Percentage Increase Calculator

The percentage change between two values, and the figure nobody expects: the percentage needed to get back where you started is not the same one.

Change

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Change—

Absolute difference—

Multiplied by—

To get back to the start—

How this was worked out

The rule

change % = (final − initial) ÷ initial × 100

Why it works

Percentage change measures the difference against the starting value, not against the final one. That choice of reference is the whole subtlety: the same absolute difference gives a different percentage depending on which end you divide by.

How to do it by hand

Subtract the starting value from the final one
Divide the result by the starting value
Multiply by 100
A positive answer is a rise, a negative one a fall

What is worth knowing

The asymmetry catches everyone out. A 50 % rise is undone by a 33.3 % fall, not by another 50 %, because the second percentage is taken from a bigger number. That is why a stock that drops 50 % needs to double just to break even, and why a shop can advertise '50 % off' and then '50 % extra' and end up nowhere near where it started. Whenever a percentage is quoted, the question worth asking is: a percentage of what?

Frequently asked questions

How do you calculate percentage increase?

Subtract the old value from the new one, divide by the old value, and multiply by 100.

Why does a 50 % rise need a 33 % fall to undo it?

Because the fall is taken from a larger base. Going from 100 to 150 is +50 %, and going back from 150 to 100 is −33.3 %.

What if the starting value is zero?

The calculation is undefined: you cannot measure a proportional change against nothing. Only the absolute difference means anything.

Is percentage change the same as percentage difference?

No. Percentage change has a clear before and after; percentage difference compares two values against their mean, with no direction.