Most shopping math comes down to three questions: what will this cost after the discount, what will it cost after tax, and how much should I tip? You can answer all three in your head to within a few cents with one trick: find 10% first, then build everything else from it.
Here's how that works, plus the two places where quick math goes wrong: stacked discounts and "percent off" claims that don't add up.
Note: these are quick estimates for everyday use, not financial or tax advice. Your receipt is the final word on what you paid.
Start with 10%
To find 10% of any amount, move the decimal point one place to the left:
- 10% of $64.50 is $6.45
- 10% of $120 is $12
- 10% of $8.90 is $0.89
From there, most common percentages are one small step away:
| You want | Do this | Example on $64.50 |
|---|---|---|
| 5% | Half of 10% | $3.23 (half of $6.45) |
| 15% | 10% plus 5% | $6.45 + $3.23 = $9.68 |
| 20% | Double 10% | $12.90 |
| 25% | Divide by 4 | $16.13 |
| 1% | Move the decimal two places | $0.65 |
One more shortcut: percentages are reversible. 8% of 25 is the same as 25% of 8, which is 2. If one way looks hard, try the other.
Discounts: figure what you pay, not what you save
The fastest way to price a sale item is to subtract the discount from 100% first, then take that percentage of the price.
- 30% off $85: you pay 70%. 10% of $85 is $8.50, so 70% is $59.50.
- 25% off $120: you pay 75%, which is three quarters: $90.
- 75% off $48: you pay 25%, a quarter: $12.
To check how big a discount really is, divide the savings by the original price. A $20 coupon on an $80 order is 20 ÷ 80 = 25% off.
Stacked discounts don't add up
"Take an extra 20% off sale prices" sounds like it adds to the first discount. It doesn't. The second discount applies to the already reduced price.
A $120 jacket marked 25% off, with an extra 20% off at checkout:
$120 × 0.75 = $90 (25% off)
$90 × 0.80 = $72 (extra 20% off)You pay $72, so you saved $48. That's 48 ÷ 120 = 40% off, not 45%. The shortcut is to multiply what you pay at each step: 0.75 × 0.80 = 0.60, so you pay 60% of the original.
The same thing explains why a 50% increase followed by a 50% decrease doesn't get you back where you started. $100 up 50% is $150; $150 down 50% is $75. Percent changes compound on whatever the number is at that moment, which is also the root of the confusion covered in Percent Change vs Percentage Points.
Sales tax
Sales tax is a percentage added to the price, and the rate depends on where you buy. As USA.gov puts it, "most states and municipalities have a sales tax and charge different percentages on different goods, or not at all for other items." Your combined state and local rate is printed on most receipts.
To add tax in your head, split the rate into easy pieces. With an 8.25% rate on $72:
8% of $72 = $5.76 (1% is $0.72, times 8)
0.25% of $72 = $0.18 (a quarter of 1%)
Tax = $5.94
Total = $77.94For a rough check, round the rate. At 8.25%, "a little over 8%" gets you within a few cents on most purchases.
Discount first or tax first?
When both are percentages, the order doesn't change the result: $120 × 0.75 × 1.0825 is the same as $120 × 1.0825 × 0.75, because multiplication works in any order. Order matters when a discount is a fixed dollar amount. A $10 coupon taken off before tax saves you the tax on that $10 as well. Whether tax is charged on the price before or after a coupon depends on the coupon type and your state's rules, so check the receipt if it matters.
Taking tax back out
To find the pre-tax price from a total, divide by 1 plus the rate. Don't subtract the rate from the total, which takes off too much.
Total $108.25 at 8.25% tax
$108.25 ÷ 1.0825 = $100.00 (correct)
$108.25 − 8.25% = $99.32 (wrong)In the Percentage Calculator, the "X is Y% of what number?" card does this: enter 108.25 and 108.25, and it returns 100.
Tips
Using the 10% anchor on a $64.50 check:
| Tip | Mental math | Exact |
|---|---|---|
| 15% | $6.45 + about $3.23 = about $9.70 | $9.675 |
| 18% | 20% minus 2%: $12.90 − $1.29 = $11.61 | $11.61 |
| 20% | Double 10%: $12.90 | $12.90 |
| 25% | A quarter: about $16.13 | $16.125 |
A quick 20% trick: take 10%, double it, and round up to a convenient number. For 18%, subtract a fifth of 10% from 20%.
Whether to tip on the amount before or after tax is a matter of custom, not math. Tipping on the pre-tax subtotal is common. On the $72 example above, 20% of the subtotal is $14.40; 20% of the $77.94 total would be $15.59.
Is it really "40% off"?
Price tags don't always match their percentages, and rounding goes both ways. To check a claim, take the difference between the old and new price and divide by the old price.
A tag that says "was $149.99, now $89.99, 40% off": the difference is $60, and $60 ÷ $149.99 is 40.0027%. That one's honest. If the "was" price were $139.99, the same $89.99 would be only 35.7% off.
The Percentage Calculator shows the exact figure in its "Percentage change" card: from 149.99 to 89.99 is a decrease of 40.002667%.
Which size is the better deal?
A percentage discount on a big pack doesn't always beat the regular price of a smaller one. Compare the price per unit instead: divide the price by the quantity.
12 oz for $4.29 → $4.29 ÷ 12 = $0.358 per oz
32 oz for $9.99 → $9.99 ÷ 32 = $0.312 per ozThe big jar is cheaper per ounce by about 4.5 cents, or roughly 13%. Many store shelf tags show a unit price already, but check that both tags use the same unit (per ounce versus per pound is a common mismatch). And a lower unit price only saves money if you'll actually use it all.
Common mistakes
- Adding stacked discounts. 25% plus 20% off is 40% off, not 45%.
- Subtracting the tax rate from a total to get the pre-tax price. Divide instead.
- Reversing a discount with the same percentage. A $90 price that was 25% off wasn't $112.50; it was $120 ($90 ÷ 0.75).
- Rounding too early. Round once, at the end. Rounding at every step can push the answer off by several cents.
- Mixing up percent and percentage points when comparing tax rates or interest rates.
When to use a calculator instead
Mental math is great at the register. For anything you're going to sign, such as a loan, a big purchase with financing, or a budget, use exact numbers; the Loan Calculator shows what financing really costs over the full term. The Percentage Calculator shows the formula it used with every answer, so you can see exactly what was computed.
FAQ
How do I calculate 20% off in my head?
Find 10% by moving the decimal one place left, double it to get 20%, and subtract it from the price. Or multiply by 0.8: 20% off $45 is $36.
How do I work out the original price before a discount?
Divide the sale price by what you paid as a decimal. If $63 is the price after 30% off, the original was $63 ÷ 0.70 = $90.
Is 50% off plus another 20% off the same as 70% off?
No. You pay 0.50 × 0.80 = 40% of the original, which is 60% off.
Should I tip on the total with tax?
It's up to you. Many people tip on the pre-tax amount. Tipping on the total makes the tip bigger by the tax rate: at 8.25% tax, a 20% tip on the $72 example grows from $14.40 to $15.59.
