Compare two values and see the percent increase or decrease. With direction indicator and step-by-step working shown for every answer.
Percent change measures how much a value has grown or shrunk relative to its original value:
percent change = (new − old) ÷ old × 100A positive result is an increase; a negative result is a decrease. Going from 80 to 100 is a 25% increase. Going from 100 to 75 is a 25% decrease.
This is the most common pitfall. A 50% increase followed by a 50% decrease does NOT return to the original.
100 × 1.50 = 150 (after 50% increase)
150 × 0.50 = 75 (after 50% decrease)To return from 150 back to 100, you need a 33.3% decrease, not 50%. This is why percent change always needs a clear “from” value.
Use percent change when there’s a clear chronological order or one value is the baseline (stock prices over time, year-over-year revenue).
Use percentage difference when comparing two values neither of which is clearly the “original” (gas prices in two cities, scores from two teams). Percentage difference uses the average of the two values as the denominator, making it symmetric.
A 25% increase. The math: (100 − 80) ÷ 80 × 100 = 20 ÷ 80 × 100 = 25%.
Because the second percentage is taken from the increased value, not the original. $100 + 50% = $150, then $150 − 50% = $75. To return to $100 from $150 needs only a 33.3% decrease.
Percent change measures relative size: going from 5% to 10% is a 100% increase. Percentage points measures absolute size: going from 5% to 10% is a 5 percentage point increase. These are confused in media reporting all the time.
Yes. A negative value indicates a decrease. Going from 100 to 75 is a −25% change (or equivalently, a 25% decrease).
Percent change is undefined when the old value is zero — you cannot divide by zero. In practice, just describe the new value as “new” rather than expressing as a percent change.