General
Percentage Calculator
Works percentages, where the base and the wording decide the answer.
Result
Percentage difference is measured against the average of the two numbers, which is the symmetric definition. Percentage change from one value to another is a different calculation. Use the increase or decrease calculator for that.
Get a Free Business AuditHow the calculation works
A percentage is a proportion expressed per hundred, so a percentage of a number is that number multiplied by the percentage divided by a hundred. The three common questions are what a percentage of a number is, what percentage one number is of another, and what number a given percentage represents, and they take the three rearrangements of the same relationship.
What moves the number
- Which number is the base.
- Whether the question is a percentage of, or a percentage change.
- Whether the result should be a percentage or a percentage point difference.
- Rounding, where percentages are chained.
Where this one goes wrong
A percentage point and a percent are different things, so a rate moving from 4% to 5% has risen by one percentage point and by 25%, and using the wrong one changes a statement's meaning entirely. Say which you mean. The base is the other ambiguity, since a discount of 20% then a tax of 10% applies the tax to the discounted figure, and reversing the order gives a different total.
Before you quote
- Be clear which number is the base.
- Distinguish percentage points from percent.
- Note that chained percentages depend on their order.
Questions
About this calculator
What is the difference between a percent and a percentage point?
A rate moving from 4% to 5% has risen by one percentage point and by 25%. Both are correct and they mean different things, so using the wrong one changes a statement's meaning entirely rather than slightly.
Does the order of percentages matter?
Yes. A 20% discount then 10% tax applies the tax to the discounted figure; reversing the order gives a different total. Each percentage applies to whatever the running figure is at that point, not to the original.
How do I find what percentage one number is of another?
Divide the part by the whole and multiply by a hundred. The common error is dividing the wrong way round, which is why identifying which number is the base before calculating is worth the moment it takes.
The formula
part ÷ whole × 100 = percentage
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How to use this calculator
- First number (the part). Enter your own figure; the page starts at 25.
- Second number (the whole). Enter your own figure; the page starts at 200.
- Percentage (%). Used for the “X% of the whole” result below.
The result updates as you type, so you can try a figure, see what it does to first is this % of second, and change it back. Nothing you enter is sent anywhere or saved.
A worked example
These are the figures the calculator opens with. Every number in the results column below is produced by the same calculation the page runs, so you can follow it through before putting your own figures in.
What goes in
| Input | Value |
|---|---|
| First number (the part) | 25 |
| Second number (the whole) | 200 |
| Percentage | 15% |
What comes out
| Result | Value |
|---|---|
| First is this % of second main result | 12.50% |
| That % of the second number | 30 |
| Difference between the two | 175 |
| Percentage difference | 155.56% |
25 is 12.50% of 200, and 15% of 200 is 30.
How sensitive the answer is
Holding everything else steady and changing only first number (the part), this is what happens to first is this % of second. It is worth knowing which of your inputs the answer actually hinges on, and which barely move it.
| First number (the part) | First is this % of second |
|---|---|
| 12.5 | 6.25% |
| 18.75 | 9.38% |
| 25 example above | 12.50% |
| 37.5 | 18.75% |
| 50 | 25.00% |
Every other input is held at the example value while this one changes, which is not how a real job behaves. Treat it as a guide to which number matters most, not as five separate quotes.
What each figure means
- First number (the part)
- A number, starting at 25.
- Second number (the whole)
- A number, starting at 200.
- Percentage (%)
- Used for the “X% of the whole” result below.
What the results tell you
| Result | What it is |
|---|---|
| First is this % of second | The headline result. A percentage. |
| That % of the second number | A number. |
| Difference between the two | A number. |
| Percentage difference | A percentage. |
Keep going
Related calculators
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Open calculatorPercentage Decrease Calculator
Works a percentage decrease, where reversing it needs a different percentage.
Open calculatorDiscount Calculator
Works a discount and what it costs, where the margin effect is the real figure.
Open calculatorRunning a business, not just a calculation?
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