The percentage change formula
Percentage change compares a new value against where it started:
A positive answer is an increase, a negative answer is a decrease, and the old value is always the base. That last part matters: a rise from 80 to 100 is +25%, but the return journey from 100 to 80 is only −20%, because each is measured against its own starting point.
Worked examples
Change or difference? Pick the right one
Percentage change has a direction and a starting point, so use it whenever time is involved: prices going up, traffic going down, growth between two dates. Percentage difference compares two values that are simply alternatives (two quotes, two brands), has no direction, and uses the average of the two as its base.
If you already know the percentage and want to apply it to a number, that is the percentage increase calculator's job instead.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new value, divide by the old value, then multiply by 100. From 80 to 100 the change is ((100 − 80) ÷ 80) × 100 = +25%. A positive result is an increase and a negative result is a decrease.
Why is the old value used as the base?
Percentage change measures movement relative to where you started. Going from 80 to 100 is a 25% increase, but going from 100 to 80 is a 20% decrease. The two directions give different percentages because the starting base is different.
How do I calculate a percentage decrease?
Use the same formula. If the new value is smaller, the result is negative. From 1,500 to 1,200 the change is ((1,200 − 1,500) ÷ 1,500) × 100 = −20%, a 20% decrease.
Can percentage change be more than 100%?
Yes, when something more than doubles. From 40 to 100 the change is ((100 − 40) ÷ 40) × 100 = +150%. Decreases, however, cannot go below −100%, which would mean losing more than everything.
What if the starting value is zero?
Percentage change from zero is mathematically undefined, because you cannot divide by zero. Any growth from nothing is infinite in percentage terms, so state the change in absolute numbers instead.