📈 Percentage Change Calculator
Work out the percent increase or decrease between two numbers, the symmetric percentage difference, or what a value becomes after a percentage change.
Quick answer: Percentage change = (new − old) ÷ |old| × 100, so going from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase, while the symmetric percentage difference between 80 and 100 is 22.22%.
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Percentage Change Calculator inputs
Result
Percentage change from 80 to 100
+25%
A 25% increase
- Absolute change
- +20
- Multiplier (new ÷ old)
- 1.25×
- Percentage difference
- 22.22%
| Old value | 80 |
| New value | 100 |
| Change | +20 |
| Percentage change | +25% |
Step by step
- Change: new − old = 100 − 80 = 20
- Divide by the old value: 20 ÷ |80| = 0.25
- Multiply by 100: 0.25 × 100 = +25%
- Positive, so it is a 25% increase
80 increased and decreased by common percentages
| Change | Increase | Decrease |
|---|---|---|
| 1% | 80.8 | 79.2 |
| 5% | 84 | 76 |
| 10% | 88 | 72 |
| 15% | 92 | 68 |
| 20% | 96 | 64 |
| 25% | 100 | 60 |
| 50% | 120 | 40 |
| 75% | 140 | 20 |
| 100% | 160 | 0 |
How to calculate percentage change
Subtract the old value from the new one, divide by the old value and multiply by 100. A positive answer is an increase and a negative answer is a decrease.
% change = (New − Old) ÷ |Old| × 100
Example: a price rises from 80 to 100. The change is 20, and 20 ÷ 80 × 100 = 25% increase. Going the other way, from 100 to 80, is a 20% decrease – the base is different.
Percentage difference
When neither number is the “before” value – two measurements, two shops’ prices – use the percentage difference, which divides by the average:
% difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
For 80 and 100: 20 ÷ 90 × 100 = 22.22%.
Applying and reversing a percentage
| Question | Formula | Example |
|---|---|---|
| Increase X by P% | X × (1 + P/100) | 80 + 25% = 100 |
| Decrease X by P% | X × (1 − P/100) | 100 − 20% = 80 |
| Original before a P% increase | Final ÷ (1 + P/100) | 120 ÷ 1.2 = 100 |
| Original before a P% decrease | Final ÷ (1 − P/100) | 80 ÷ 0.8 = 100 |
Common mistakes
- Dividing by the wrong value. Percentage change always divides by the starting value.
- Adding percentages in sequence. A 10% rise followed by another 10% rise is 21%, not 20%, because the second rise applies to a larger base.
- Confusing percent with percentage points. An interest rate moving from 4% to 5% is a 1 percentage-point rise but a 25% increase.
Frequently asked questions
What is the difference between percentage change and percentage difference?
Percentage change has a direction: it compares a new value with an old (reference) value and divides by the old one. Percentage difference compares two values on an equal footing and divides by their average, so 80 vs 100 and 100 vs 80 both give 22.22%.
Why isn’t a 20% decrease undone by a 20% increase?
Each percentage is taken of a different base. 100 decreased by 20% is 80, but 80 increased by 20% is only 96. To undo a 20% decrease you need a 25% increase (20 ÷ 80).
How do I find the original price before a percentage increase?
Divide the final value by the multiplier, not subtract the percentage. If a price is 120 after a 20% rise, the original is 120 ÷ 1.20 = 100 – not 120 − 24 = 96. Choose “Find the original value” above.
What if the old value is negative?
The calculator divides by the absolute value of the old number, so moving from −50 to −25 is reported as a +50% change (the value went up). Percentage change from exactly 0 is undefined.