Percentage Change Calculator
Enter an old (starting) value and a new (ending) value to instantly see the percentage change between them, whether that change is an increase or a decrease, and the raw numeric difference.
How this calculation works
Percentage change measures how much a value has grown or shrunk relative to where it started. The formula is: percent change = (new value − old value) ÷ |old value| × 100. The old value is always the base — that is what "relative to" means here.
Because the old value is the base, a rise and an equivalent fall are not symmetric. Going from 50 to 100 is a 100% increase, but going back from 100 to 50 is only a 50% decrease, even though the raw difference (50) is identical both times.
If the old value is zero, percentage change is mathematically undefined (you cannot divide by zero) — this calculator reports it as undefined rather than showing a misleading number.
Worked example
Increase vs. decrease, at a glance
Whether a change counts as an increase or a decrease depends only on the sign of the difference (new value minus old value). A positive difference is an increase, a negative difference is a decrease, and a difference of exactly zero means no change occurred.
| Old value | New value | Difference | % change | Direction |
|---|---|---|---|---|
| 80 | 100 | +20 | +25.00% | Increase |
| 100 | 80 | −20 | −20.00% | Decrease |
| 50 | 75 | +25 | +50.00% | Increase |
| 200 | 150 | −50 | −25.00% | Decrease |
| 40 | 40 | 0 | 0.00% | No change |
Why the old value is always the base
Think of percentage change as answering "how big is the move, relative to where I started?" That framing only makes sense if the starting point is the denominator. It also keeps the math consistent with everyday language: if a 100 item is discounted by 25%, it drops to 75 — a change of −25/100 = −25%, using the original 100 as the base, not the new 75.
Percentage change vs. percentage points
- Percentage change is relative: it compares the size of the difference to the old value (a ratio).
- A percentage point is absolute: it is simply the arithmetic difference between two percentage figures.
- Example: unemployment moving from 4% to 6% is a 2 percentage point rise, but a 50% relative increase (2 ÷ 4 × 100).
- Financial, medical, and political reporting often blur these two — always check which one a headline is using.
- This calculator computes relative percentage change, the ratio-based figure, not percentage points.
Common real-world uses
Percentage change shows up constantly outside pure math homework. Retailers use it to describe price rises and markdowns; investors use it to describe stock or portfolio returns; analysts use it to compare sales, traffic, or population figures year over year; and scientists use it to express the relative size of an experimental effect.
In every case the same rule applies: identify which figure is the "before" (old) value, and divide the change by that number, never by the "after" (new) value.