Percentage Calculator
Percentage Calculator
The three everyday percentage questions — X% of Y, X as a percentage of Y, and the percentage change from one number to another — plus the one people most often get wrong: the price before a percentage was added.
Percentage
What is 18% of 2,500?
Four percentage questions
- X
- the percentage, the part, or the starting value, depending on the question
- Y
- the whole, the new value, or the amount after the increase
- % change
- measured on the starting value; with a negative start the page divides by its size, |X|
- percentage points
- the plain difference between two percentages: 8% to 10% is 2 percentage points, and a 25% rise
Worked example
What is 18% of 2,500?
18 × 2,500 ÷ 100 = 450
So 2,500 plus 18% is 2,500 + 450 = 2,950
Going back: 2,950 ÷ 1.18 = 2,500 — not 2,950 − 18% = 2,419
The change from 2,950 back to 2,500 is −15.25%, not −18%
One pair of numbers, five questions
| Question | Working | Answer |
|---|---|---|
| 18% of 2,500 | 18 × 2,500 ÷ 100 | 450 |
| 450 is what % of 2,500 | 450 ÷ 2,500 × 100 | 18% |
| From 2,500 to 2,950 | (2,950 − 2,500) ÷ 2,500 × 100 | +18% |
| From 2,950 to 2,500 | (2,500 − 2,950) ÷ 2,950 × 100 | −15.25% |
| 2,950 after 18% was added | 2,950 ÷ 1.18 | 2,500 |
Every percentage is a percentage of something
A percentage is a fraction with 100 underneath, so every percentage question comes down to one thing: of what? 18% of 2,500 is 450. The percentage change from 2,500 to 2,950 is +18%, measured on 2,500, where you started. But the change from 2,950 back to 2,500 is −15.25%, because now the starting point is the bigger number. That is also why a price that rises 20% and then falls 20% ends lower than it began: 100 becomes 120 and then 96.
The most common mistake runs the other way. A bill or a price tag shows an amount after a percentage was added — tax, a markup, a hike — and you want the amount before it. 2,950 after 18% was added was 2,950 ÷ 1.18 = 2,500. Taking 18% off 2,950 gives 2,419, which is 81 too little, because the 18% was worked out on the smaller, original amount, not on the total. Choose the last question in the calculator to do it the right way. The same division takes a tax out of a tax-inclusive price (the GST calculator does it for GST) and undoes a discount (the discount calculator).
When the two numbers are themselves percentages, there are two ways to describe the change and they are easily confused. An interest rate that goes from 8% to 10% has risen by 2 percentage points — the plain difference — and by 25% relative to where it was. Both are correct; they answer different questions. News reports and loan offers sometimes use whichever sounds bigger or smaller, so check which one is meant. The same care applies to a salary rise (the salary hike calculator) or to a markup against a margin (the markup calculator): each is a percentage of a different base.
A change from zero has no percentage, because nothing can be divided by zero; the calculator then shows no answer. With a negative starting value the page divides by its size, so a move from −50 to −25 reads as a 50% increase — towards zero. This is arithmetic on the figures you enter, not financial advice.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. 18% of 2,500 is 18 × 2,500 ÷ 100 = 450.
How do I find the price before tax or a percentage was added?
Divide by (1 + the percentage ÷ 100). A price of 2,950 after 18% was added was 2,950 ÷ 1.18 = 2,500. Subtracting 18% of 2,950 gives 2,419, which is wrong.
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages. A rate that moves from 8% to 10% rises by 2 percentage points, which is a 25% increase on the old rate.
Why doesn’t a 20% rise followed by a 20% fall bring me back?
Because the fall is 20% of a bigger number. 100 rises to 120, and 20% off 120 is 24, leaving 96.
Related calculators
References
- Eurostat. Statistics Explained, Glossary: Percentage point — “used when comparing two different percentages … A rate was 10% and it increased to 12%, then it increased by 2 percentage points.”
- National Council of Educational Research and Training (NCERT). Mathematics: Textbook for Class VIII, chapter “Comparing Quantities”: percentages, and percentage increase and decrease, measured on the original amount.