Percentage Change Calculator
Percentage change = (new value - old value) / old value x 100.
Set the old and new values
Enter the old value first and the new value second. The order matters because the calculator measures movement from the old value to the new value. Use this for prices, scores, counts, measurements, traffic, grades or any before and after comparison.
Do not use this tool when neither value is the starting point. If you are comparing two estimates or two measurements without direction, percentage difference may describe the situation better.
Increase or decrease in plain English
A positive result means the new value is higher than the old value. A negative result means it is lower. The number tells you the size of the movement relative to the old value.
For example, going from 50 to 65 is a 30 percent increase. Going from 65 to 50 is about a 23.08 percent decrease. The two directions are not mirror images because the base changes.
Percentage change formula
Percentage change = (new value - old value) / old value x 100. The subtraction gives the amount of change. Dividing by the old value turns that change into a relative comparison. Multiplying by 100 expresses it as a percent.
If the old value is zero, the normal formula breaks. You cannot divide by zero. In that case, describe the absolute change instead of forcing a percent change.
From 50 to 65
Suppose a count rises from 120 to 150. The change is 30. Divide 30 by the old value, 120, then multiply by 100. The result is 25 percent. If the count falls from 150 to 120, the change is -30. Divide -30 by 150 and multiply by 100. The decrease is -20 percent.
This explains why people often get different answers when they reverse the inputs. The base value changed.
The old value mistake
The most common mistake is putting the new value in the denominator. The old value belongs there because it is the reference point for the change.
Another mistake is using percentage change when the question asks for percentage difference. If one value came first in time, use change. If neither value is the original, use difference.
Percentage Change Calculator FAQ
How do I calculate percentage change?
Subtract the old value from the new value. Divide that change by the old value. Multiply by 100. The formula is (new - old) / old x 100.
For a move from 50 to 65, the change is 15. Divide 15 by 50 and multiply by 100. The result is 30 percent.
Why does the old value go in the denominator?
The old value is the starting point. Percentage change asks how large the movement is compared with where the value began.
If you use the new value instead, you are measuring the same difference against a different base. That produces a different percent and answers a different question.
Can percentage change be negative?
Yes. A negative percentage change means the new value is lower than the old value. For example, moving from 100 to 80 gives (80 - 100) / 100 x 100, which is -20 percent.
The negative sign is useful because it shows direction. Removing it can hide whether the value increased or decreased.
What if the old value is zero?
The standard percentage change formula cannot be used when the old value is zero. Division by zero is undefined. A move from 0 to 10 is an absolute increase of 10, but it is not a normal percent increase from zero.
Use wording such as increased by 10 units, or explain the starting value was zero.
Is percentage change the same as percentage difference?
No. Percentage change has direction and uses the old value as the base. Percentage difference compares two values without choosing an original value, often using their average as the base.
Use percentage change for before and after situations. Use percentage difference for side by side comparisons.