Percentage and percentage change calculator
X% of V = (X/100) × V
Five percentage calculations in one tool: X% of a value, what percentage a value represents of another, increasing or decreasing a value by X%, the percentage variation between an old and a new value, and finding the original value after a known increase or decrease.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasX% of V = (X/100) × V
X% of V = (X/100) × V
A is (A/B) × 100% of B
new value = V × (1 + X/100)
percentage change = ((new − old) / old) × 100
original value = current value / (1 + X/100)
One idea behind all five formulas: a percentage is a ratio multiplied by 100. Increasing, decreasing. Adding or removing a percentage are mathematically the same operation, a signed percentage (positive to increase, negative to decrease) applied to the factor (1 + X/100).
- 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. Never the new one.
- Finding the original value
- · the reverse of an increase or decrease: divide by (1 + X/100), never subtract X% from the current value.
Validity domainA percentage change is undefined when the old value is zero (division by zero): the result would depend on a comparison base that doesn't exist.
A percentage change is undefined when the old value is zero (division by zero): the result would depend on a comparison base that doesn't exist. Likewise, recovering the original value after a 100% decrease is impossible: any starting value gives 0 after a 100% decrease, so the reverse operation is undetermined.
Common pitfall: two opposite changes don't cancel outIncreasing a value by 20% and then decreasing it by 20% does not return to the starting value: 100 → 120 (+20%) → 96 (−20% of 120, not of 100).
Increasing a value by 20% and then decreasing it by 20% does not return to the starting value: 100 → 120 (+20%) → 96 (−20% of 120, not of 100). The decrease acts on a larger base than the original increase, so its absolute effect is larger. That asymmetry is exactly what separates "decrease by X%" from "find the value before a X% increase". Two different operations, not the same one.