Step-by-step guide: How to Calculate Percentages: Formulas and Examples
How to use the Percentage Calculator
- Find the question that matches yours. Each section solves a different type of percentage problem.
- Type the two values into that section. Results appear as you type, with no button to press.
- Read the formula under each answer to see exactly how it was worked out.
- Values can include decimals and thousands separators, such as
1,250.5, and negative numbers where they make sense.
Example: the “reverse percentage” trap
A shop sells a jacket for 120 after a 20% price increase. What was the price before?
A common mistake is to take 20% off 120, giving 96. That is wrong, because the 20% was calculated on the old price, not the new one. The correct calculation uses the fifth section: 120 is 120% of the original, so
original = 120 ÷ 120 × 100 = 100
Check: 100 + 20% of 100 = 120. ✓
The formulas behind each answer
| Question | Formula |
|---|---|
| What is X% of Y? | Y × X ÷ 100 |
| X is what % of Y? | X ÷ Y × 100 |
| % change from X to Y | (Y − X) ÷ |X| × 100 |
| Increase Y by X% | Y × (1 + X ÷ 100) |
| Decrease Y by X% | Y × (1 − X ÷ 100) |
| X is Y% of what? | X ÷ Y × 100 |
Percentage change divides by the absolute value of the starting number, so a move from −50 to −25 is correctly reported as an increase of 50%. When the starting value is zero, percentage change is undefined, and the calculator says so instead of showing an infinite result.
Percentage points versus percent
When a rate itself changes, the difference can be described in two ways. If an interest rate rises from 4% to 5%, it has risen by 1 percentage point, but by 25 percent (because 1 is 25% of 4). News reports and financial documents sometimes blur the two, which can make changes look much larger or smaller than they are. The “percentage change” section gives the percent figure; the percentage-point figure is simply the difference.
When people use it
Checking a pay rise or a price increase, working out tips and tax, reading statistics in reports, calculating test scores, comparing sales figures month to month, and setting prices. For shop discounts with several reductions, the Discount Calculator handles stacked discounts and sales tax directly.
Limitations to keep in mind
- Results are rounded to six significant decimals for display; the underlying calculation uses full precision.
- Percentage change is undefined when the starting value is zero.
- For money, round the final answer according to your currency’s rules; intermediate values are not rounded.
How your data is handled
All calculations run in your browser. The numbers you enter are not sent or stored.
Frequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 50 to 65: (65 − 50) ÷ 50 × 100 = 30%.
Is a 50% increase followed by a 50% decrease back to the start?
No. 100 increased by 50% is 150; 150 decreased by 50% is 75. Each percentage applies to a different base, so equal increases and decreases do not cancel out.
How do I remove VAT or sales tax from a price?
Use the last section. If 120 includes 20% tax, 120 is 120% of the pre-tax price: 120 ÷ 120 × 100 = 100.
Can I enter negative numbers?
Yes, where they make sense — for example a change from a loss of −50 to a profit of 20. The calculator explains the result when signs are involved.