What is the percentage change formula?

Subtract the old value from the new value, divide by the absolute old value, then multiply by 100.

Why is change from zero undefined?

A zero old value cannot be used as the denominator, so the percentage change is not mathematically defined.

Yes. A move from 100 to 250 is a 150% increase.

Calculate percentage increase or decrease from an old value to a new value, including signed percent change, absolute difference, and multiplier.

Old value

New value

Percentage change is directional. It answers how much a value increased or decreased from an old value to a new value.

P_{c han g e} = \frac{n e w - o l d}{∣ o l d ∣} \cdot 100%, ∣ o l d ∣ \neq = 0

P_change is the signed percentage change, old is the starting value, and new is the ending value.

If the old value is zero, percentage change is undefined because the formula divides by the old value.

Use it for before/after values such as price, revenue, count, test score, or measurement changes.
Use a positive result for increase and a negative result for decrease.
Use percentage difference instead when the two values are peers and neither one is the starting point.

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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