Percentage Calculator
Calculate percentages instantly; find X% of Y, what percent X is of Y, or percent change between two numbers.
Enter values in any section and click Calculate.
How Does the Formula Work?
This calculator answers three kinds of percentage question, each in its own section.
X is what % of Y = (X ÷ Y) × 100
% Change = ((New − Old) ÷ |Old|) × 100
Mode 1 answers "What is 15% of 200?"; useful for tips, discounts, and tax. Mode 2 answers "24 is what percent of 80?"; useful for test scores, completion rates, and ratios. Mode 3 answers "What is the percent change from 50 to 75?"; useful for price changes, growth rates, and performance comparisons.
Quick Checks You Can Do in Your Head
10% = divide by 10. 25% = divide by 4. 33% ≈ divide by 3. 50% = divide by 2. 75% = divide by 4, multiply by 3. These mental shortcuts help verify your calculator results quickly.
Everyday Percentage Applications
To work out a tip quickly, take 10% by moving the decimal point one place to the left, then add half of it for 15% or double it for 20%. On a $64 bill, 10% is $6.40, so 15% is $9.60 and 20% is $12.80.
To take sales tax back out of a total, divide by 1 plus the tax rate. With 8% tax, a $108 total becomes $108 ÷ 1.08 = $100 before tax.
Stacked discounts can mislead: a 30% off coupon plus an extra 20% off is NOT 50% off. It is 100% × 0.70 × 0.80 = 56%, which means a 44% total discount. Use Mode 3 (percent change) to verify the real discount by comparing the original price to the final price.
Financial Percentages
Card interest is quoted as an annual percentage rate (APR). A $5,000 balance at 24% APR accrues about $100 of interest in a month, because 24% ÷ 12 = 2% and 2% of $5,000 is $100. Mortgage rates, investment returns and inflation are expressed as percentages too. An employer that matches 50 percent of what you put in, up to 6 percent of salary, adds 3 percent of your salary when you contribute the full 6.
Three Ways to Ask a Percentage Question
Here are three ways a percentage question can be put. Type 1: What is X percent of Y? Multiply Y by X divided by 100. Example: 15 percent of 200 is 200 times 0.15, which is 30. Type 2: X is what percent of Y? Divide X by Y and multiply by 100. Example: 45 divided by 180, times 100, gives 25 percent. Type 3: X is Y percent of what number? Divide X by Y divided by 100. Example: 36 ÷ 0.20 = 180, so 36 is 20 percent of 180. This calculator has a section for the first two types; the answer to the third is quick to check in Mode 1, where 20% of 180 comes back as 36. Mode 3 answers a different question, the percent change between two values.
Percentage Change
Percentage change measures how much a value has risen or fallen relative to where it started: (New minus Old) divided by the absolute value of Old, times 100. If a stock goes from $50 to $65, the change is (65 minus 50) divided by 50, times 100, which is 30 percent. If it then drops from $65 to $52, the change is (52 minus 65) divided by 65, times 100, which is minus 20 percent. So a 30 percent rise followed by a 20 percent fall ends at $52, 4 percent above the starting $50: each change is measured against a different starting value, so the two do not cancel out.
Building Blocks for Mental Math
Mental math shortcuts make percentage calculations faster. To find 10 percent move the decimal one place left: 10 percent of 85 is 8.5. To find 5 percent halve the 10 percent result: 5 percent of 85 is 4.25. To find 15 percent add 10 percent plus 5 percent: 15 percent of 85 is 8.5 plus 4.25 equals 12.75. To find 20 percent double the 10 percent: 20 percent of 85 is 17. To find 1 percent move the decimal two places: 1 percent of 85 is 0.85. These building blocks let you estimate any percentage quickly. For exact calculations use this tool.
Percentage vs Percentage Points
This distinction matters in finance and statistics. If an interest rate rises from 5 percent to 7 percent, that is a 2 percentage point increase but a 40 percent increase. If unemployment drops from 6 percent to 4.5 percent, that is a 1.5 percentage point decrease but a 25 percent decrease. When comparing rates, say whether a change is in percentage points or a percentage of the original rate.
Weighted Grades
A weighted grade multiplies each score by the share of the grade it carries. If homework counts for 20 percent and exams for 80 percent, a student with 95 on homework and 75 on exams gets 0.20 × 95 + 0.80 × 75 = 19 + 60 = 79. Mode 1 gives each piece: 20% of 95 is 19 and 80% of 75 is 60.
Tips & Recommendations
To calculate a 15% tip on $48: 10% = $4.80, plus half of that ($2.40) = $7.20 tip.
A 20% discount followed by an extra 10% off is NOT 30% off. It is 100% × 0.8 × 0.9 = 72%, so a 28% total discount.
A 50% increase followed by a 50% decrease does NOT return to the original. 100 → 150 → 75. Always use the original as the base.
A 50% markup on cost $100 = $150 selling price. But the profit margin is 33% (50/150), not 50%.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. Example: 25% of 80 = 0.25 × 80 = 20.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. Example: 24 out of 80 = (24/80) × 100 = 30%.
How do I calculate percent change?
Subtract the old value from the new, divide by the absolute value of the old, and multiply by 100. Example: from 50 to 75 = ((75-50)/50) × 100 = 50% increase.
What is the difference between percent and percentage points?
If an interest rate goes from 5% to 8%, the change is 3 percentage points but a 60% increase (3/5 × 100).
Can percent change be negative?
Yes. A negative result means a decrease. From 100 to 75 = −25% change.
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