Percentage Calculator
Three common percentage questions, answered instantly.
How to use the Percentage Calculator
Three modes in one place: find a percentage of a number, work out what percentage one number is of another, and calculate the change between two values.
How it works
A percentage is a ratio, not an amount. x% of y = y × x ÷ 100. A percentage change is (new − old) ÷ old × 100 — the denominator is always the original value, which is the single most common source of error when reading reports. Asymmetry follows: a 50 percent rise needs a 50 percent fall to undo it, but the reverse is not true.
When to use it
Use it to work out a discount, to read a growth or decline figure in the news correctly, and to convert between shares and percentages when splitting costs.
Worked example
Percentages behave asymmetrically:
| Movement | Net result |
|---|---|
| +20% then −20% | 0.96 × original (4% down) |
| −20% then +20% | 0.96 × original (same) |
| +50% then −50% | 0.75 × original (25% down) |
| −50% then +100% | 1.00 × original (break even) |
Assumptions and limitations
Check whether a reported figure is a percentage change or a percentage-point change: a rate moving from 2% to 3% is a one-point rise but a 50 percent relative increase. Small differences in very large samples can also be statistical noise rather than a real change.
Frequently Asked Questions
How do I calculate percentage change?
Subtract the old value from the new one, divide by the old value and multiply by 100. A positive result is an increase, negative is a decrease.
Is X% of Y the same as Y% of X?
Yes — multiplication is commutative, so 8% of 50 equals 50% of 8. It is a handy trick: 50% of any number is just half of it.
Can a percentage decrease exceed 100%?
No. A 100% decrease means the value reaches zero; there is nothing left to reduce. Percent increases, however, can exceed 100% without limit.
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