Percentage Change vs Percentage Difference

Percentage language gets sloppy fast. A price can rise by 20%, two measurements can differ by 20%, and two interest rates can differ by 2 percentage points. Those are not interchangeable statements.

Percentage Change

Use percentage change when one value is the baseline and the other is the new value:

Percentage change = (new - old) / old x 100

If revenue grows from $80,000 to $100,000, the increase is 25%. The old value is the denominator because it is the starting point. If revenue falls from $100,000 to $80,000, the decrease is 20%. Percentage changes are not symmetric because the denominator changes.

The percentage calculator handles increase and decrease cases directly.

Percentage Difference

Use percentage difference when neither value is the baseline. The denominator is the average of the two values:

Percentage difference = |A - B| / ((A + B) / 2) x 100

This is useful for comparing two lab measurements, estimates, quotes, or peer values. It answers "how far apart are these numbers relative to their typical size?" rather than "how much did one change from the other?"

Percentage Points

Use percentage points when subtracting two percentages or rates:

7% - 5% = 2 percentage points

Calling that a "2% increase" is wrong. Moving from 5% to 7% is a 40% relative increase because 2 / 5 = 40%. Mortgage rates, tax rates, click-through rates, and margins often need this distinction.

Percent Of Total

Percent of total answers a different question:

part / whole x 100

If $30 of a $120 bill is tax and tip, that portion is 25% of the total. That is not a percentage change unless there is a before-and-after value.

Quick Decision Rule

• Old value to new value: percentage change.
• Two peer values: percentage difference.
• Two percentages or rates: percentage points.
• One part of a whole: percent of total.

Use the formula that matches the question. Most percentage mistakes come from choosing the denominator too casually.