How to Calculate Percentages in Your Head

Start with 10%, 5% and 1%

The fastest way to find any percentage in your head is to build it from three easy pieces: 10%, 5% and 1%. Almost every other percentage is a combination of these.

10% means moving the decimal point one place to the left. 10% of $64 is $6.40. 10% of $240 is $24.

5% is half of 10%. Since 10% of $64 is $6.40, 5% is $3.20.

1% means moving the decimal point two places to the left. 1% of $240 is $2.40.

Once you have those pieces, you add or multiply them:

• 15% = 10% + 5%. On $64, that is $6.40 + $3.20 = $9.60.
• 20% = 10% doubled. On $47.50, 10% is $4.75, so 20% is $9.50.
• 3% = 1% times three. On $240, that is $2.40 times 3 = $7.20.
• 12% = 10% + 1% + 1%. On $240, that is $24 + $2.40 + $2.40 = $28.80.

Use the swap trick for awkward percentages

When a percentage looks hard, flip it. x% of y always equals y% of x, because both are just x times y divided by 100.

That turns ugly problems into easy ones:

• 8% of 25 is the same as 25% of 8. A quarter of 8 is 2.
• 4% of 75 is the same as 75% of 4. Three quarters of 4 is 3.
• 16% of 50 is the same as 50% of 16, which is 8.

The trick works best when one of the two numbers is a friendly percentage like 10, 20, 25 or 50. If neither number is friendly, go back to the building blocks.

Everyday examples you can do at the table

These are the situations where mental percentages save you the most time. Each one uses only the building blocks above.

A small set of fraction equivalents makes many of these instant: 1/2 is 50%, 1/4 is 25%, 3/4 is 75%, 1/5 is 20%, 1/8 is 12.5% and 1/10 is 10%.

Work out percent change

Percent change compares the difference to the starting value. Subtract the old number from the new one, divide by the old number, then multiply by 100.

Say your salary goes from $52,000 to $54,600. The difference is $2,600. Divide by the old salary: 2,600 / 52,000 = 0.05. That is a 5% raise. For the mental version, ask what 1% of the old number is ($520), then count how many of those fit into the change. $2,600 is five of them.

Prices work the same way. If a gadget drops from $80 to $68, the change is −$12. 10% of $80 is $8 and 5% is $4, so $12 is 15%. The price fell 15%.

Always divide by the starting value. Dividing by the new value is the most common mistake, and it gives a different answer.

Reverse a percentage to find the original number

To undo a percentage, divide by the multiplier instead of subtracting the percent. You cannot simply add the percentage back.

Suppose a jacket costs $48 after 20% off. You paid 80% of the original, so the original was $48 / 0.80 = $60. Adding 20% of $48 back would give $57.60, which is wrong because the 20% was taken from the original price, not the sale price.

The same idea works for tax. If a receipt shows $54 including an 8% example tax rate, the price before tax was $54 / 1.08 = $50.

Watch out for percentages that do not cancel

A percentage increase followed by the same percentage decrease does not bring you back to where you started. You end up lower.

Start with 100. Raise it 25% and you get 125. Now cut 25% of 125, which is 31.25, and you land on 93.75. The second percentage was taken from a bigger number, so it removed more than the first one added.

This matters when you read about stock prices, rent increases or prices that rise and then go on sale. It also explains why two discounts in a row are worth less than their sum. A 30% discount followed by another 20% saves you 44%, not 50%.

A quick routine for any percentage

When you face a new problem, run through these steps in order:

1. Check whether the swap trick makes it easier.
2. If not, break the percentage into 10%, 5% and 1% pieces.
3. Round when you only need an estimate, then adjust.
4. For change, divide by the starting number.
5. To reverse a percentage, divide by the multiplier.

With a few days of practice on receipts and price tags, the building blocks become automatic. When the numbers matter, such as a loan or a pay stub, confirm the answer with a calculator.