# Percentage Calculator

> A percentage calculator handles the four questions that actually come up: what is X% of Y, X is what percent of Y, the percentage change between two numbers, and removing a percentage from a total. Each has a different formula and mixing them up is the usual source of error.

Source: https://rankcert.com/tools/percentage-calculator
Free, no signup. Updated: 2026-08-29

## How to use it

1. Choose which of the three questions you are asking.
2. Enter the two numbers.
3. Read the answer and the sentence that spells out what it means.

## The four percentage formulas

Nearly every percentage error is using one of these formulas where another was needed.

| Question | Formula | Worked example |
| --- | --- | --- |
| What is X% of Y? | Y x (X / 100) | 15% of 240 = 240 x 0.15 = 36 |
| X is what percent of Y? | (X / Y) x 100 | 36 of 240 = (36 / 240) x 100 = 15% |
| Percentage increase | (new - old) / old x 100 | 240 to 300 = 60 / 240 = 25% |
| Percentage decrease | (old - new) / old x 100 | 300 to 240 = 60 / 300 = 20% |
| Add a percentage | Y x (1 + rate) | 100 plus 20% VAT = 100 x 1.2 = 120 |
| Remove a percentage | Y / (1 + rate) | 120 minus 20% VAT = 120 / 1.2 = 100 |
| Reverse a discount | price / (1 - rate) | 56 after 30% off = 56 / 0.7 = 80 |
| Compound change | Y x (1 + rate)^n | 5% monthly for 12 months = 1.05^12 = +79.6% |

## Questions

### How do I calculate a percentage increase?

Subtract the old value from the new, divide by the old value, multiply by 100. Going from 40 to 50 is a 25% increase, because 10 divided by 40 is 0.25.

### Why is a 50% rise then a 50% fall not back to the start?

Because the second percentage applies to a larger base. 100 up 50% is 150; 150 down 50% is 75. Percentage changes do not cancel out.

### What is the difference between percent and percentage points?

Moving from 10% to 12% is a rise of 2 percentage points but a 20% increase. Confusing the two is the most common error in reporting statistics.

### How do I remove a percentage from a total?

Divide, do not subtract. To remove 20% VAT from 120, divide by 1.2 to get 100 - subtracting 20% gives 96, which is wrong.

### How do I calculate a discount?

Multiply by one minus the discount. 30% off 80 is 80 x 0.7 = 56. To find the original price from a discounted one, divide: 56 / 0.7 = 80.

### How do I work out VAT or sales tax?

To add 20%, multiply by 1.2. To remove it from a gross figure, divide by 1.2. Subtracting 20% from the gross gives the wrong answer.

### What is the formula for percentage change?

(new - old) / old x 100. Use the old value as the denominator; using the new one gives a different and usually wrong number.

### How do I calculate a percentage of a percentage?

Multiply the decimals. 20% of 50% is 0.2 x 0.5 = 0.1, which is 10% of the original.

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