Percentage and percentage change calculator
Percentage of a value, ratio, increase or decrease, variation between two values, or the original value recovered.
Result
Awaiting the quantities required for the calculation.
Calculation, assumptions and sources
OverviewFive percentage calculations: X% of a value, the percentage one value represents of another, an increase or decrease by X%, the percentage change between an old and a new value, and the original value before a known increase or decrease.
Five percentage calculations: X% of a value, the percentage one value represents of another, an increase or decrease by X%, the percentage change between an old and a new value, and the original value before a known increase or decrease.
Method & formulasX% of V = (X/100) × V
A percentage is a ratio multiplied by 100. An increase or decrease by X% multiplies the value by (1 + X/100), X being positive for an increase, negative for a decrease.
- Ratio
- the proportion a value represents of another, expressed as a percentage.
- Percentage change
- the relative gap between an old and a new value, measured against the old value.
- Finding the original value
- the reverse of an increase or decrease: divide by (1 + X/100).
Validity domainThe percentage change is undefined for a zero old value.
The percentage change is undefined for a zero old value. After a 100% decrease, the original value is undetermined: any starting value gives 0.
Successive changesA 20% increase followed by a 20% decrease gives 100 → 120 → 96: the decrease acts on 120.
A 20% increase followed by a 20% decrease gives 100 → 120 → 96: the decrease acts on 120. This asymmetry separates "decrease by X%" from "find the value before an X% increase".