Percentage Change Calculator
Going from 40 to 50 is a 25% increase, but going from 50 back to 40 is only a 20% decrease. This percentage change calculator finds the change between an old value and a new value using ((new - old) / old) x 100. The direction matters, which is why the same 10-point gap gives two different percentages.
Quick answer
Percentage change measures how much a value grew or shrank relative to where it started.
Percentage change
25% increase
Difference
10
Direction
increase
What this tells you
- •Percentage change measures how much a value grew or shrank relative to where it started.
- •The formula is ((new - old) / old) x 100. The starting value is always the base.
- •A positive result is an increase, a negative result is a decrease.
- •Because the base changes, a 25% rise followed by a 25% fall does not bring you back to the start.
How to Use
- 1Enter the original (old) value.
- 2Enter the new value.
- 3Read the percentage change, labeled as an increase or decrease.
- 4The raw difference between the two numbers is shown below the main result.
How It Works
Formula
percentage change = ((new - old) / |old|) x 100Subtract the old value from the new value, divide by the old value, and multiply by 100. From 40 to 50 the difference is 10, divided by the base 40 gives 0.25, so the change is a 25% increase. From 50 to 40 the difference is -10 against a base of 50, a 20% decrease. When the old value is negative, dividing by its absolute value keeps the increase and decrease labels pointing the right way.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Price rises from $40 to $50
The $10 rise is a quarter of the $40 starting price.
Traffic drops from 12,000 to 9,000 visits
The 3,000-visit fall is 25 percent of the 12,000 starting point.
Salary grows from $65,000 to $70,200
The $5,200 raise divided by the $65,000 base is 0.08.
Percentage Change Quick Reference
Common old-to-new pairs and the resulting change.
| Old value | New value | Change |
|---|---|---|
| 100 | 125 | +25% |
| 100 | 75 | -25% |
| 50 | 75 | +50% |
| 80 | 100 | +25% |
| 200 | 150 | -25% |
| 25 | 100 | +300% |
Common mistakes
- Dividing by the new value instead of the old one. The starting value is always the base, which is why 40 to 50 is +25% but 50 to 40 is -20%.
- Confusing percentage change with percentage points. A rate moving from 10% to 12% is a 2 point rise but a 20% relative increase.
- Expecting changes to cancel. A 50% drop needs a 100% gain to recover, because the base shrank.