Percentage Change Calculator
Calculate the percentage increase or decrease between two values. Enter the original value and the new value — the calculator shows the percentage change, the absolute change, and whether it is an increase or decrease.
What Is Percentage Change?
Percentage change measures the difference between an old value and a new value as a percentage of the old value. It is the standard way to express growth, decline, inflation, sales performance, price changes, and countless other comparisons.
A 20% increase means the new value is 20% larger than the old value. A 20% decrease means the new value is 20% smaller than the old value. The direction is critical — a 20% increase followed by a 20% decrease does not return to the starting point (see FAQ below).
Percentage Change Formula
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
Expanded:
- Positive result — increase (new value is larger)
- Negative result — decrease (new value is smaller)
- Zero result — no change
Multiplier = New Value ÷ Old Value
Worked Examples
Example 1 — Increase: Old = 1000, New = 1200
Change = (1200 − 1000) ÷ 1000 × 100 = +20%
Absolute change = +200
Multiplier = 1.20×
Example 2 — Decrease: Old = 1200, New = 1000
Change = (1000 − 1200) ÷ 1200 × 100 = −16.67%
Absolute change = −200
Multiplier = 0.833×
Note: a 200 increase from 1000 is 20%, but a 200 decrease from 1200 is 16.67% — the base matters.
Frequently Asked Questions
Why is a 20% increase followed by a 20% decrease not zero?
Because the percentages are calculated on different bases. Start with 100: +20% = 120. Then −20% of 120 = 120 − 24 = 96. You end up at 96, not 100. The decrease is calculated on the new, higher amount. The general rule: (1 + x)(1 − x) = 1 − x² — so a 20% increase then 20% decrease always gives a net loss of 4%, not 0%.
What if the old value is zero?
Percentage change from zero is mathematically undefined — you cannot divide by zero. If the old value is zero, any new value is technically an "infinite" percentage change. In practice, do not use percentage change when the base is zero. Instead, report the absolute change ("went from 0 to 500") or use a different measure (e.g., growth rate over time, or absolute difference).
What is the difference between percentage change and percentage point change?
Percentage change is relative to the old value. Percentage point change is an absolute difference between two percentages. For example: if an interest rate goes from 5% to 7%, that is a 2 percentage point increase, but a 40% increase in the rate itself (2 ÷ 5 × 100). These are often confused in finance and economics reporting. Both are correct, but the meaning is very different.
Can percentage change be negative?
Yes — negative percentage change means the value decreased. A result of −20% means the new value is 20% lower than the old value. This is normal for declining values (prices, revenue, market share). Negative change is not an error; it is a direction indicator. A −100% change means the value dropped to zero.
Does the sign of the change matter?
Yes — the sign indicates direction. Positive = increase, negative = decrease. This matters because a 10% increase and a 10% decrease have different absolute effects and different implications. When reporting percentage change, always specify the direction ("increased by 10%" or "decreased by 10%") rather than only the magnitude.
How do I calculate percentage change between multiple periods?
For two periods, use the formula above. For multiple periods, you can calculate year-over-year change for each period (e.g., 2024 vs 2023, then 2025 vs 2024), or calculate a compound annual growth rate (CAGR) across the whole period: CAGR = ((End Value ÷ Start Value)^(1/Years)) − 1. CAGR gives a single average annual rate, which is more useful than the raw total change over multiple years. CAGR is the more honest measure of growth than the average of individual percentage changes.