Free tool · Math
Percentage Change Calculator
Enter an old value and a new value to see the percentage increase or decrease, with the working shown.
Change from 80 to 100?
+25%
80 → 100 is an increase of 25%
How to use this percentage change calculator
- Enter the old (starting) value — the amount before the change.
- Enter the new (ending) value — the amount after the change.
- Read the percentage change. A positive number is an increase; a negative number is a decrease. The answer updates as you type.
- Check the step-by-step working under the result to see exactly how the answer was reached.
The percentage change formula
Percentage change = ((New − Old) ÷ Old) × 100
A positive result is an increase; a negative result is a decrease. The old value is the base of the calculation, which is why direction matters: the same jump of 20 is a bigger share of 80 than of 100.
Worked example — a price rises from $80 to $100
- Subtract the old value from the new value: 100 − 80 = 20.
- Divide by the old value: 20 ÷ 80 = 0.25.
- Multiply by 100: 0.25 × 100 = +25%.
Worked example — a price falls from $100 to $80
- Subtract the old value from the new value: 80 − 100 = −20.
- Divide by the old value: −20 ÷ 100 = −0.20.
- Multiply by 100: −0.20 × 100 = −20%.
Notice the two answers are not mirror images: rising from 80 to 100 is +25%, falling back from 100 to 80 is −20%. The change is the same 20 in both directions, but the base — the old value — is different.
Examples
| Old value | New value | Percentage change |
|---|---|---|
| $80 | $100 | +25% |
| $100 | $80 | −20% |
| $3,000 | $3,450 | +15% |
| 90 kg | 81 kg | −10% |
Frequently asked questions
What does a negative percentage change mean?
It means the value went down. Going from $100 to $80 is −20%, because the new value is lower than the old one.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. Going from $80 to $100: (100 − 80) ÷ 80 × 100 = +25%.
How do I calculate a percentage decrease?
Use the same formula — the result comes out negative when the value fell. Going from $100 to $80: (80 − 100) ÷ 100 × 100 = −20%.
Why does going from 80 to 100 give +25%, but 100 to 80 gives −20%?
Because the starting value is the base. Rising from 80 to 100 is a gain of 20 on a base of 80, which is 25%. Falling from 100 to 80 is a loss of 20 on a base of 100, which is 20%. The same 20 is worth more against the smaller base.
Is percentage change the same as percentage difference?
No. Percentage change is directional: it measures movement from an old value to a new one. Percentage difference compares two values as equals, using their average, so order does not matter. When neither value is a clear “before”, use the Percentage Difference Calculator.
Can percentage change be more than 100%?
Yes — whenever the new value is more than double the old one. The formula has no upper limit; it simply measures the increase relative to the starting value.