Percentage Calculator — Percent Of, Change & Increase
Four percentage calculators in one: a percent of a value, one number as a percent of another, the percentage change between two values, and increasing or decreasing by a percent.
What is X% of Y?
X is what percent of Y?
Percentage change
Increase or decrease by a percent
What this calculator does
Percentages are a way of writing a proportion with 100 as the base, and almost every percentage problem is one of four shapes. This page gives each its own quick calculator so you can work out a percent of a value, express one number as a percent of another, measure the change between two values, or move a value up or down by a given percent — without reaching for a spreadsheet.
The four calculations
| Question | Method | Example |
|---|---|---|
| What is p% of y? | y × p ÷ 100 | 15% of 80 = 12 |
| x is what percent of y? | x ÷ y × 100 | 20 of 80 = 25% |
| Change from a to b | (b − a) ÷ |a| × 100 | 80 → 100 = +25% |
| Increase / decrease by p% | y × (1 ± p/100) | 100 + 20% = 120 |
The change is signed: a move from 100 down to 80 is −20%. That is different from the symmetric “percentage difference”, which divides by the average of the two values and so does not depend on which one you call the start.
Why a 20% cut needs a 25% rise
The most common percentage mistake is assuming a decrease can be undone by an equal increase. It cannot, because each percentage is taken on a different base. Cutting 100 by 20% gives 80; raising 80 by 20% gives only 96, because the second 20% is calculated on the smaller number. Recovering the loss takes a rise of 25% (80 × 1.25 = 100). Keeping the base in mind is the whole trick to percentage problems.
Percentage points are not percent
A change between two percentages is measured in percentage points when you subtract them, and in percent when you divide by the starting percentage. An interest rate rising from 4% to 5% has gone up by 1 percentage point — and by 25% relative to where it started. Both statements are true; they answer different questions. The same distinction applies to polling, where a lead moving from 40% to 44% is four points but a 10% relative increase, and to fees, where a charge moving from 0.2% to 0.3% is a 50% increase that sounds much smaller as “0.1 points”.
Reverse percentages
“The price after a 20% discount is 80 — what was it before?” is the question that catches people out. The discount was taken on the original, so 80 is 80% of the original: divide by 0.8 to get 100. Adding 20% to 80 gives 96 and is wrong, because 20% of 80 is not the amount that was removed. The same logic applies to VAT, tips and commission: to recover a base from a value that includes a percentage, divide by (1 + rate), and to recover a base from a value after a deduction, divide by (1 − rate).
Successive changes multiply
A 10% rise followed by a 10% fall is not zero: 1.10 × 0.90 = 0.99, a 1% net loss. The two changes act on different bases, and the fall is taken on the larger post-rise number, so it removes more than the rise added. This is why “up 50% then down 50%” loses a quarter of the value, and why a portfolio that falls 30% needs a 43% gain to recover — the required gain is r ÷ (1 − r), not r.
Mistakes that change the answer
- Adding percentages instead of multiplying them. Two successive 10% changes are not 20%.
- Reversing a percentage by applying it again. A 20% discount is undone by dividing by 0.8, not by adding 20%.
- Using the wrong base for a change. The denominator is the starting value; switching it flips 25% and 20% for the same move.
- Confusing points with percent. A “2% rise” in an interest rate can mean 2 points or 2% relative — a difference of orders of magnitude at low rates.
- Applying a percentage to a number that already includes it. Adding tax to a tax-inclusive price, or a tip to a bill that already has service, double-counts.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100 — 15% of 80 is 80 × 15 ÷ 100 = 12. The first calculator on this page does exactly that; type the percent and the value and the answer appears as you type.
What is the difference between percentage change and percentage difference?
Percentage change is directional and uses the starting value as the base: going from 80 to 100 is a 25% increase, while going from 100 to 80 is a 20% decrease. Percentage difference is symmetric: it compares two values against their average, so the order does not matter. Use change when one value is the “before” and the other the “after”, and difference when neither is a baseline.
How do I work out “X is what percent of Y”?
Divide the part by the whole and multiply by 100 — 20 is 20 ÷ 80 × 100 = 25% of 80. The second calculator does this, and it is the one to reach for when a score, share or proportion needs to be expressed as a percentage.
How do I add or remove a percentage (increase and decrease)?
To increase a value by p%, multiply it by 1 + p/100; to decrease it, multiply by 1 − p/100. The last calculator applies either direction, which is useful for a price rise, a discount, a tax or a pay change.
Why can a 20% fall not be undone by a 20% rise?
Because each percentage applies to a different base. Falling from 100 to 80 is a 20% decrease, but rising from 80 by 20% only returns you to 96 — the second percentage is taken on the smaller number. Recovering a 20% fall needs a 25% rise, which is why percentage change is not reversible by applying the same rate.
What is the difference between percent and percentage points?
A percentage point is the arithmetic difference between two percentages, while a percent change is relative to the starting figure. An interest rate moving from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms. News reports mix the two constantly; which one is meant changes the size of the story.
How do I find the original price after a discount?
Divide by the remaining fraction rather than adding the discount back. A price of 80 after a 20% discount means 80 is 80% of the original, so the original is 80 ÷ 0.8 = 100. Adding 20% to 80 gives 96, which is the classic reverse-percentage error — the discount was taken on 100, not on 80.
Do successive percentage changes add up?
No, they multiply. A 10% rise followed by a 10% fall leaves 1.10 × 0.90 = 0.99, a 1% net loss, not zero. The order does not matter for the product, but the base does: each change applies to the result of the previous one, so equal and opposite percentages never cancel unless the base is the same.
How do I take a percentage of a percentage?
Multiply the two fractions. 0.5% of 1,000,000 is 0.005 × 1,000,000 = 5,000; “20% of 30%” is 0.2 × 0.3 = 0.06, or 6%. The result is smaller than either factor, which is why a fee charged on an already-discounted price is smaller than the headline rate suggests.
Is anything sent to a server?
No. Every calculation runs in your browser; nothing is uploaded.
Go deeper
Longer explanations of the problems this tool solves:
Everything runs in your browser — nothing you type is uploaded.