Time & Numbers

Percentage Change Without Confusion

Calculate increases, declines, and base effects. Read a concrete example, examine the trade-offs, and try a small exercise to see whether the principle applies to your situation.

The core rule or calculation

Start here. Subtract the old value from the new value, then divide by the old value.
Add context. A fall of 20% needs a rise of 25% to return to the original level.
Keep in mind. If the old value is zero, ordinary percentage change is undefined.

Work through an example

If a price rises from $80 to $100, the increase is 25% because the change of $20 is divided by the original $80. If it later falls from $100 to $80, the decline is 20% because the new baseline is $100.

BlogJD editorial perspective

The denominator carries the story; without identifying the baseline, a percentage can mislead even when the arithmetic is correct.

A conventional percent change from zero is undefined because division by zero is impossible. In a report, say the quantity increased from zero to the new value, or compare absolute amounts instead. Inventing an infinite percentage is rarely useful for decision-making.

A zero baseline needs special care

The standard percent-change formula is (new − old) ÷ old × 100. With an old value of 80 and a new value of 100, the numerator is 20 and the denominator is 80, producing 25%. Reversing the trip produces (80 − 100) ÷ 100 = −20%. Both results are correct for their own starting points.

The formula and denominator

Where calculations go wrong

Equal percentage rises and falls do not cancel. Using the ending number instead of the starting number changes the question being answered.

Try the method

Write “(new − old) ÷ old × 100” beside two prices and calculate the direction. Repeat the reverse trip to see why the answer is different.

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Published October 9, 2026 · BlogJD Editorial Desk · How we prepare and correct content · Report a correction.