A discount is just a percentage taken off a price, but the moment a store slaps a red tag on something, the mental math gets slippery. Is 25 percent off a good deal? What do you actually pay? And when a sign says "take an extra 20 percent off already reduced items," are you getting half off? This guide walks through every version of the discount question: finding the amount you save, finding the final sale price, working backward to the original price, and figuring out the percent off when you only know the two prices. The formulas are short and you can do most of them in your head once you learn a few tricks.
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The core formula
Every discount problem is built on two lines of math. First you find the discount amount, then you subtract it from the original price:
discount amount = original price × discount percent ÷ 100
sale price = original price − discount amount
The word "of" in everyday English means multiply, and "percent" means "out of 100." So "25 percent of 80 dollars" is literally 80 × 25 ÷ 100, which equals 20. That 20 dollars is your saving. Subtract it and the sale price is 60 dollars.
There is a faster one-step version that skips straight to the price you pay. If something is 25 percent off, you pay the other 75 percent, so:
sale price = original price × (100 − discount percent) ÷ 100
Using the same numbers: 80 × 75 ÷ 100 = 60 dollars. Same answer, one line instead of two. Use whichever version you find easier to hold in your head.
A worked example, step by step
Say a jacket is listed at 80 dollars with a 25 percent off tag. Here is the full walkthrough:
- Original price: 80 dollars.
- Discount percent: 25 percent.
- Discount amount: 80 × 25 ÷ 100 = 20 dollars saved.
- Sale price: 80 − 20 = 60 dollars to pay.
So a 25 percent discount on an 80 dollar jacket saves you 20 dollars and you pay 60. Notice that the saving (20) and the price you pay (60) always add back up to the original (80). That is a handy sanity check: if your saving plus your final price does not equal the starting price, something went wrong.
Let the calculator do it
Quick mental math tricks
You rarely need a calculator for the common discounts. A handful of shortcuts cover most of what you will see on a sale rack:
- 10 percent off: move the decimal point one place left. 10 percent of 45 dollars is 4.50.
- 20 percent off: find 10 percent, then double it. 10 percent of 45 is 4.50, so 20 percent is 9.
- 25 percent off: take a quarter, which means divide by 4. A quarter of 80 is 20.
- 50 percent off: cut it in half. Half of 90 is 45.
- 5 percent off: find 10 percent and halve it. 10 percent of 60 is 6, so 5 percent is 3.
- 15 percent off: 10 percent plus half of that again. 10 percent of 40 is 4, plus 2 is 6.
Chain these together for oddball numbers. For 35 percent off, add 25 percent (a quarter) and 10 percent (move the decimal). For 40 percent off, find 10 percent and multiply by 4. Because these building blocks are all easy, you can estimate almost any discount in a few seconds.
Estimate first, then confirm
Stacking discounts is not simple addition
This is where most people lose money in their heads. If an item is 30 percent off and you have a coupon for an extra 20 percent off, that is not 50 percent off. The second discount applies to the already-reduced price, not the original, so the percentages do not add.
Take a 100 dollar item to see it clearly. The 30 percent off brings it to 70 dollars. The extra 20 percent then comes off that 70, not off the original 100:
- Start: 100 dollars.
- After 30 percent off: 100 × 0.70 = 70 dollars.
- After an extra 20 percent off the 70: 70 × 0.80 = 56 dollars.
- Total saved: 44 dollars, which is 44 percent off, not 50 percent.
A cleaner way to combine two discounts is to multiply the amounts you actually pay. You pay 70 percent after the first cut and 80 percent after the second, so you pay 0.70 × 0.80 = 0.56, meaning 56 percent of the original, which is 44 percent off. The order of the two discounts does not change the final price, since multiplication is the same either way.
Stacked percentages always add up to less
Working out the percent off from two prices
Sometimes you see the original and the sale price and want to know the actual percentage off, maybe to compare two deals. The formula reverses the first one:
percent off = (original − sale) ÷ original × 100
Suppose a pair of shoes was 90 dollars and is now 63 dollars. The saving is 90 − 63 = 27 dollars. Divide by the original: 27 ÷ 90 = 0.30, then multiply by 100 to get 30 percent off. Always divide by the original price, not the sale price, or your percentage will come out too high.
This is the number to trust when comparing sales across stores. A 40 dollar shirt marked down to 28 is a bigger percentage deal than a 40 dollar shirt down to 32, even though both say "on sale." The first is 30 percent off and the second is 20 percent off.
Finding the original price from a sale price
This trips people up because you cannot just add the percentage back on. If a tag reads "40 dollars, 20 percent off," the 40 is what you pay, and it represents 80 percent of the original. To recover the original, divide by that remaining fraction:
original price = sale price ÷ (100 − discount percent) × 100
So 40 ÷ 80 × 100 = 50 dollars. The item was originally 50 dollars. A quick check confirms it: 20 percent of 50 is 10, and 50 minus 10 is 40. Note the common mistake here. Adding 20 percent back to 40 gives 48, not 50, because 20 percent of 40 is smaller than 20 percent of 50. The percentage was always based on the larger original number.
Common discounts on common prices
The table below shows the final price you pay after applying a few popular discount rates to typical price points. Use it as a quick reference or to double-check your mental math.
| You pay after 20% off | You pay after 50% off | |
|---|---|---|
| $10 item | $8.00 | $5.00 |
| $25 item | $20.00 | $12.50 |
| $40 item | $32.00 | $20.00 |
| $60 item | $48.00 | $30.00 |
| $80 item | $64.00 | $40.00 |
| $100 item | $80.00 | $50.00 |
| $150 item | $120.00 | $75.00 |
| $250 item | $200.00 | $125.00 |
For 25 percent off, take a quarter off the "20 percent" logic or just divide the original by 4 and subtract. For 30 percent off, the price you pay is 70 percent of the original, so a 100 dollar item lands at 70 and a 40 dollar item lands at 28.
Discounts, sales tax, and tips
In most places the discount comes off first and sales tax is charged on the reduced price, which works in your favor. A 100 dollar item at 20 percent off is 80 dollars, and an 8 percent tax on 80 is 6.40, for a total of 86.40. You are taxed on what you actually pay, not the original sticker. Tips at restaurants work the other way around and are usually figured on the pre-tax total, so keep the two ideas separate when you are checking a bill.
Frequently asked questions
How do I calculate 20 percent off?
Find 10 percent of the price by moving the decimal one place left, then double it to get 20 percent, and subtract that from the original. For 20 percent off 45 dollars: 10 percent is 4.50, doubled is 9, so you save 9 and pay 36. In one step, multiply by 0.80, since you pay 80 percent when 20 percent is taken off: 45 × 0.80 = 36.
How do stacked discounts work?
Each discount applies in turn to the price left after the previous one, so the percentages never simply add. Multiply the fractions you pay instead. For 30 percent off followed by an extra 20 percent off, you pay 0.70 × 0.80 = 0.56, which is 56 percent of the original, or 44 percent off in total. Two stacked discounts are always worth less than adding them together.
How do I find the original price before a discount?
Divide the sale price by the fraction you paid. If an item is 40 dollars after 20 percent off, you paid 80 percent, so the original was 40 ÷ 0.80 = 50 dollars. Do not add the percentage back onto the sale price, because that percentage was based on the larger original number and adding it back will undershoot.
How do I work out the percent off from two prices?
Subtract the sale price from the original, divide that difference by the original, and multiply by 100. For an item that dropped from 90 to 63 dollars: (90 − 63) ÷ 90 × 100 = 30 percent off. Dividing by the original rather than the sale price is what keeps the answer correct.
How much do I save with a discount?
Your saving is the original price times the discount percent divided by 100. A 25 percent discount on an 80 dollar item saves 80 × 25 ÷ 100 = 20 dollars. The amount you save plus the amount you pay always equals the original price, which is the quickest way to check your work.