Three percentage questions on one page: a percentage of a number, what share one number is of another, and the change between two numbers. Switch between them with the buttons; the working is shown underneath the answer.
Key terms
- Per cent — literally “per hundred”. 15% is 15 out of every 100, or 0.15.
- Base — the number a percentage is measured against. Almost every percentage mistake is a disagreement about which number is the base.
- Percentage change — how much a number moved, relative to where it started.
How it works
The three forms
P% of V = V × P ÷ 100 · A is A ÷ B × 100 of B · change = (B − A) ÷ |A| × 100
Each is the same relationship rearranged. Knowing any two of the part, the whole and the percentage gives you the third.
Percentage changes do not cancel out
This is the one that costs people money. A 25% rise followed by a 20% fall puts you exactly back where you started — not 5% ahead. 200 rises to 250, and 20% of 250 is 50, which takes it back to 200.
The reason is that the two percentages are measured against different bases: the rise against the old number, the fall against the new larger one. A 50% loss needs a 100% gain to recover from. Whenever two percentages are combined, check what each one is a percentage of.
Percentage points are not percentages
If a rate moves from 4% to 5%, that is a rise of one percentage point — and a 25% increase. Both statements are true and they describe the same move. Reports that mix the two up can make a small change sound dramatic, or a large one sound trivial.
How to use this calculator
- Pick which of the three questions you are asking.
- Enter the two numbers. The answer updates as you type.
- Read the working line to check the numbers went into the slots you intended.
- For a change, note the difference as well as the percentage — 50% of a small number is still a small number.
Frequently asked questions
How do I take a percentage off a price?
Work out the percentage of the price, then subtract it. For 20% off 80: 20% of 80 is 16, so the price is 64. You can also multiply by 0.8 directly.
Can a percentage be more than 100?
Yes. If the part is larger than the whole, the answer is over 100% — 250 out of 200 is 125%. Only for shares of a fixed total, like a vote count, does going above 100% mean something has gone wrong.
Why is the change from zero not defined?
Because percentage change is measured against the starting number, and nothing is a meaningful share of zero. Going from 0 to 50 is an increase of 50, but there is no percentage that describes it. The calculator declines rather than showing infinity.
What about a change from a negative number?
The direction is kept: −50 to −25 is reported as a rise, because the number got larger. The change is measured against the size of the starting number, ignoring its sign.
How do I reverse a percentage increase?
Divide rather than subtract. If a price is 120 after a 20% rise, the original was 120 ÷ 1.2 = 100. Taking 20% off 120 gives 96, which is a different — and wrong — answer.
