Percentage Calculator
Five different questions get called a percentage calculation, and they use different formulas. This tool covers all of them: a percentage of a number, what percentage one number is of another, percentage change between two values, and adding or subtracting a percentage.
Formula
Percentage change = (new − old) ÷ old × 100
- X% of Y = Y × X ÷ 100
- X as a % of Y = X ÷ Y × 100
40 to 50: (50 − 40) ÷ 40 × 100 = 25% increase
Percentage Change
The formula works for both directions. A positive answer is an increase, a negative one a decrease:
Percentage Change = ((New − Old) ÷ Old) × 100
A salary rising from £28,000 to £29,540 is (1,540 ÷ 28,000) × 100 = a 5.5% increase.
The critical detail is the denominator: always divide by the original value, never the new one.
The Other Two Questions
A percentage of a number: (percentage ÷ 100) × number.
18% of 250 = 0.18 × 250 = 45.
What percentage one number is of another: (part ÷ whole) × 100.
35 out of 140 = 35 ÷ 140 = 25%.
Why Percentages Do Not Cancel Out
Add 50% to £100 and you have £150. Take 50% off that and you land on £75, not £100. The rise was calculated on the smaller figure and the fall on the larger one.
To reverse an increase you always need a smaller percentage decrease: undoing +50% takes −33.3%, and undoing +100% takes −50%.
Quick Reference
| Increase | Decrease needed to return to start |
|---|---|
| 10% | 9.09% |
| 25% | 20% |
| 50% | 33.3% |
| 100% | 50% |
| 200% | 66.7% |
Frequently Asked Questions
- How do I calculate percentage increase?
- Subtract the old value from the new one, divide by the old value, then multiply by 100. Dividing by the new value instead is the most common error.
- What is the difference between a percentage and a percentage point?
- If a rate moves from 2% to 3%, that is a rise of 1 percentage point but a 50% relative increase. Use "percentage points" when the underlying figure is itself a percentage.
- How do I work backwards from a sale price?
- Divide rather than add. An item costing £48 after 20% off was £48 ÷ 0.80 = £60. Adding 20% back to £48 gives the wrong answer.
- How do I turn a decimal percentage into minutes or pence?
- Multiply the part after the decimal point by the number of units. 5.5% of an hour is 0.5 × 60 = 30 minutes, not 50.