Percentage Calculator: Of, Change, Increase & Decrease

The four questions, and the formula behind each

Almost every percentage problem is one of four. Naming which one you have is most of the work:

• What is X% of Y? Multiply: X ÷ 100 × Y. Tips, commission, a share of a budget.
• X is what percent of Y? Divide, then scale: X ÷ Y × 100. Test scores, conversion rates, market share.
• What is the percentage change from X to Y? (Y − X) ÷ X × 100. The starting value is the base. Get that backwards and every answer is wrong.
• What is X increased or decreased by Y%? Multiply by 1 + Y ÷ 100 or 1 − Y ÷ 100. Price rises, pay rises, markdowns.

Two shortcuts worth memorising

Percentages commute: X% of Y always equals Y% of X. Eight percent of 25 looks awkward; 25% of 8 is obviously 2. Same answer, no calculator. And 10% is a decimal point moved one place left, so 5% is half of that and 15% is 10% plus 5%. Most restaurant arithmetic never needs anything else.

Percent versus percentage point

These are different quantities and the difference is not pedantry. If an interest rate goes from 2% to 3%, that is a rise of one percentage point and a 50% increase. Both statements are true. Only one of them sounds alarming, which is why the choice between them is sometimes not innocent.

The rule: use percentage points when you are talking about the gap between two percentages, and percent when you are talking about the size of a change relative to where it started. A poll moving from 40% to 44% moved four points, or ten percent.

Why percentage changes do not cancel out

Add 10% to 100 and you get 110. Remove 10% from 110 and you get 99, not 100. Nothing has gone wrong: the second percentage is taken from a larger number, so it is worth more. The general rule is that a rise of p% is undone by a fall of p ÷ (100 + p)%, not by a fall of p%.

The dramatic version is a 50% loss. Halve an investment and you need it to double — a 100% gain — just to get back to where you started. This asymmetry is why "average annual return" quoted as a simple mean is misleading, and why a stock that falls 20% then rises 20% is still down 4%.

Percentages of percentages

A discount of 30% followed by a further 20% is not 50% off. Multiply what survives instead of adding what is removed: 0.7 × 0.8 = 0.56, so 44% off. The stacked discount calculator does this arithmetic for you, but the principle is the useful part — it applies to compounding growth, staged tax reliefs and tiered commissions just as much as to sale racks.

Where this calculator falls short

Three honest limits.

• Rounding. Results are rounded for display — four decimals for ordinary numbers, two for anything over a thousand. The underlying arithmetic is JavaScript binary floating point, the same as a spreadsheet, so a value like 0.1 + 0.2 is genuinely 0.30000000000000004 before it is rounded. For display purposes this never matters. For an invoice that must balance to the cent, use a tool built for money: the VAT calculator rounds and reconciles deliberately.
• Zero and negative bases. Percentage change from zero is undefined, and the tool says so rather than showing infinity. Change from a negative number is calculated against the absolute value, which keeps the sign sensible, but the result is close to meaningless — a business going from a loss of 10 to a profit of 5 has not improved by 150% in any way worth reporting. Use the absolute difference.
• Number parsing. The boxes accept both 1,234.56 and 1.234,56 and ignore currency symbols. The unresolvable case is a lone comma with exactly three digits after it: 1,500 is read as fifteen hundred. If you meant one and a half, type 1.5.

One thing no calculator can do for you: check that the base is the number you think it is. "Sales are up 200%" means nothing until someone says up from what, and over what period. Most misleading percentages are not arithmetic errors. They are correct arithmetic on a base that was chosen to flatter.

Frequently asked questions

How do I work out what percentage one number is of another?

Divide the part by the whole, then multiply by 100. 12 out of 80 is 12 ÷ 80 = 0.15, so 15%. The part always goes on top. Putting the whole on top is the single most common mistake and produces a number far bigger than 100.

What is the difference between 5% and 5 percentage points?

Percentage points measure the gap between two percentages; percent measures a change relative to the starting value. Going from 20% to 25% is a rise of 5 percentage points, and also a 25% increase. Both are correct and they are not interchangeable.

Why does adding 20% and then taking 20% off not return the original number?

Because the second percentage is taken from a bigger number. 100 plus 20% is 120; 20% of 120 is 24, so you land on 96. To reverse a 20% increase you need a 16.67% decrease.

Can I calculate percentage change when the starting value is zero?

No, and neither can anything else. The formula divides by the starting value, so the answer is undefined rather than infinite or 100%. Report the absolute change instead: "went from 0 to 40" is clear where "up 4000%" is nonsense.

Is anything I type sent anywhere?

No. The arithmetic runs in this tab, in JavaScript, with no network request and nothing written to storage. Reload the page and the numbers are gone.

Last updated September 19, 2026