Five percentage tricks to do in your head
Mental math shortcuts for tips, discounts, and tax — the kind of fast estimation that beats reaching for your phone every time.
Percentages don’t have to mean reaching for a calculator every time. A few mental tricks turn 80% of everyday percentage questions into a one-second answer. Here are the five that come up most often.
1. X% of Y equals Y% of X
This is the most useful identity in percentage arithmetic and most people don’t know it: X% of Y is the same as Y% of X.
Quick: what’s 18% of 50?
That’s hard. But 50% of 18 is easy — it’s 9. Same answer, much easier route.
Whenever a percentage is awkward, try flipping it. 4% of 75 = 75% of 4 = 3. 22% of 200 = 200% of 22 = 44.
2. Build any percentage from 10%, 5%, and 1%
To find 10% of any number, slide the decimal point one place left. 10% of 240 = 24. 10% of 87 = 8.70.
From there:
- 5% is half of 10%
- 1% is one-tenth of 10%
- 15% is 10% + 5%
- 20% is 10% × 2
- 25% is 10% × 2 + 5%
A 15% tip on a $48 bill: 10% is $4.80, half of that is $2.40, sum is $7.20. Two seconds, no phone.
3. Discount stacking is multiplication, not addition
If something is 30% off and you have a coupon for an extra 20% off, that is not 50% off.
The first discount leaves 70% of the price. The second leaves 80% of that. Total: 0.7 × 0.8 = 0.56 — you pay 56%, not 50%. The combined discount is 44%.
This is why “stacking” deals are usually less impressive than they look, and why a single 50% sale beats two 25%-off coupons every time.
4. Tax is a multiplier, not a separate step
If sales tax is 8.25%, every receipt is just price × 1.0825. Don’t compute the tax and add it — compute the final price in one shot. It’s faster and avoids rounding mistakes.
For a 20%-off sweater that costs $40 with 8% tax: $40 × 0.80 × 1.08 = $34.56.
5. Percentage change is a ratio, not a difference
If a stock goes from $50 to $60, the change is (60 − 50) / 50 = 20%. The denominator is the starting number, not the ending one.
This matters because the math isn’t symmetric. Going from $50 to $60 is +20%. Going back from $60 to $50 is −16.7%. A 20% loss after a 20% gain doesn’t put you back where you started — it leaves you 4% poorer.
This is the mistake behind a lot of “this year was up X% but last year was down X%” headlines that don’t quite balance.
When the mental math fails
For anything multi-step or involving compound interest, just use the Percentage Calculator. The tricks above are for the 80% of cases that should never have required a calculator in the first place.