Finance

Percentage Calculator

Calculate percentages instantly: X% of Y, what percentage a value represents, the change between two figures, or apply an increase/discount.

Percentages are one of the most widely used mathematical tools in everyday life: calculating VAT on a price, the discount in a sale, an annual pay rise or the change in a stock index. Despite being a basic concept, their practical application often causes confusion, especially when dealing with compound percentages or relative changes.

This calculator solves the four most common cases: calculating X% of a number, finding what percentage A represents of B, calculating the percentage change between two values, and applying an increase or discount to a base price. Select the type of operation and you will get the result instantly.

What do you want to calculate?

Percentage (X)

Amount (Y)

Results are mathematically exact. In tax or financial contexts, always verify amounts with your adviser.

How percentages are calculated

A percentage expresses a proportion out of a total of 100. Calculating 'X% of Y' means dividing the percentage by 100 and multiplying it by the amount: result = (X / 100) × Y. It is the operation behind discounts, taxes, commissions and tips.

This calculator covers the four most common calculations: X% of an amount, what percentage a value represents of a total, the percentage change between two figures, and applying an increase or discount. Choose the mode you need and the formula is applied automatically.

Example

20% of 150 is (20 / 100) × 150 = 30. And if a €60 shirt has a 15% discount, the saving is (15 / 100) × 60 = €9, so the final price is €51.

Percentage points versus percentage

This is a distinction constantly confused in the press and in conversation, and it completely changes the meaning of a figure. If an interest rate goes from 2% to 3%, it has risen one percentage point, but in relative terms it has increased by 50%, because 1 is half of 2. Likewise, if unemployment falls from 12% to 9%, it has dropped 3 percentage points or, equivalently, 25% in relative terms. When comparing quantities already expressed as percentages, always state whether you mean points or relative change, because both readings are correct but convey very different messages.

Worked example

To calculate 15% of €240: multiply 240 × 0.15 = €36. To find what percentage 36 represents of 240, do the inverse operation: (36 / 240) × 100 = 15%. And to calculate the change between two values, for instance a price going from €240 to €288, apply ((288 − 240) / 240) × 100 = (48 / 240) × 100 = a 20% rise. Note that the denominator is always the starting value, never the final one: using the final value is the most frequent error when calculating percentage changes.

Common discounts applied to €100

Discount	Final price
10%	90,00 €
20%	80,00 €
25%	75,00 €
30% + extra 20%	56,00 €
50%	50,00 €
70%	30,00 €

Common mistakes when working with percentages

Beyond the arithmetic, three common traps are worth watching. The first is chaining discounts as if they added up: 30% plus an additional 20% is not 50% but 44%, because the second applies to the already reduced price. The second is confusing the percentage of a quantity with the percentage that quantity represents: these are inverse operations and give different results. The third is forgetting the reference base when communicating a change: saying something has risen 200% means it has tripled, not doubled, because the increase is added to the original value.

Frequently asked questions

Divide the percentage by 100 and multiply by the amount. For example, 20% of 150 is (20 / 100) × 150 = 30. This operation is the basis of commercial discounts: if a shirt costs €60 and there is a 15% discount, the saving is (15 / 100) × 60 = €9 and the final price is €51.

Subtract the initial value from the final, divide by the initial value and multiply by 100: ((final − initial) / initial) × 100. If a product went from €200 to €250, the change is ((250 − 200) / 200) × 100 = 25%. A negative result indicates a decrease. This formula is used in finance to calculate returns, CPI and price variations.

Use 'X% of Y' to apply discounts, taxes (VAT, income tax) or commissions. Use 'X is what % of Y' when you need to know what proportion a value represents of a total, such as the error rate in a process or the percentage of correct answers in a test. Use '% change' to compare two figures over time, such as sales growth or inflation.

Because each percentage is applied to a different base. If a product costs €100 and rises by 20%, it becomes €120. Applying a 20% discount afterwards, that reduction is calculated on €120 and not on the initial €100: 120 − 24 = €96. The result is 4% below the starting price. The general rule is that an x% rise followed by an x% fall always leaves a final price below the original, and the loss equals x²/100 per cent. This effect explains many commercial offers that appear to return the initial price but do not.

You have to divide, not subtract. A very common mistake is subtracting 21% from the VAT-inclusive price, which gives an incorrect result. The correct operation is to divide by 1.21: if a product costs €121 including VAT, the taxable base is 121 / 1.21 = €100, and VAT is the remaining €21. If you subtracted 21% from €121 you would get €95.59, almost five euros below the real value. The same logic applies to any tax rate: for the reduced 10% VAT you divide by 1.10 and for the super-reduced 4% by 1.04.