Quick Answers
Almost every percentage you need day to day can be worked out in two steps without a calculator. Here is the method, the examples, and the places it goes wrong.
Every percentage question is one of three shapes
People ask percentage questions in dozens of different ways, but underneath there are only three. Recognizing which one you are looking at tells you which operation to reach for, and that is most of the work.
The first shape asks for a part of a known whole, as in what is 20% of $47. You multiply. The second asks for a rate, as in 43 out of 50 is what percent. You divide the part by the whole and multiply by 100. The third works backwards from a part to the whole, as in 30% off leaves $31.50, so what was the original price. You divide by the decimal that remains, in this case 0.70.
The third shape is where most mistakes happen, because the instinct is to add the percentage back rather than divide it out. More on that below.
The 10% anchor
You do not need to memorise percentages. You need one number, 10%, which you get by sliding the decimal point one place to the left. Everything common is built from that in a single move. Nobody multiplies by 0.15 in their head at a dinner table, and they do not need to.
10% -- Move the decimal one place left
10% of $47 is $4.70
1% -- Move the decimal two places left
1% of $86 is $0.86
20% -- Double your 10%
20% of $132 is $13.20 doubled, or $26.40
5% -- Halve your 10%
5% of $80 is $8.00 halved, or $4.00
15% -- Add 10% and 5% together
15% of $47 is $4.70 plus $2.35, or $7.05
25% -- Take a quarter, or halve it twice
25% of $80 is $20.00
Awkward rates work the same way once you stop treating them as special. An 18% tip is easier as 20% minus 2% than as anything else. A sales tax of 8.25% is 8% plus a quarter of 1%. You are always assembling the number from pieces you already have.
Worked examples
Each of these shows the route, not just the destination. The point is that the route is short enough to run in your head while the waiter is standing there.
20% tip on a $47 bill
10% is $4.70, doubled → $9.40
15% tip on a $47 bill
$4.70 plus half of it, $2.35 → $7.05
18% tip on an $86 bill
20% is $17.20, minus 2% at $1.72 → $15.48
20% tip on a $132 bill
10% is $13.20, doubled → $26.40
25% off an $80 jacket
a quarter off is $20 saved → pay $60.00
30% off a $45 shirt
10% is $4.50, tripled to $13.50 → pay $31.50
40% off a $120 pair of boots
10% is $12, times four is $48 → pay $72.00
7% sales tax on $250
1% is $2.50, times seven → add $17.50
43 out of 50
43 divided by 50 is 0.86 → 86%
17 out of 20
17 divided by 20 is 0.85 → 85%
78 out of 90
78 divided by 90 is 0.8667 → 86.7%
3% raise on a $75,000 salary
1% is $750, tripled → $2,250
Where the shortcut breaks
The 10% anchor handles a single percentage of a single number. The moment percentages stack, reverse, or get compared to each other, the intuition stops being reliable. These four cases account for most of the wrong answers people arrive at confidently.
Stacked discounts do not add up
Take 20% off a $100 item and you are at $80. Take another 10% off and you are at $72, not $70. The second discount applies to the already reduced price, so 20% and 10% combine to 28% off, not 30%. This is why a coupon stacked on a sale rarely feels as good as the arithmetic suggests.
An increase and an equal decrease do not cancel
A $100 stock that gains 50% sits at $150. If it then loses 50%, it lands at $75, not back at $100. The gain was calculated on $100 and the loss on $150, so they are not the same size in dollars. Recovering from a 50% loss takes a 100% gain.
Removing a percentage is not the same as subtracting it
If something costs $107 including 7% tax, the pre-tax price is not $107 minus 7%, which would give $99.51. The tax was applied to the smaller number, so you divide instead: $107 divided by 1.07 gives exactly $100. The same trap catches anyone working backwards from a total that already includes a markup or a tip.
Percent and percentage points are different units
If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points but a 50% increase in the rate itself. Both statements are true and they describe the same event. Headlines tend to pick whichever sounds larger, which is worth remembering when a figure seems dramatic.
Common questions
What is the fastest way to work out a percentage in my head?
Find 10% first by moving the decimal one place to the left, then build from there. Every common percentage is a short hop from 10%: double it for 20%, halve it for 5%, add those two for 15%, and move the decimal one more place for 1%. Almost no everyday percentage needs more than two of these steps.
How do I calculate what percentage one number is of another?
Divide the part by the whole, then multiply by 100. If you scored 43 out of 50, that is 43 divided by 50, which gives 0.86, or 86%. The order matters: dividing 50 by 43 gives a number above 1 and is the answer to a different question.
Is a 20% tip calculated before or after sales tax?
Tipping on the pre-tax subtotal is the conventional approach in the United States, since the tax is not part of the service. Tipping on the total is common and nobody will object to it. On a $50 meal the difference is usually well under a dollar, so it matters less than it seems.
Why do two 10% discounts not equal 20% off?
The second discount is applied to the price after the first one has already come off. Two successive 10% reductions on $100 give $90, then $81, which is 19% off in total rather than 20%. The gap widens as the individual discounts get larger.
How do I find the original price before a discount?
Divide rather than add the percentage back. If an item is 30% off and costs $31.50, you are paying 70% of the original, so divide $31.50 by 0.70 to get $45. Adding 30% to $31.50 gives $40.95, which is the wrong answer to a slightly different question.
Do I need a calculator for percentages at all?
For a tip or a rough sale price, mental math is usually faster and accurate enough. A calculator earns its place when the numbers are awkward, when several percentages stack, or when being off by a few dollars actually costs you something, such as a salary negotiation or a margin calculation.
Numbers too awkward for mental math?
The calculators handle any figure instantly and show the formula alongside the result.