What next?
Percentages underpin most of the site. These are the common specific cases.
How to use this calculator
- Pick the calculation you need — percent of a number, what percent, or change.
- Enter the two values.
- Read the answer instantly.
What your result means
Each mode answers a different everyday question: a share of a total, one number as a percentage of another, or the percent increase or decrease between two figures. Note a rise then an equal-percent fall does not return to the start, because the base changes.
Why this one is different
Three separate questions rather than one box: what is X% of Y, X is what percent of Y, and the percentage increase or decrease between two numbers — the third being the one most calculators leave out and most people actually need. Each shows the arithmetic, not just the answer.
Why percentages confuse even confident adults
Percentages are everywhere — sales, tips, stats, interest — yet the "percent of" versus "percent change" distinction trips up most people daily. A price that drops 50% then rises 50% doesn’t return to where it started, and that surprises almost everyone.
Getting percentages right protects you from misleading headlines, dodgy discounts and bad financial decisions. This tool answers the three questions you actually ask.
How it works
A percentage is just a fraction out of 100. To find a percentage of a number, multiply by the percentage over 100. To find what percent one number is of another, divide and multiply by 100. Percentage change compares the difference to the original value.
Formulas
pct = part ÷ whole × 100
change = (new − old) ÷ old × 100
The three questions this actually answers
Almost every percentage problem is one of three shapes. "What is 15% of 240?" multiplies: 0.15 × 240 = 36. "36 is what percent of 240?" divides: 36 ÷ 240 = 15%. "36 is 15% of what?" divides the other way: 36 ÷ 0.15 = 240. Naming the shape before reaching for the arithmetic is what prevents the classic error of dividing when you meant to multiply, and it is the reason this calculator asks which question you are answering rather than presenting one box.
Successive percentages do not add
A 20% rise followed by a 20% fall does not return to the start: 100 becomes 120, then 96. Percentages compose by multiplication, so the combined effect of two changes is 1.20 × 0.80 = 0.96, a 4% net fall. The same arithmetic explains why stacked discounts are worth less than their sum — 30% off then a further 10% off is 37% off, not 40% — and why recovering from a 50% loss takes a 100% gain. Whenever two percentage changes apply in sequence, multiply the factors rather than adding the rates.
Frequently asked questions
How do I add a percentage to a price?＋
Use the first box to find the percentage, then add it on. For example 20% of 50 is 10, so 50 plus 20% is 60.
Why is my change negative?＋
A negative result means the value went down. The third box shows increases in green and decreases in the accent colour.
What is the difference between percent and percentage points?＋
A rise from 4 percent to 5 percent is one percentage point but a 25 percent increase. Confusing the two is the most common way statistics get misreported.
How do I reverse a percentage increase?＋
Divide, do not subtract. A price that rose 20 percent to 120 was 100, found by dividing by 1.2. Taking 20 percent off 120 gives 96, which is the wrong answer.
Why does a 50 percent fall need a 100 percent rise to recover?＋
Because each change is measured against a different base. Falling from 100 to 50 is half of 100; getting back to 100 means adding 50 to a base of 50, which is a doubling.
How do I find what percentage one number is of another?＋
Divide the part by the whole and multiply by 100. Eighteen out of 24 is 0.75, or 75 percent.
Example calculation
Two common questions:
Change from 50 to 65 = (65 − 50) ÷ 50 × 100 = +30%
Assumptions & limitations
- Percentage change is undefined when the starting value is zero.
- “Percentage points” and “percent” differ: a rise from 10% to 15% is +5 percentage points, but a +50% relative increase.
- Results may be rounded for display.
Related calculators
Further reading
Sources & references
Percentage conventions and terminology on this page follow standard curriculum definitions:
- NCETM — multiplicative relationships, covering percentages and proportional reasoning
- Office for National Statistics — percentage change versus percentage point change