Percentage Change Calculator
Enter the old value and the new value. The calculator subtracts to find the change, divides it by the old value and multiplies by 100, giving the percentage increase or decrease.
Answer
Percentage increase
+25%
From 80 to 100 is a 25% increase, a change of +20.
- change in value
- +20
- new ÷ old
- 1.25
Check the work
Every line comes from the same calculation as the answer.
change = (new − old) ÷ |old| × 100
| change | 100 − 80 | 20 |
|---|---|---|
| percentage | 20 ÷ 80 × 100 | 25% |
How it works
Percentage change always compares against where you started. A price that goes from 80 to 100 has risen by 20, and 20 is 25% of the old price of 80. The same 20 measured against the new price would be 20%, which is why the direction matters.
A fall works the same way and comes out negative: from 100 to 80 is −20%. Notice that a 25% rise followed by a 20% fall returns to the starting value, because each percentage is taken from a different base.
Percentage change is not the same as a change in percentage points. If an interest rate moves from 2% to 3%, it has risen by one percentage point but by 50% in relative terms. The calculator gives the relative change; the difference line shows the change in the units you entered.
Formula
percentage change = (new − old) ÷ |old| × 100
The change is divided by the size of the starting value and expressed per hundred.
Worked examples
- Try these numbers
A price rising from 80 to 100
- The change is 100 − 80 = 20.
- 20 ÷ 80 = 0.25.
- 0.25 × 100 = 25%.
A 25% increase.
- Try these numbers
A score falling from 100 to 80
- The change is 80 − 100 = −20.
- −20 ÷ 100 = −0.2, which is −20%.
A 20% decrease.
- Try these numbers
A loss shrinking from −50 to −25
- The change is −25 − (−50) = 25.
- Divided by the size of the old value, 50: 25 ÷ 50 = 0.5.
A 50% improvement — the loss halved.
Inputs and results
- Old value
- The starting value the change is measured from.
- New value
- The value after the change.
- Change
- New value minus old value, in the units entered.
- Percentage change
- The change divided by the old value, times 100; negative for a decrease.
When to use it
- Comparing a price, a salary or a bill with what it was before.
- Reporting growth or decline in sales, visitors or a score between two periods.
- Checking a quoted rise or fall in a news story against the underlying numbers.
Common mistakes
- Dividing by the new value instead of the old one, which understates rises and overstates falls.
- Adding a percentage rise and fall and expecting them to cancel; +25% then −20% returns to the start, not +5%.
- Calling a change from 2% to 3% a 1% increase; it is one percentage point, or a 50% relative increase.
What it does not do
- It compares two values only; for growth over several periods, a compound rate is a different calculation.
- It is undefined when the old value is zero, because there is no base to compare against.
- It does not interpret whether a change is significant; small bases can produce very large percentages.
Method and assumptions
The change is the new value minus the old value. It is divided by the absolute value of the old value and multiplied by 100, so increases are positive and decreases negative whatever the sign of the starting value.
No rounding is applied before display; the shown percentage is shortened to two decimal places, with the exact figure in the working.
Assumptions
- The old value is the reference point.
- Both values are in the same unit.
Edge cases
- An old value of zero has no percentage change; the field is flagged instead of showing infinity.
- Equal values give a change of 0%.
- Crossing zero, such as from −10 to 10, gives 200%, which is correct but rarely meaningful.
Sources and corrections
This calculator uses an elementary formula, so it needs no outside data source. The method, the rounding rules and how a reported error is corrected are set out in the site standards.
Result looks wrong?
Send the inputs you used and the answer you expected. Every report is checked against the formula and its tests, and confirmed errors are corrected in public.