How to use the Percentage Calculator
- Find the box that matches your question, such as What is X% of Y? or Percentage change.
- Type your numbers into that box. The sample values show how each sentence reads.
- Read the answer as you type, with the formula and working shown underneath.
- For increases, decreases and reverse percentages, use the switch to pick the direction.
Features
- Six percentage calculators on one page
- Answers update instantly as you type
- Shows the formula and working for every result
- Reverse percentages to find the value before a change
- Percentage change and symmetric percentage difference
- Handles decimals, negatives and very large numbers
Percentage formulas at a glance
"Percent" means "per hundred", so 15% is 15 ÷ 100 = 0.15. Every calculator on this page is built on that idea.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × X ÷ 100 | 15% of 200 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 is 15% of 200 |
| % change from X to Y | (Y − X) ÷ |X| × 100 | 50 → 75 is +50% |
| Increase X by P% | X × (1 + P ÷ 100) | 200 + 15% = 230 |
| Decrease X by P% | X × (1 − P ÷ 100) | 200 − 15% = 170 |
| Original before a P% increase | Result ÷ (1 + P ÷ 100) | 230 ÷ 1.15 = 200 |
| % difference between X and Y | |X − Y| ÷ average × 100 | 40 and 60 differ by 40% |
Percentage change vs percentage difference
Percentage change has a direction: it compares a new value with an old one, and the old value is the base. Going from 50 to 75 is a 50% increase, but going back from 75 to 50 is a 33.3% decrease, because the base is now 75.
Percentage difference has no direction. It compares two values on equal terms, such as the same item's price in two shops, by dividing the gap by their average. 40 and 60 differ by 20 and average 50, so the percentage difference is 40% whichever order you enter them in.
Reverse percentages: finding the original
A common mistake is undoing an increase by subtracting the same percentage. If a price rose 15% to $230, the original was not $230 − 15% = $195.50. The 15% was taken from the original price, so divide instead: $230 ÷ 1.15 = $200. The same idea removes sales tax from a total or finds the price before a discount: a jacket that costs $68 after 15% off was $68 ÷ 0.85 = $80. For shopping maths, the Discount Calculator and Sales Tax Calculator do this for you.
Percent vs percentage points
When an interest rate rises from 4% to 5%, it has gone up by one percentage point, but by 25% in relative terms (1 ÷ 4 × 100). News reports and loan offers mix these up often, so check which one is meant before comparing numbers.
Why +10% then −10% is not zero
Raising 100 by 10% gives 110. Cutting 110 by 10% removes 11, leaving 99. Successive percentage changes multiply rather than add: 1.10 × 0.90 = 0.99, a net 1% fall. To combine changes, multiply their factors and convert back: a 20% rise followed by a 5% rise is 1.20 × 1.05 = 1.26, a 26% increase in total.
Quick mental tricks
- 10% of a number: move the decimal point one place left (10% of 240 is 24). 5% is half of that, and 1% is one more place left.
- Percentages can be flipped: 8% of 50 equals 50% of 8, which is 4.
- To add a percentage in one step, multiply by 1 plus the rate: adding 7% is the same as multiplying by 1.07.
Working with a whole list of numbers? The Statistics Calculator finds averages and spread.
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 a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. Going from 50 to 75 is (75 − 50) ÷ 50 × 100 = 50%.
What is the difference between percentage change and percentage difference?
Percentage change measures a move from an old value to a new one and uses the old value as the base. Percentage difference compares two values without a direction and divides by their average.
How do I reverse a percentage?
Divide by the change factor instead of subtracting. A value that is 230 after a 15% increase was 230 ÷ 1.15 = 200; a value that is 68 after a 15% decrease was 68 ÷ 0.85 = 80.
Can a percentage be more than 100%?
Yes. 300 is 150% of 200, and a price that triples has risen by 200%. Only a decrease is limited, because nothing can fall by more than 100% of itself and stay positive.