Case 1
- Original value
- 100
- New value
- 125
25.00%
Open with these valuesPercentage Change Calculator
25.00%
Result: 25.00 %Subtract the original value from the new one, divide by the original, multiply by 100. A rise is positive, a fall is negative: 200 down to 150 is −25 %. From an original of zero there is no answer, because every rise would be infinitely large.
The numbers at a glance
Held fixed: Original value 100.0000.
| New value | Result (%) |
|---|---|
| 0.0000 | -100.00 |
| 50.0000 | -50.00 |
| 100.0000 | 0.00 |
| 125.0000Your value | 25.00 |
| 150.0000 | 50.00 |
| 200.0000 | 100.00 |
| 250.0000 | 150.00 |
Worked examples
Case 2
- Original value
- 200
- New value
- 150
-25.00%
Open with these valuesCase 3
- Original value
- 12.5
- New value
- 15
20.00%
Open with these valuesHow it's calculated
Change = (new − old) ÷ old × 100
- StepEnter the value you started from — the earlier one.
- StepEnter the value you ended up with.
- ResultRead the change: positive is a rise, negative is a fall.
What this number means
The denominator is the value you started from
A percentage change divides by the original value, never by the new one and never by the average of the two. That is why the direction of the comparison is part of the answer.
Swapping the two values changes the answer
From 100 to 125 is +25 %, but from 125 to 100 is −20 %. The gap is 25 either way; only the value in the denominator differs.
An original of zero has no percentage
The formula divides by the original value, so from 0 there is nothing to divide by and the page shows no result. Compare the plain difference instead.
Negative values keep their sign in the denominator
From −100 to −50 the absolute change is +50, but the percentage change is −50 %, because the division runs through −100. Taking the size of the original value instead would lose the sign.
Commonly misread
A fall of 50 % and a later rise of 50 % bring you back to where you started.
100 dropping 50 % gives 50, and 50 rising 50 % gives 75. Each percentage is taken from a different base, so they do not cancel out.
Percentage change and percentage difference are two names for one measure.
Change needs a before and an after and divides by the original value. Difference has no direction and divides by the average of the two values.
It makes no difference which of the two values goes in the first field.
The first field holds the value you started from. Enter 125 there and 100 second, and +25 % turns into −20 %.
A change from −100 to −50 goes upwards, so the result has to be positive.
The original value stays in the denominator with its own sign, which makes the result −50 %.
Reference table
| Old, new | Direction | Change (%) |
|---|---|---|
| 50, 75 | Rise | 50 |
| 100, 125 | Rise | 25 |
| 12.5, 15 | Rise | 20 |
| 80, 80 | No change | 0 |
| 200, 150 | Fall | -25 |
| -100, -50 | Fall | -50 |
| 100, 0 | Fall to zero | -100 |
Questions
How do I calculate percentage change?
Subtract the original value from the new value, divide by the original value, and multiply by 100. From 100 to 125 that is (125 − 100) ÷ 100 × 100 = 25 %.
What is the difference between a percentage increase and a decrease?
They use the same formula — the sign of the result tells them apart. A positive percentage is a rise, a negative one a fall. From 200 to 150 is −25 %, a decrease.
Why can I not calculate a percentage change from zero?
The formula divides by the original value, and dividing by zero is undefined. Starting from 0, any increase is infinitely large in percentage terms, so no percentage exists. Compare the plain difference instead.
What is the difference between percentage change and percentage difference?
Percentage change has a clear before and after, and divides by the original value. Percentage difference compares two values with no direction, dividing by their average. Use change when one of the two values came first.
Does a 50 % drop followed by a 50 % rise return to the start?
No. 100 dropping 50 % gives 50, and 50 rising 50 % gives 75. Each percentage is taken from a different base, so percentage changes do not cancel out.
Sources and last check
Information, not professional advice.