What this calculator does
Percentage change measures movement from a starting value to a new one, always relative to where it started. Because the base is the original value, an increase and a decrease of the same size are not symmetric: a rise from 100 to 150 is a 50% increase, but the fall back from 150 to 100 is a 33% decrease.
Percentage difference is a separate measure that avoids choosing a base at all, dividing by the average of the two values instead. It is the right tool when neither value is naturally the starting point: comparing two measurements, or two competing estimates.
The formula
Change divides the difference by the original value. Difference divides the absolute gap by the mean of the two, which makes it symmetric: you get the same answer whichever order you enter the numbers.
| Term | Meaning |
|---|---|
| Change | (new − old) ÷ old × 100. Direction matters. |
| Difference | |a − b| ÷ ((a+b)/2) × 100. Order-independent. |
| Multiplier | new ÷ old. A multiplier of 1.5 is a 50% increase. |
The inputs explained
| Field | What to enter |
|---|---|
| Original value | The original or earlier value: the base the change is measured against. |
| New value | The new or later value. |
When to use it
Reporting growth
Revenue, users, prices or population between two periods. The signed change is the figure to quote, and the direction is part of the answer.
Comparing two independent measurements
When neither value is the original, two lab results, two estimates, two suppliers, percentage difference is the honest measure, because change would arbitrarily privilege one as the base.
Understanding asymmetry after a fall
A 50% loss requires a 100% gain to recover. Running both directions makes this concrete, and it is one of the more consequential facts in investing.
Converting to a multiplier
For large changes, multipliers are clearer than percentages. A 400% increase is a fivefold multiplier, and the second phrasing is far less ambiguous.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Change from a base of 120
Moving from 120 to a range of new values.
| New value | Signed change | Absolute change | Percentage difference | Multiplier |
|---|---|---|---|---|
| 60 | -50.0% | -60.000 | 66.7% | 0.5000× |
| 96 | -20.0% | -24.000 | 22.2% | 0.8000× |
| 120 | 0.000% | 0 | 0.000% | 1.000× |
| 150 | 25.0% | 30.000 | 22.2% | 1.250× |
| 180 | 50.0% | 60.000 | 40.0% | 1.500× |
| 240 | 100.0% | 120.000 | 66.7% | 2.000× |
The asymmetry of gains and losses
Starting from various values and returning to 100 shows how much larger the recovery must be than the fall was.
| Fell from | Signed change | Multiplier |
|---|---|---|
| 110 | -9.09% | 0.9091× |
| 125 | -20.0% | 0.8000× |
| 150 | -33.3% | 0.6667× |
| 200 | -50.0% | 0.5000× |
| 300 | -66.7% | 0.3333× |
| 500 | -80.0% | 0.2000× |
Questions
Why is a 50% loss not undone by a 50% gain?
Because the second percentage applies to a smaller base. Falling from 100 to 50 is a 50% loss; gaining 50% of 50 returns only 75. A 100% gain is needed to get back to 100.
What is the difference between percentage change and percentage difference?
Change measures movement from a specific starting value and is directional. Difference compares two values symmetrically using their average as the base, giving the same answer in either order. Use change for before-and-after, difference for two peers.
How do I handle a change from zero?
You cannot express it as a percentage: dividing by zero is undefined. Report the absolute change instead, or describe it in words.
What if both values are negative?
The arithmetic still works, but interpretation gets slippery. A move from −100 to −50 is a 50% change, though describing it as an improvement is clearer than describing it as a percentage.
When should I use multipliers instead?
For large changes. "Grew fivefold" is immediately clear; "grew 400%" invites confusion with 500%. Multipliers also compose cleanly: two doublings is a multiplier of 4.
For the everyday percentage forms, use the percentage calculator. For annualised growth, see CAGR.