Percentage Calculator

What is X% of a number, and how the percentage calculator finds it

This is the most common percentage question: a percent of some base value, which is why this calculator is sometimes searched for as a percent of calculator, or more precisely a percent of a number calculator. The formula divides the percent by 100 to turn it into a decimal fraction, then multiplies that fraction by the base number. That first division is exactly what a percent to decimal calculator does on its own: 20% becomes 0.20, and 8.5% becomes 0.085, before either number is multiplied by anything.

Worked example. A store lists an item at 150 and advertises a 20% discount, the same scenario a discount percentage calculator is usually opened for. To find the size of that discount in the store's own currency, compute 20% of 150: (20 ÷ 100) × 150 = 0.20 × 150 = 30. That 30 is the discount amount, not the final price; the final price is 150 minus 30, which is 120. This is exactly the mixup covered further down: “20% of 150” and “20% off 150” answer two different questions.

X is what percent of Y?

This question flips the first one around: instead of starting from a percent, you start from two plain numbers and ask what percentage relationship connects them. The formula divides the first number (the part) by the second number (the whole), then multiplies by 100 to express that ratio as a percentage: part/whole × 100. It lives in the “Percentage Calculator in Common Phrases” block below the main calculator, alongside two closely related phrasings of the same underlying idea.

Worked example. A student scores 30 marks out of a possible 150 on a quiz. To express that as a percentage: (30 ÷ 150) × 100 = 0.20 × 100 = 20%. The same formula works for anything expressed as a fraction of a total, whether that is marks out of a paper, a discount amount out of a listed price, or a completed task count out of a total task list.

The same block also answers a third phrasing, “X is Y% of what?”, the algebraic inverse of the very first question on this page: instead of a percent and a base producing a share, a share and a percent produce the base, whole = part/(p/100). If 30 is 20% of some number, that number is 30 ÷ 0.20 = 150, the same relationship as the worked example above, just solved for the opposite unknown.

Percentage change from X to Y

Percentage change measures how much a number has moved, as a percentage of where it started. The formula subtracts the starting value from the ending value, divides that difference by the starting value, and multiplies by 100. A positive result means an increase; a negative result means a decrease.

Worked example. A monthly expense rises from 100 to 150. The change is ((150 − 100) ÷ 100) × 100 = (50 ÷ 100) × 100 = +50%, an increase. If the same expense later fell back from 150 to 100, the change would be ((100 − 150) ÷ 150) × 100 = (−50 ÷ 150) × 100, which rounds to −33.33%, a decrease. Notice the two percentages are not mirror images of each other even though the amount of money involved, 50, is identical both times. That is because each calculation divides by a different starting number: 100 in the first case, 150 in the second. This calculator works as a percentage increase calculator whenever the ending value is larger, and a percentage decrease calculator, or simply a decrease calculator, whenever it is smaller, since the same percent change formula covers both directions.

Percentage difference between two numbers

Percentage change and percentage difference both compare two numbers, but they answer different questions. Percentage change is directional: one number is the starting point, the other is where it ended up, and swapping them flips the sign. Percentage difference, often searched as a percentage difference calculator, percent difference calculator, or simply a difference calculator, has no starting point at all; it simply measures how far apart two numbers are, relative to their shared average, and gives the identical answer no matter which one is entered first, which is exactly what makes it a genuine difference percentage calculator rather than a directional one. This percent difference formula, also written the percentage difference formula, divides the absolute difference between the two numbers by their average, then multiplies by 100.

Worked example. In the Percentage Difference Calculator, enter both numbers being compared; the order does not matter, since the result is the same either way. Between 100 and 150, the percentage difference is 40%: the absolute difference of 50 divided by the average of 125, times 100. The percentage change from 100 to 150 is +50%, and from 150 to 100 is −33.33%, different numbers from the 40% difference, because change is directional and difference is not. All three figures describe the identical pair of numbers; they simply answer three different questions about them. One pair the Percentage Difference Calculator cannot handle is two numbers that average to exactly zero, such as 5 and -5, since dividing by an average of zero has no meaningful result; the calculator reports an error in that specific case rather than a number that looks plausible but is not.

Percentage difference shows up most often when two measurements of the same kind have no natural “before” value: two lab readings, two competing price quotes, two survey results. When one number genuinely came first, percentage change is the better tool, since it keeps the direction that percentage difference discards. In science and engineering the same calculation is called relative percent difference, used to check how closely two independent measurements agree; only the setting changes, not the formula.

Percent off and sale prices

A percent off calculator, or percentage off calculator, is the first card plus one subtraction. To work out percentage off, multiply the price by the discount as a decimal, then subtract that saving from the price. The shortcut skips the subtraction: multiply the price by one minus the discount, so 25% off leaves 75% of the price. That is how to do percentages off in your head, and the table applies it to an $80 item.

Fractions and scores as percentages

How to turn a fraction into a percent takes one division and one multiplication: divide the top by the bottom, then multiply by 100. What is 1/8 percent, or what is the percent for 1/8? One divided by 8 is 0.125, so 12.5%. Improper fractions pass 100%: 5/4 in percentage terms is 125% and 3/2 as percent is 150%. A mixed number such as 1 1/4 to percent works out as 1.25, or 125%, and the percentage for 1/3 repeats forever, 33.33% rounded. Going the other way, how to turn percent into decimal is a division by 100, so 12.5% is 0.125.

Marks out of 20 are the easiest scores to convert, because 100 divided by 20 is 5: multiply the mark by 5. So 16 out of 20 as a percentage is 80%, and a mark of 14 is 70%. Other totals use the same part-over-whole formula, and the table reads off the ones that come up most.

Everyday uses for each calculator

A tip on a restaurant bill is a plain "X% of a number" question: 18% of a $64 bill is (18 ÷ 100) × 64 = $11.52, the Percentage Calculator's formula with the tip rate as the percent and the bill as the base. Sales tax uses the identical formula: a 7% tax on a $50 purchase adds (7 ÷ 100) × 50 = $3.50.

A test or assignment score is usually the "X is what percent of Y" row: getting 42 correct out of 50 questions is (42 ÷ 50) × 100 = 84%, the same arithmetic whether the numbers come from a quiz, a survey response rate, or a completed-task count. The "X is Y% of what" row in the same block answers a genuine reverse-percentage question directly: if 30 is 20% of some number, that number is 30 ÷ 0.20 = 150. A related but distinct reverse question is worth flagging separately since it looks deceptively similar: if a paycheck already has 22% withheld and the deposited amount is $780, the original amount before withholding is $780 ÷ (1 − 0.22) = $1,000, not $780 ÷ 0.22, because "22% withheld" means the deposit is the remaining 78%, not that the deposit itself is 22% of the original.

Common mixups

• “20% of” versus “20% off”. “Of” gives the share itself (30 in the example above); “off” gives what remains after removing that share (120). Confusing the two is the most frequent percentage mistake, especially when reading a discount sign quickly.
• Mixing up the part and the whole. In “X is what percent of Y”, Y is always the denominator. Swapping the two numbers by mistake, for example computing “150 is what percent of 30” instead of “30 is what percent of 150”, gives a completely different and usually much larger answer.
• Reading percentage change against the wrong starting point. A value that rises by 50% and then falls by 50% does not return to where it started, because the second 50% is calculated against the new, higher number, not the original one. Always check which number the percentage change is measured from.
• Forgetting the sign. A percentage change can be negative, which means a decrease. Dropping the minus sign when reporting a decline turns a loss into what reads like a gain.
• Treating percentage change and percentage difference as the same thing. They use different denominators (one number alone versus the average of both), so they generally produce different results even from the identical pair of numbers, as the 40% versus +50%/−33.33% example above shows. Use change when direction matters; use difference when it does not.