Work · 18+
Increase, Decrease, and Reverse Lookup
Enter two values to find the percentage change between them — positive for an increase, negative for a decrease. You can also enter an original value and a percentage to find the new value, or enter a final value and a percentage to work back to the original.
Percentage change measures how much a value has shifted relative to its starting point:
% change = ((new value − old value) / |old value|) × 100
A positive result means the value increased. A negative result means it decreased. The absolute value of the original is used in the denominator so that results are directionally intuitive even when the original is negative.
| Scenario | Original | New | % Change |
|---|---|---|---|
| Price drop | $120 | $95 | −20.83% |
| Salary raise | $65,000 | $72,000 | +10.77% |
| Investment return | $10,000 | $14,500 | +45.00% |
| Inflation adjustment | $3.50 | $4.20 | +20.00% |
These two concepts are frequently confused. If a tax rate rises from 20% to 25%, the change is 5 percentage points — but the percentage change in the tax rate is (25 − 20) / 20 × 100 = +25%.
Percentage points are an absolute difference between two values already expressed as percentages. Percentage change is a relative shift from a base value. Financial reporting and medical research use both; mixing them up changes the meaning significantly.
A 50% drop followed by a 50% gain does not restore the original value. $100 drops 50% to $50 — then a 50% gain on $50 only brings it to $75. To fully recover, the gain must be 100% on the reduced base.
This asymmetry means consecutive percentage changes do not cancel in a simple way. For modeling multiple compounding periods, use a compound interest calculator.
FAQ
Short answers for readers and answer engines.
Percentage change is a relative shift — (new − old) / old × 100. Percentage points are an absolute difference between two values that are already expressed as percentages. If an approval rating goes from 40% to 55%, that is 15 percentage points but a 37.5% percentage change.
Because the base changes. A 50% loss on $100 leaves $50. A 50% gain on $50 brings you to $75, not $100. To recover $50 from a $50 base requires a 100% gain. Percentage changes compound on the new base, not the original.
Mathematically yes, but interpretation requires care. The formula still works for negative original values — it uses |original| in the denominator to maintain an intuitive sign. Whether the result matches field-specific conventions (finance, science) depends on context.
Percentage change is undefined. The formula divides by the original value, and division by zero has no result. Describe the change as an absolute value instead.
A single percentage change applies once to a fixed base. Compound interest applies a rate repeatedly, with each period's result becoming the new base. For modeling multiple periods of growth or decline, use a compound interest calculator.
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