Calculate percentages, percentage change, percentage difference, increases, decreases and reverse percentages with clear working.
Choose a calculation
Result
Percentage formulas
| Calculation | Formula |
|---|---|
| X% of Y | Y × X ÷ 100 |
| X as a percentage of Y | X ÷ Y × 100 |
| Percentage change | (New − Original) ÷ Original × 100 |
| Percentage difference | |A − B| ÷ ((A + B) ÷ 2) × 100 |
| Increase by X% | Value × (1 + X ÷ 100) |
| Reverse an increase | Final value ÷ (1 + X ÷ 100) |
Percentage change versus percentage difference
Percentage change is directional and uses the original value as the denominator. Use it when a price, salary, population or measurement moves from an old value to a new value. Percentage difference treats both values equally and divides the absolute difference by their average, so it is useful when neither value is the starting point.
Reverse percentages
A reverse percentage finds the original value before an increase or decrease. If a £120 price already includes a 20% increase, the original was £120 ÷ 1.20 = £100. Subtracting 20% from £120 would give £96 and would be incorrect because the percentage bases are different.
Everyday examples
- 20% of £250 is £50.
- 45 out of 60 is 75%.
- A price rising from £80 to £100 is a 25% increase.
- Increasing £200 by 15% gives £230.
For UK VAT calculations, use our VAT Calculator UK.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply the result by the number.
How do I find what percentage one number is of another?
Divide the first number by the second and multiply by 100.
Can percentage change be negative?
Yes. A negative percentage change means the new value is lower than the original value.
What is the difference between percent and percentage points?
Percentage points are the direct difference between two percentage rates. Moving from 10% to 12% is 2 percentage points but a 20% relative increase.
Why can’t I reverse a rise by subtracting the same percentage?
The increase and decrease are calculated from different base values. Reverse calculations divide by the change multiplier.