Working out a percentage change
A percentage increase or decrease measures how much a number has changed relative to where it started. The method is simple: take the difference between the new and old values, divide by the old value, and multiply by 100. A positive result is an increase, a negative one is a decrease. This calculator does both directions from the same two inputs.
Two examples
A price rises from 80 to 100. The change is 20, and 20 divided by 80 is 0.25, so that is a 25% increase. Notice it is measured against the original 80, not the new 100.
Now a price falls from 200 to 150. The change is minus 50, and 50 divided by 200 is 0.25, so that is a 25% decrease. Same 25%, opposite direction, and both are worked out against the starting value.
What is the mistake to avoid?
Always divide by the original value, not the new one. A rise from 80 to 100 is a 25% increase, but the reverse, a fall from 100 to 80, is only a 20% decrease, because the starting point changed. Percentage increases and decreases are not symmetric, which trips people up constantly with prices and discounts.
Frequently asked questions
How is percentage change calculated?
Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive answer is an increase, a negative one a decrease.
Why isn't a 25% rise cancelled by a 25% fall?
Because each percentage is measured against a different starting value. A rise from 80 to 100 is 25% up, but the fall back from 100 to 80 is only 20% down.
Can the result be negative?
Yes. A negative percentage means the value went down. The calculator shows the direction along with the size of the change.
What if the original value is zero?
Percentage change is undefined from a starting value of zero, since you cannot divide by zero. You need a non-zero original value for the percentage to mean anything.