged on the reduced price: 100 at 20% off is 80, then 15% tax makes 92. Rules vary by country and promotion, so treat the receipt as the final word, but discount-then-tax is the common order.