Percentage calculator

How to use the percentage calculator

The calculator asks three questions, each as a sentence with boxes to fill:

1. What is X% of Y? For a part of a number: a tip, a discount, a share.
2. X is what percent of Y? For a part as a percentage: a test score, a share of a budget.
3. X is Y% of what? For the whole from a part: the price before a discount, a full amount from a share.

Type your numbers in the boxes of the question you need. The answer shows under it as you type, with the working that gives it, so you can check it or copy the method.

The three questions start filled in with one example, read three ways: 20% of 150 is 30. Replace the numbers with your own.

The three formulas

“Per cent” means “out of a hundred”: 20% is 20 out of every 100, or 0.2. Every percentage question comes back to one of these:

Question	Formula	Example
What is X% of Y?	X ÷ 100 × Y	15% of 80 = 12
X is what percent of Y?	X ÷ Y × 100	18 of 24 = 75%
X is Y% of what?	X ÷ Y × 100	45 is 75% of 60

The second and third use the same working: what changes is which number you know.

Examples from everyday life

• A tip: 15% of a bill of 64 is 15 ÷ 100 × 64 = 9.6.
• A test score: 42 right answers out of 50 is 42 ÷ 50 × 100 = 84%.
• The price before a sale: you paid 45 with 25% off, so you paid 75% of the price. 45 is 75% of 60: the price before the sale.
• A pay rise: 3% of a salary of 32,000 is 960, so the new salary is 32,960.
• A share of a budget: rent of 1,200 out of an income of 3,200 is 37.5% of the income.

Mistakes to avoid

• Going up then down by the same percentage doesn’t bring you back. 100 plus 20% is 120; 120 minus 20% is 96. The second 20% is of a bigger number.
• Percent and percentage points aren’t the same. A rate going from 4% to 5% rises by 1 percentage point, but by 25% of itself.
• Watch which number is the whole. “What percent of 50 is 10?” (20%) and “What percent of 10 is 50?” (500%) give very different answers.
• Percentages of different wholes don’t add up. 10% off, then 10% off the sale price, is 19% off, not 20%.

Working out percentages in your head

• 10%: move the decimal point one place to the left. 10% of 250 is 25.
• 5%: half of 10%. 5% of 250 is 12.5.
• 1%: move the decimal point two places. 1% of 250 is 2.5, so 3% is 7.5.
• 25% and 50%: a quarter and a half.
• Swap the numbers when it’s easier: X% of Y is the same as Y% of X. 8% of 50 is 50% of 8, which is 4.
• Build from pieces: 15% is 10% plus 5%. 15% of 60 is 6 plus 3, which is 9.