The Percentage Change Formula
Percentage change is one of the most frequently used calculations in business, science, finance, and everyday life. It expresses the magnitude and direction of a change relative to the original value, normalising changes of different absolute sizes onto a common percentage scale for direct comparison.
The Calculation Protocol
A positive result indicates an increase. A negative result indicates a decrease. The absolute value in the denominator handles cases where the original value is negative.
Key Concepts
Percentage Change vs Percentage Difference
These are different calculations. Percentage change uses the original value as base — it is directional and order-dependent. Percentage difference uses the average of both values as base and is symmetric (order does not matter). Use percentage change for before/after comparisons. Use percentage difference when comparing two equivalent measurements with no reference point.
The Multiplier
The multiplier is the ratio of the new value to the original. A 25% increase has a 1.25× multiplier. A 50% decrease has a 0.5× multiplier. Multipliers are essential for chaining changes: a value that increases 20% then decreases 20% has chained multipliers of 1.20 × 0.80 = 0.96 — a net decrease of 4%, not zero.
When the Original Value Is Zero
Percentage change is mathematically undefined when the original value is zero — you cannot divide by zero. In practice, a metric moving from zero to any positive value is described as an infinite increase or simply not calculable as a percentage. This is why the calculator requires a non-zero original value.