Percentage Calculator

How to use the percentage calculator

1. Pick the question you want answered with the tabs: P% of Y, X is ?% of Y or % change.
2. Type your two numbers. The question above the fields repeats them, decimals and negative numbers work, and the result updates as you type.
3. Check the Formula line: it repeats the calculation with your own numbers, so you can follow it or copy it into homework or a report.
4. Click Copy to copy the result.

The three percentage formulas

A percentage is a number out of 100. Almost every percentage question is one of these three:

• What is P% of Y? P ÷ 100 × Y. Use it for discounts, tips, tax and commission.
• X is what percent of Y? X ÷ Y × 100. Use it for test scores, shares of a budget or completion rates.
• Percentage change from A to B: (B − A) ÷ |A| × 100. A positive answer is an increase, a negative answer a decrease. Use it for price changes, salary raises and growth.

The calculator rejects divisions by zero with a message instead of showing a meaningless result: you cannot ask what percent something is of 0, and a change from 0 has no percentage. It also hides the tiny rounding errors computers make with decimals, so 10% of 3 shows as 0.3 rather than 0.30000000000000004.

Worked examples

• Discount: a jacket costs $49.99 and is 20% off. 20 ÷ 100 × 49.99 = 9.998, so you save about $10.00 and pay $39.99.
• Test score: you answered 45 of 60 questions correctly. 45 ÷ 60 × 100 = 75%.
• House price: a home bought for $250,000 sells for $287,500. (287,500 − 250,000) ÷ 250,000 × 100 = +15%.
• Pay cut: hours go from 100 to 80 a month. (80 − 100) ÷ 100 × 100 = −20%, a 20% decrease.
• More than 100%: 150% of 40 is 60, and 120 is 150% of 80. Percentages above 100 simply mean more than the whole.

Common percentage mistakes

• Increases and decreases are not symmetric. 80 rising by 25% gives 100, but 100 falling by 25% gives 75. To undo a 25% rise you need a 20% fall.
• Percent versus percentage points. If a savings rate goes from 4% to 5%, it rose by 1 percentage point, but by 25% in relative terms. News reports often mix the two.
• Stacked discounts do not add up. 20% off and then an extra 10% off is 28% off in total (0.8 × 0.9 = 0.72), not 30%.
• Choose the right base. In a percentage change, always divide by the original (old) value, not the new one.
• Negative starting values. The calculator divides by the absolute value, so a loss shrinking from −50 to −25 shows as a 50% improvement rather than a confusing negative number.

Quick mental math tricks

• 10%: move the decimal point one place left. 10% of 350 is 35; 5% is half of that, 17.5.
• 1%: move it two places. 1% of 2,400 is 24, so 3% is 72.
• Swap the numbers: x% of y equals y% of x. 8% of 50 is the same as 50% of 8, which is 4.
• 15% tip: take 10%, then add half of it. On a $60 bill: 6 + 3 = $9.

Frequently asked questions