Percentage Calculator
A percentage is a fraction out of 100. Find a percentage of a number, what percentage one number is of another, the percentage change or difference between two values, the result of an increase or a discount, or the original value before a change — with every step written out.
What Is a Percentage?
Per cent means “out of a hundred”: 15% is 15/100 = 0.15. So a percentage is just a fraction with denominator 100, which makes amounts of different sizes easy to compare. To take a percentage of a number, multiply by the percentage and divide by 100.
A percentage change compares a new value with an old one: it is relative to where you started. That is why a 50% rise followed by a 50% fall does not bring you back: 100 → 150 → 75. A percentage difference compares two values without a “before” and “after”, relative to their average. And a change in percentage points is the plain difference between two percentages: from 4% to 5% is 1 percentage point, but a 25% rise.
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%Step-by-Step Solution
Worked Techniques
Turn the percentage into a decimal (divide by 100), then multiply.
New minus old, divided by the old value. A negative answer is a decrease.
A price of 96 including a 20% increase was 80 before, not 96 − 20% = 76.80: undo a change by dividing, not by subtracting.
Sources & Verification
- H.-H. Wu, Understanding Numbers in Elementary School Mathematics, American Mathematical Society, 2011 — Ch. 19 (Percent, ratio and rates).
- OECD, Glossary of Statistical Terms — “percentage change” and “percentage point”.
Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. Example: 15% of 80 = 0.15 × 80 = 12. It works both ways round: 15% of 80 is the same as 80% of 15.
How do I work out what percentage one number is of another?
Divide the part by the whole and multiply by 100. Example: 18 out of 24 is 18 / 24 = 0.75, so 75%.
How do I calculate a percentage increase or decrease?
Percentage change = (new − old) / old × 100%. Example: a price goes from 48 to 60.
1. New minus old: 60 − 48 = 12.
2. Divide by the old value: 12 / 48 = 0.25.
3. Multiply by 100: an increase of 25%. A negative answer is a decrease: from 60 back to 48 is −20%, not −25%, because the starting value is now 60.
What is the difference between percentage change and percentage difference?
A percentage change has a direction: from an old value to a new one, relative to the old value. A percentage difference compares two values without a before and after, relative to their average: |X − Y| / ((X + Y)/2) × 100%. For 40 and 50 that is 10 / 45 = 22.2%, while the change from 40 to 50 is 25%.
How do I calculate a discount or add VAT?
Multiply by 1 minus or plus the percentage as a decimal. A 30% discount on 59.99: 59.99 × 0.70 = 41.99 (you save 18.00). Adding 21% VAT to 250: 250 × 1.21 = 302.50.
How do I find the original price before a percentage change?
Divide by the multiplier, do not subtract the percentage. If a price of 96 includes a 20% increase, the original was 96 / 1.20 = 80. Taking 20% off 96 gives 76.80, which is wrong, because the 20% was taken of the original 80, not of 96. For a price after a 25% discount of 60, the original was 60 / 0.75 = 80.
What is a percentage point?
The plain difference between two percentages. When an interest rate goes from 4% to 5%, it rises by 1 percentage point, but by 25% (because 1 is a quarter of 4). News reports often mix the two up.