Percentage Calculator — Percent Of, Change, Difference & Reverse
Every common percentage question on one page, each showing the formula with your numbers. Plus fraction ↔ decimal ↔ percent.
What is X% of Y?
15 ÷ 100 × 80 = 12
X is what percent of Y?
24 ÷ 160 × 100 = 15%
Percentage increase or decrease from X to Y
(150 − 120) ÷ 120 × 100 = 25%
X increased or decreased by Y%
250 × (1 + 12 ÷ 100) = 250 × 1.12 = 280
Percentage difference between two numbers
|40 − 50| ÷ ((40 + 50) ÷ 2) × 100 = 22.222222%
Y is X% of what? (reverse percentage)
45 ÷ (30 ÷ 100) = 150
Percentage points vs percent
Fraction ↔ decimal ↔ percent converter
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This percentage calculator answers the seven questions people actually ask about percentages, each in its own small box: what is X% of Y, X is what percent of Y, the percentage increase or decrease from one number to another, a number increased or decreased by a percentage, the percentage difference between two numbers, and the reverse question, Y is X% of what. Every answer updates as you type and shows the formula with your own numbers substituted, so you can check the working or do the next one by hand.
Most percentage mistakes come from dividing by the wrong number, not from arithmetic. Percent change divides by the starting value, percent difference divides by the average of the two, and a reverse percentage divides by the percentage itself. The page keeps them separate and labels which is which. It also shows the difference between percentage points and percent, and converts between fractions, decimals and percentages, giving exact fractions (0.375 = 3/8) rather than rounded ones.
How to use
- Find the box that matches your question, for example “Percentage increase or decrease from X to Y”.
- Type your two numbers. Commas, a $ sign or a % sign are fine; the result appears immediately.
- Read the formula line under the result to see exactly how it was worked out.
- Copy the answer with the Copy button, or use the converter at the bottom to turn a fraction or decimal into a percentage.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 15 ÷ 100 × 80 = 12. A quick mental shortcut: 10% is the number with the decimal point moved one place left, so 15% is 10% plus half of that again (8 + 4 = 12).
How do I calculate percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 120 to 150: (150 − 120) ÷ 120 × 100 = 25% increase. A negative answer is a decrease. Always divide by the starting value, which is why going from 150 back to 120 is a 20% decrease, not 25%.
What is the difference between percent change and percent difference?
Percent change has a direction: it measures movement from an original value to a new one and divides by the original. Percent difference compares two values where neither is the starting point (two prices, two measurements) and divides the gap by their average, so the answer is the same whichever value you put first. 40 and 50 are 22.22% apart as a percent difference, while 40 to 50 is a 25% increase and 50 to 40 a 20% decrease.
How do I find the original number before a percentage was added or taken off?
Divide by the multiplier, not by subtracting the percentage. If a price after a 13% increase is $113, the original is 113 ÷ 1.13 = $100. If 45 is 30% of a number, the number is 45 ÷ 0.30 = 150. Taking 13% off $113 gives $98.31, which is wrong, because the 13% was calculated on the smaller original.
What is the difference between percentage points and percent?
Percentage points are the plain subtraction between two percentages; percent is the relative change. An interest rate rising from 4% to 5% has gone up 1 percentage point, which is a 25% increase in the rate itself. News reports that say “up 1%” in this situation are ambiguous at best.
How do I convert a fraction to a percentage?
Divide the top number by the bottom number and multiply by 100. 3/8 = 3 ÷ 8 = 0.375 = 37.5%. To go the other way, write the percentage over 100 and simplify: 37.5% = 37.5/100 = 375/1000 = 3/8. The converter on this page does both and gives the exact fraction.
Which formula for which question
• X% of Y: X ÷ 100 × Y. Tips, commissions, tax on a price, a share of a budget.
• X is what % of Y: X ÷ Y × 100. A test score (42 out of 50 = 84%), a share of the total.
• Percent change from A to B: (B − A) ÷ A × 100. Price rises, growth, year-over-year figures.
• A increased or decreased by P%: A × (1 ± P ÷ 100). Applying a raise, a markup or a discount.
• Percent difference between A and B: |A − B| ÷ ((A + B) ÷ 2) × 100. Comparing two quotes or two measurements.
• Reverse, B is P% of what: B ÷ (P ÷ 100). The original price before a discount or tax.
The one word that decides the formula is “of”, or “from”. Whatever comes after it is the number you divide by.
Why percentages don't cancel out
A 50% rise followed by a 50% fall does not bring you back to where you started. 100 up 50% is 150; 150 down 50% is 75. The second percentage is taken from a bigger number, so it removes more than the first one added. The same asymmetry means a 20% loss needs a 25% gain to recover, and a 50% loss needs a 100% gain.
Successive percentages multiply. Two 10% increases are 1.1 × 1.1 = 1.21, a 21% increase in total, not 20%. Stacked discounts work the same way in reverse: 20% off and then a further 10% off is 0.8 × 0.9 = 0.72 of the price, or 28% off.
Rounding and display
Results show up to six decimal places and drop trailing zeros, so 1 ÷ 3 appears as 33.333333%. Copy the value you need and round it for your context: money to the cent, survey results usually to one decimal place. Fractions from the converter are exact for any terminating decimal, and the converter also suggests the closest simple fraction (denominator up to 100) when the exact one is unwieldy.
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