Percentage calculator for the three questions people actually ask
Percentages cause trouble because three different questions all get called "percentage": a share of an amount, a ratio expressed as a percent, and a change between two values. They need different arithmetic, so each one gets its own mode here.
Part of SolveStep's algebra solver. For percentages inside a larger expression, use the fraction calculator.
Three questions, three different calculations
The word "percent" just means "per hundred", so every percentage problem is really a fraction with 100 on the bottom. What changes between problems is which number goes where, and that is what people get wrong far more often than the arithmetic.
A worked example of the classic trap: a price rises from 80 to 100, a 25% increase. Drop it back from 100 to 80 and that is a 20% decrease, not 25%. The amount of change is identical both times; the number you compare it against is not.
X% of Y
15% of 200 = 30
A share of an amount. Convert the percentage to a decimal, then multiply. This is the one that appears in tips, discounts and tax.
X is what % of Y
30 is 15% of 200
A ratio expressed as a percentage. Divide the part by the whole, then multiply by 100. This is the one used for test scores.
Percentage change
80 → 100 is +25%
How much something grew or shrank, measured against where it started. The starting value is always the denominator.
Change from zero
0 → 50 = undefined
Not an error in the calculator. There is no starting amount to compare against, so no percentage exists. The tool says exactly that rather than inventing a number.
Two percentage problems, step by step
A share of an amount
15% of 200- Convert the percentage to a decimal by dividing by 100: 15% = 15 ÷ 100 = 0.15.
- Multiply the decimal by the amount: 0.15 × 200.
- This works because "of" means multiply: 15% of something is 0.15 lots of it.
Increase, and why the reverse differs
80 → 100- Find the actual change: 100 − 80 = 20.
- Compare it to the starting value, not the new one: 20 / 80 = 0.25.
- Convert to a percentage: 0.25 × 100 = 25% increase.
- Going back the other way, the same change of 20 is compared to 100 instead: 20 / 100 = 20% decrease. Same amount, different reference point.
Percentage calculator FAQ
Why is a 25% increase not cancelled by a 25% decrease?
Because the two percentages are measured against different starting numbers. Going 80 → 100 compares the change of 20 against 80. Going 100 → 80 compares the same 20 against 100. The change is the same; the base is not.
How do I work out a discount?
Use the first mode to find the discount amount, so 20% of 45 is 9, then subtract that from the original price. Or find 80% of 45 directly, which gives the final price in one step.
What does percentage change from zero give?
Nothing. It is undefined, and the calculator says so rather than returning infinity or an error. Percentage change measures growth relative to a starting amount, and there is no such thing as a proportion of zero.
Can I use decimals and negative numbers?
Yes, both. Decimal percentages like 12.5% work normally, and negative values are handled correctly in percentage change, so a move from −20 to −10 is reported against the size of the starting value.
How do I convert a percentage to a fraction?
Put it over 100 and reduce: 15% is 15/100, which simplifies to 3/20. The fraction calculator will reduce it for you.
Is percentage the same as percentage points?
No, and the difference matters. If a rate goes from 4% to 6%, that is a rise of 2 percentage points but a 50% increase. News stories mix these up constantly.