Why is a rise of 50% then a fall of 50% not back where it started?

Because each percentage applies to a different base. 100 rises to 150, and 50% off 150 is 75. To undo a rise of x% you divide by (1 + x/100) rather than subtracting the same percentage.

What happens when the starting value is zero?

There is no percentage change from zero. Any increase from nothing is infinite in percentage terms, so this tool declines rather than reporting a very large number. Report the absolute change instead.

Math & Statisticspercentage

Percentage Change Calculator

Percentage change between two values, in either direction, with the absolute change shown alongside. Handles a negative starting value, which most calculators get wrong.

Also called: percent change, percentage difference between two numbers.

Percentage change

24%

From 250 to 310 is a an increase of 24%, an absolute change of 60.

Absolute change

Size of the change (%)

Direction

an increase

How this is calculated

Method and background

How this is calculated

The difference over the original value. The subtlety is the denominator: dividing by the absolute value of the start keeps the sign of the change meaningful when the starting figure is negative. A loss shrinking from −100 to −50 is a 50% improvement, not a −50% one.

change = (to - from) / abs(from) * 100

V_1: The earlier value
V_2: The later value

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

250 to 310 is +24%

From: 250
To: 310

Percentage change24%

arithmetic identity

Open this example

a negative start still gives a sensible sign

From: -100
To: -50

Percentage change50%

boundary: a shrinking loss is an improvement

Open this example

from zero is undefined, not infinite

From: 0
To: 50

Percentage change0%

degenerate case: guarded division

Open this example

Frequently asked questions

Why is a rise of 50% then a fall of 50% not back where it started?: Because each percentage applies to a different base. 100 rises to 150, and 50% off 150 is 75. To undo a rise of x% you divide by (1 + x/100) rather than subtracting the same percentage.
What happens when the starting value is zero?: There is no percentage change from zero. Any increase from nothing is infinite in percentage terms, so this tool declines rather than reporting a very large number. Report the absolute change instead.