Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Percentage change measures a move against where it started, and that choice makes rises and falls asymmetric. A value that goes from 80 to 100 rises 25 percent, but a fall from 100 back to 80 is only a 20 percent drop, because the base is now larger. That is why a 50 percent loss needs a 100 percent gain to recover. The absolute change, 20 here, is the same either way, and it is often the clearer number.
Before you rely on it
What to check
Say which value is the starting point before you quote a percent. A change reported against the wrong base can look bigger or smaller than it really is.
The common error
Where people go wrong with percentage change calculator
Adding and subtracting percentages as if they were the same size. A 20 percent rise followed by a 20 percent fall leaves you below where you began.
Sensitivity evidence
How original value changes the percentage change
| Original value | Percentage change | Absolute change |
|---|---|---|
| 64 | 56.3% | 36 |
| 72 | 38.9% | 28 |
| 80worked example | 25.0% | 20 |
| 88 | 13.6% | 12 |
| 96 | 4.2% | 4 |
Every input, tested
Which input moves the percentage change most
| Input | Tested from | To | Percentage change at each end | Swing |
|---|---|---|---|---|
| New value | 90 | 110 | 12.5% to 37.5% | 25.0% (100%) |
| Original value | 72 | 88 | 38.9% to 13.6% | 25.3% (101%) |
Two variables at once
Percentage change by original value and new value
| Original value \ New value | 80 | 100 | 120 |
|---|---|---|---|
| 64 | 25.0% | 56.3% | 87.5% |
| 72 | 11.1% | 38.9% | 66.7% |
| 80 | 0.000% | 25.0% | 50.0% |
| 88 | -9.1% | 13.6% | 36.4% |
| 96 | -16.7% | 4.2% | 25.0% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Original value | 80 |
| New value | 100 |
| Percentage change | 25.0% |
| Absolute change | 20 |
Where the inputs come from
Original value is the starting number and new value is the number it changed to. Both should be measured in the same units and on the same basis, such as the price per unit or the total for a comparable period. The order matters: the change is measured relative to the original. If the original is zero, the percentage change is undefined, so use the absolute change instead.
When the result stops applying
Percentage change is not additive across periods: two 10% increases make 21%, not 20%. For rates and percentages, use percentage points to describe the difference. Negative originals cause confusing results.
What to compare it with
Find what percent one number is of another on the percentage calculator, and see the effect of a raise on the raise calculator. The inflation and CAGR pages apply changes over many years. The discount calculator applies a percentage decrease to a price.
People also ask
Frequently asked questions
How do I calculate percentage change?
Subtract the original from the new value, divide by the original, and multiply by 100. From 80 to 100 gives 20 divided by 80, or 25%.
Why is a 25% rise not undone by a 25% fall?
Because the fall applies to the larger, new amount. A 25% rise from 80 to 100 needs a 20% fall to return to 80.
What if the original value is zero?
The percentage change is undefined because you cannot divide by zero, so report the absolute change or use a different measure.