All percentage formulas at a glance
What a percentage is
A percentage is a dimensionless number expressing a ratio relative to 100. It is written with the percent symbol %. The number 25% means 25 per hundred, which equals the decimal 0,25 and the fraction 1/4. These three representations — percentage, decimal, and fraction — are interchangeable and represent the same proportion.
To convert a percentage to a decimal, divide by 100: 37% = 0,37. To convert a decimal to a percentage, multiply by 100: 0,08 = 8%. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100: 3/8 = 0,375 = 37,5%.
Percentages allow quantities of different scales to be compared on a common basis. A company reporting a 15% profit margin and another reporting a 23% profit margin can be directly compared regardless of their absolute revenue sizes. This standardisation is why percentages appear in almost every quantitative field.
Finding a percentage of a number
Worked examples — every type of percentage calculation
(15 / 100) x 240 = 0,15 x 240 = 36. Practical uses: calculating 21% VAT on a 240 price gives 0,21 x 240 = 50,40. Calculating a 15% service charge on a 240 restaurant bill gives 36.
Percentage increase = (new - old) / old x 100 = (2.300 - 2.000) / 2.000 x 100 = 300 / 2.000 x 100 = 15%. The denominator is always the original (old) value. Dividing by the new value instead would give 300 / 2.300 x 100 = 13%, which is wrong.
Percentage decrease = (old - new) / old x 100 = (80 - 60) / 80 x 100 = 20 / 80 x 100 = 25%. The denominator is still the original (old) value. Note that a 25% decrease followed by a 25% increase does not return to the original: 80 x 0,75 = 60, then 60 x 1,25 = 75, not 80. Percentage changes are not symmetric.
After a 20% discount, the price represents 80% of the original. So: original = 160 / 0,80 = 200. The most common error is to add 20% back to the sale price: 160 x 1,20 = 192. This gives the wrong answer because 20% of 160 is not the same amount as 20% of 200. The reverse percentage formula divides by (1 - discount rate) for a discount, or (1 + increase rate) for an increase.
Percentage = (part / whole) x 100 = (38 / 50) x 100 = 0,76 x 100 = 76%. This formula answers the question 'what percentage is X of Y?' It is used for pass rates, market share, survey results, and any ratio expressed as a percentage.
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Calculate percentage of a number, percentage change, percentage difference, and reverse percentages with full step-by-step working.
Common percentage to decimal and fraction conversions
| Percentage | Decimal | Fraction | Quick mental method |
|---|---|---|---|
| 1% | 0,01 | 1/100 | Divide by 100 |
| 5% | 0,05 | 1/20 | Divide by 20 |
| 10% | 0,10 | 1/10 | Divide by 10 |
| 12,5% | 0,125 | 1/8 | Divide by 8 |
| 20% | 0,20 | 1/5 | Divide by 5 |
| 25% | 0,25 | 1/4 | Divide by 4 |
| 33,3% | 0,333 | 1/3 | Divide by 3 |
| 50% | 0,50 | 1/2 | Divide by 2 |
| 75% | 0,75 | 3/4 | Multiply by 3, divide by 4 |
| 100% | 1,00 | 1/1 | The full number unchanged |
Percentage points vs percentages — a critical distinction
A percentage point is an absolute difference between two percentages. A percentage is a relative change. These are not the same, and confusing them is a common error in financial and political reporting.
Example: a central bank raises the interest rate from 2% to 3%. This is a 1 percentage point increase. But it is a 50% increase in the interest rate itself, because (3 - 2) / 2 x 100 = 50%.
A party's vote share rising from 20% to 25% is a 5 percentage point increase. Saying it is a 5% increase is incorrect — the correct statement is a 25% increase in vote share (5 / 20 x 100 = 25%).
In finance: if a fund's annual return falls from 8% to 6%, it falls by 2 percentage points but by 25% in relative terms (2 / 8 x 100 = 25%). Both descriptions are technically correct but mean very different things. Always specify which type of change is being described.
VAT and tax percentage calculations
VAT calculations require understanding the difference between adding tax to a pre-tax price and extracting tax from a tax-inclusive price.
Adding VAT: multiply the pre-tax price by (1 + VAT rate). At 21% VAT: 100 x 1,21 = 121 including VAT.
Extracting VAT from an inclusive price: the VAT element is not 21% of the inclusive price. It is calculated as: VAT = inclusive price x (VAT rate / (100 + VAT rate)). At 21% VAT: VAT = 121 x (21 / 121) = 121 x 0,1736 = 21. The net price is 121 - 21 = 100.
The most common error is calculating 21% of the inclusive price: 21% of 121 = 25,41, which is wrong. The correct method uses the fraction 21/121, not 21/100, to extract VAT from an inclusive price.
Common mistakes
Methodology
All percentage formulas in this guide follow standard mathematical conventions. Percentage change always uses the original value as the denominator. Reverse percentage uses division by the decimal multiplier. VAT extraction uses the fraction method (rate / (100 + rate)) rather than simple percentage of the inclusive price.
These are universal mathematical definitions. There is no regional variation in how percentages are calculated, though VAT rates and tax rules vary by country.
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Frequently asked questions
Formula based on standard mathematical and financial methods. Results are for informational purposes. Last reviewed May 2026. Version 3.