How to Calculate Percentage

A percentage is a fraction with 100 on the bottom. Once that clicks, every percentage question — a percent of a number, a test score, a discount, a price rise — is the same three-piece puzzle.

See what a percent is

Drag the slider to shade the grid. Then change what the whole grid stands for and watch the same percentage turn into a different amount.

That is the whole idea: 35% means 35 of every 100 equal parts, whatever the whole is. When the whole is 60, each of the 100 squares is worth 0.6, so 35% of 60 is 35 × 0.6 = 21. The same visual thinking drives ahaboo, where you can adjust a tax bracket model and see the marginal and effective rates shift.

The three percentage questions

1. Find a percent of a number. Divide the percent by 100, then multiply. 35% of 60 = 0.35 × 60 = 21.
2. Find what percent one number is of another. Divide the part by the whole, then multiply by 100. 21 out of 60 = 21 ÷ 60 × 100 = 35%.
3. Find the whole from a part. Divide the part by the percent as a decimal. If 21 is 35% of a number, the number is 21 ÷ 0.35 = 60.

Percent change

To see how much something grew or shrank, subtract to find the change, divide by the original value, and multiply by 100. A price going from $40 to $50 is a 10 ÷ 40 = 25% increase. Coming back down from $50 to $40 is a 10 ÷ 50 = 20% decrease — the starting point is different, so the percentage is too.

Doing it in your head

• 10%: move the decimal point one place left. 10% of 340 = 34.
• 5%: half of 10%. 5% of 340 = 17.
• 1%: move the decimal point two places left. 1% of 340 = 3.4.
• Swap trick: X% of Y equals Y% of X. 8% of 25 is hard; 25% of 8 is 2.

Common mistakes

• Dividing by the new value instead of the original in percent-change questions.
• Adding percentages that apply one after another: +10% then +10% is +21%, not +20%.
• Taking a percentage off the final price to “undo” a rise. To reverse a 20% increase, divide by 1.2 — don’t subtract 20%.
• Writing 0.05 as 50% — it is 5%.

Questions