Percentage Calculator
Work out a percentage of a number, what percent one number is of another, or the percentage change between two values.
What this tool does
A percentage calculator answers the three questions people actually ask about percentages: what is X% of Y, what percent is X of Y, and by what percent did a value change. Enter the two numbers, choose the question, and the result and the calculation appear instantly.
Switches between three common percentage questions and shows the answer as you type, along with the calculation that produced it.
For a percentage change it also states whether the value rose or fell and by how much, so a result like -20% is never ambiguous.
How to use it
- Pick the question you are asking from the first list.
- Enter X and Y in the two boxes - the labels in the list tell you which is which.
- Read the result at the top and the working underneath.
- Change either number to see the answer update.
- Press Copy results to paste the working into a message or document.
Why use a percentage calculator
Offers three modes in one place - X% of Y, X as a percentage of Y, and percentage change - and writes the calculation out so you can check it by hand. Percentages are used constantly - discounts, tips, grades, interest, pay rises - and the most common errors come from using the wrong base number. Seeing the working lets you confirm that the right number is being divided or multiplied.
Why we built it
We built the percentage calculator with three modes in one place - X% of Y, X as a percentage of Y, and percentage change - and it writes the calculation out so you can follow it. For prices see the discount calculator, and for tax the VAT calculator.
If your task goes further, try the Colony Counter, the Final Grade Calculator and the Decimal to Fraction Calculator.
Who this tool is for
- Students doing percentage problems
- Shoppers and business owners working out changes
- Anyone checking a figure in a report
When to use it
- Checking a discount, mark-up or pay rise.
- Working out what share one figure is of a total, such as a score or a budget line.
- Finding the percentage change between last year and this year.
- Reversing a percentage when you know the result and want the original.
How it is calculated
X% of Y is Y × X ÷ 100. X as a percentage of Y is X ÷ Y × 100. Percentage change from X to Y is (Y − X) ÷ |X| × 100, using the starting value as the base.
Worked example: 15% of 200 is 200 × 15 ÷ 100 = 30. 50 as a percentage of 200 is 50 ÷ 200 × 100 = 25%. A rise from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%.
A percentage change is not symmetric: a 50% fall followed by a 50% rise does not return you to the start, because the second percentage is taken of a smaller number.
What you enter, and what you get back
| Item | Details |
|---|---|
| X | The first number: the percentage, the part, or the starting value, depending on the mode. |
| Y | The second number: the whole, or the end value. |
| Result | The answer, with the calculation written out. |
| Direction | For percentage change: increase, decrease or no change. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| Result looks too big or too small | X and Y are the wrong way round for the question. | Check the mode wording and swap the two boxes. |
| Change from zero is refused | A percentage change from 0 is undefined. | Use the amount of change instead. |
| Different answer to another calculator | It used the end value as the base for the change. | The standard method uses the starting value, as here. |
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| What do you want to work out? | X% of Y (what is 15% of 200?) |
| X | 15 |
| Y | 200 |
With those inputs, the calculator returns:
- 15.00% of 200.00: 30
- Calculation: 15.00 ÷ 100 × 200.00
- Y plus X%: 230.00
- Y minus X%: 170.00
Assumptions and limitations
- Percentage change uses the starting value as the base, which is the standard convention.
- Very small or very large results are shown to a limited number of decimal places.
- It handles one calculation at a time, not chains of increases and decreases.
- Results are not rounded to any currency or unit.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example 15% of 200 is 200 × 15 ÷ 100 = 30.
How do I work out what percent one number is of another?
Divide the first number by the second and multiply by 100. 50 is 25% of 200 because 50 ÷ 200 × 100 = 25.
How do I calculate percentage increase or decrease?
Subtract the starting value from the end value, divide by the starting value, and multiply by 100. A positive result is an increase and a negative one is a decrease.
Why is a 50% rise after a 50% fall not back to the start?
The second percentage is taken of a smaller number. 100 falls to 50, then rises 50% of 50 to reach 75, not 100.
Can I use decimals and negative numbers?
Yes. Decimals work as normal, and a negative starting value is measured against its absolute size.