Percentage Change Calculator
Find how much something went up or down in percent, with the direction, the absolute change and the formula shown. Also compares two values without a "before" and "after".
The percentage change formula
Percentage change = (New − Old) ÷ |Old| × 100
A positive result is an increase and a negative result is a decrease. The change is always measured relative to the old value, which is why the order of the two numbers matters. The vertical bars mean the absolute value of the old value, which keeps the sign meaningful when the starting value is negative.
Example: a monthly bill rises from 80 to 100. The change is 100 − 80 = 20, and 20 ÷ 80 × 100 = 25% increase. If the bill then falls from 100 back to 80, the change is −20 ÷ 100 × 100 = 20% decrease. Same two numbers, different percentages, because the base changed.
Percentage change or percentage difference?
Use percentage change when one value clearly comes first: last year and this year, the old price and the new price. Use percentage difference when neither value is the reference, such as comparing prices in two shops or two measurements of the same thing:
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Dividing by the average of the two values makes the answer the same whichever value you call A. For 80 and 100 the difference is 20 ÷ 90 × 100 ≈ 22.22%. Some fields, such as laboratory science, use this formula routinely; in everyday use "percentage difference" is often used loosely to mean percentage change, so check which one a report means.
Percentage points are not percentages
When the values are themselves percentages, the plain subtraction is measured in percentage points. If unemployment goes from 4% to 5%, it rose by 1 percentage point, which is a 25% relative increase. News reports, interest rates and survey results are often misread because the two are mixed up. If both of your inputs are percentages, the “absolute change” shown by the calculator is the change in percentage points.
Common questions
What if the old value is zero?
Percentage change from zero is undefined: any increase from nothing is infinitely large relative to the start. The calculator shows the absolute change instead. Percentage difference still works as long as the two values are not both zero.
How do I reverse a percentage change?
To get back to the original after an increase of p%, divide by (1 + p ÷ 100). After a 25% increase to 100, the original was 100 ÷ 1.25 = 80. The required decrease is p ÷ (100 + p) × 100, which here is 20%.
How do I combine several changes in a row?
Multiply the growth factors. A 10% rise followed by a 10% rise is 1.10 × 1.10 = 1.21, a 21% total increase, not 20%. To find an average yearly rate over several years, take the n-th root of the total factor, which is a geometric average rather than an arithmetic one.