Percentage Calculator

Percentage Calculator

Every everyday percentage question in one place, each with its equation shown so you can see how the answer was reached: what a percentage of a number is, what percentage one number is of another, percentage change up or down, the percentage difference between two numbers (which is not the same thing), the original value before a percentage was added or taken away, and adding or subtracting a percentage from a number. Enter up to four percentage-of questions at once when you are working through a list.

Disclaimer: Percentages are calculated exactly from the values you enter, in your browser, for general information only. Where a rounded figure is shown, the equation line gives the values used, so the working can always be checked.

What this calculator does

Percentages are one idea wearing six different questions, and most errors come from answering a different question from the one that was asked. This page keeps the six apart, gives each its own mode, and shows the equation for every answer so the working can be checked. What is 15% of 240 is a slicing question. 50 is what percent of 240 is a comparison question. Going from 80 to 100 is a change question, and it is not symmetric: the way back down, 100 to 80, is a different percentage. Comparing 80 and 100 with no direction is a difference question, which uses the average as its base so it gives the same answer both ways round. Working backwards from a price that already has tax or a discount inside it is the reverse question, and it is the one people most often get wrong by applying the percentage to the final figure instead of the original. Adding or subtracting a percentage is the building block the others rest on.

How to use it

  1. Percent of a number takes up to four questions at once, because real work comes in lists: a basket of discounts, a set of exam marks. Each row answers its own question and also shows the rest of the number, the part the percentage did not take, which for a discount is the price you actually pay and for a tax is the amount before tax. The bar under the first answer shows the slice visually.
  2. What percent wants the part first and the whole second, and the order matters: 50 of 240 is 20.83%, while 240 of 50 is 480%. The answer also comes as a decimal and as a simplified fraction when both numbers are whole, because fractions are how percentages are often stored in recipes, ratios and odds.
  3. Percentage change needs a starting value and a new value, in that order, and it refuses a starting value of zero, because change from nothing is not a percentage at all. The sign is part of the answer: plus for an increase, minus for a decrease, always shown.
  4. Percentage difference is for comparisons with no start and no end: two prices, two measurements, two candidates. It divides by the average of the two, which is why it is symmetric, and the page shows both directional changes underneath so you can see exactly how difference and change diverge on the same pair of numbers.
  5. Find the original divides the final value by one plus or one minus the percentage as a decimal. This is the VAT and sales tax question (what was it before 20% was added) and the discount question (what was it before 20% was taken off), and it is emphatically not answered by applying the percentage to the final value, which is the single most common percentage mistake there is.
  6. Percentages over 100 and negative numbers are allowed everywhere they make sense. 150% of a number is one and a half of it. A change can exceed 100% upward but never downward past minus 100%, because a value cannot fall by more than itself, and the reverse mode enforces that boundary explicitly instead of returning nonsense.

How it is calculated

P percent of N is P times N divided by 100. X as a percentage of Y is X divided by Y times 100. Percentage change is (new minus old) divided by old times 100. Percentage difference is the absolute gap between the two values divided by their average times 100. The original before an increase is the final value divided by (1 + P/100); before a decrease, divided by (1 - P/100). Adding P percent multiplies by (1 + P/100) and subtracting multiplies by (1 - P/100). Every figure on the page is one of these six, with the substitution shown.

Worked examples

The fixtures: 20% of 250 is 50. 15% of 240 is 36, leaving 204 as the other 85%. 50 as a percentage of 240 is 20.83%, the fraction 5/24, the decimal 0.2083.

The asymmetry everyone should know: 80 to 100 is +25%, but 100 back down to 80 is -20%. The same 20 units is a quarter of 80 and a fifth of 100, and the base is the whole story. Anyone who raises a price by 25% and then discounts it by 25% has not returned to the start: they are at 93.75% of it. The percentage difference between 80 and 100, for comparison, is 22.22%, the gap of 20 measured against the average of 90, and it is the same number read either way.

Reverse: a price of 120 that already includes a 20% increase came from 100. A sale price of 80 after a 20% decrease also came from 100. Notice that 20% of 120 is 24 and 20% of 80 is 16, neither of which is the 20 that was actually added or taken off, which is why the shortcut fails and the division exists.

Reading your result

Before trusting an answer, check you asked the question you meant. "What percent is A of B" and "by what percent did A grow to B" differ by exactly 100 percentage points, because the first measures the level and the second measures the movement, and confusing them is how a rise from 2% to 3% gets reported both as a 1% rise and a 50% rise by different writers on the same day: one means percentage points, the other percent, and the limitations below untangle them. If a change looks absurdly large, check the base: percentages of small numbers explode, which is correct arithmetic and misleading rhetoric at the same time.

Limitations

  • Percentages say nothing about size. A 50% increase on 4 and on 4 million are both 50%. This page computes the rate faithfully and shows the amounts alongside wherever a mode has them, but judging whether a percentage matters requires the underlying numbers, which no percentage can carry by itself.
  • Percentage points are not percent. A rate moving from 2% to 3% rose by 1 percentage point and by 50 percent. Both statements are true, they answer different questions, and only one of them belongs in a headline. The change mode answers the percent question; subtract the two rates yourself for the points.
  • Rounding is to two decimal places. Percentages are shown to two decimals, with the equation giving the inputs so any figure can be reproduced exactly. For very small or very large values where two decimals lose meaning, the fraction and decimal lines in the what-percent mode carry extra precision.
  • Checkout questions live elsewhere. Discounts stacked at a till, coupons and tax at checkout have their own workflow on the Discount Calculator; tips have the Tip Calculator. This page is the underlying arithmetic, kept general on purpose.

Frequently asked questions

How do I work out a percentage of a number without a calculator?

Find 10% first by moving the decimal point one place left, then build from there: 1% is another place, 5% is half of 10%, and most everyday percentages are combinations of those three. 15% of 240 is 24 plus 12, which is 36. The equation line in the percent-of mode shows the formal version (percentage times number divided by 100), and the two methods agree, which is the point of showing both.

Why is a 25% rise followed by a 25% fall not back to the start?

Because the base changed between the two operations. The rise is measured against the smaller starting number and the fall against the larger risen one, so the fall takes more units away than the rise added in percentage terms. With 80: up 25% is 100, down 25% of 100 is 25 units, landing on 75. The change mode on this page lets you verify any such pair in seconds.

What is the difference between percentage change and percentage difference?

Change has a direction and a starting point, and it is measured against that start. Difference has neither: it compares two values symmetrically against their average. Use change for anything that happened over time, a price, a weight, a score. Use difference for comparing two things side by side where neither is the original, two quotes for the same job, two measurements of the same thing.

How do I find the price before VAT or sales tax?

That is the reverse mode with "increase". If the shelf price includes 20% tax, divide by 1.20: a 120 shelf price is 100 before tax, and the tax inside it is 20, not the 24 that 20% of 120 would suggest. The same method recovers an original price before a discount, with "decrease" selected.

Related calculators

Method: the six standard percentage identities, each with its substitution displayed; change measured on the starting value, difference on the average of the two values, reverse values recovered by division by (1 + P/100) or (1 - P/100), with zero and hundred-percent boundaries handled explicitly. Last reviewed: 13 October 2026.