X percent of Y
To find a part of a number, divide the percentage by 100 and multiply. 15 percent of 240 is 0.15 x 240 = 36. This is the case for tips, commissions, a share of a bill or the amount of a discount.
A mental shortcut helps: 10 percent is the number with its decimal point moved one place left. For 15 percent, take 10 percent and add half of it. For 240 that is 24 plus 12, which gives 36.
Discounts, tips and sales commissions all use this form. If you need to take a percentage away, as in a 30 percent off sticker, you can multiply by 0.70 directly instead of working out the discount and subtracting it.
Percentage change from X to Y
Percentage change is (new - old) / old x 100. If a price goes from 80 to 100, the change is 20 / 80 = 25 percent increase. If it goes from 100 back to 80, the change is -20 / 100 = 20 percent decrease. The two numbers differ because the base is different, which surprises many people.
A positive result is an increase and a negative result is a decrease. Use it for price changes, salary raises, exam score improvements, website traffic or a change in your savings between two dates.
For a drop, the sign is negative, so a fall from 250 to 200 is -20 percent. Compare like with like: monthly sales this year against the same month last year is more meaningful than against the previous month if your business is seasonal.
X is what percent of Y
To turn a part into a percentage of a whole, divide the part by the whole and multiply by 100. If you scored 42 out of 60, the result is 42 / 60 x 100 = 70 percent. This works for marks, completion rates, budget shares and survey results.
Be clear which number is the whole. Asking what percent 20 is of 80 gives 25 percent, while asking what percent 80 is of 20 gives 400 percent.
You can use it for nutrition labels too. If a snack has 12 g of fat and your daily target is 70 g, it provides about 17 percent of that target. Rounding to a whole number is usually enough, though the calculator shows more decimals if you need them.
Common mistakes to avoid
Percentage points and percent are different. If an interest rate rises from 5 to 6 percent, it went up by one percentage point, and by 20 percent in relative terms. Another trap is adding successive percentages. A 20 percent rise followed by a 20 percent fall does not return you to the start: 100 becomes 120, then 96.
When in doubt about the base, ask what the percentage is taken from. That number is the one to divide by.
Another common slip is using the wrong base for markups and margins. A 25 percent markup on cost is a 20 percent margin on the selling price. If a spreadsheet and a calculator disagree, check which number each one divides by.