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Percent Change and Fold Change Calculator

Calculate the percent change, fold change and log₂ fold change between an old and a new value, or the symmetric percent difference between two values with no reference.

Formula

percent change=new−old∣old∣×100\text{percent change} = \dfrac{\text{new} - \text{old}}{|\text{old}|}\times 100
fold change=newold;log⁡2fold change=log⁡2newold\text{fold change} = \dfrac{\text{new}}{\text{old}};\quad \log_2\text{fold change} = \log_2\dfrac{\text{new}}{\text{old}}
percent difference=∣a−b∣(∣a∣+∣b∣)/2×100\text{percent difference} = \dfrac{|a - b|}{(|a| + |b|)/2}\times 100
old, new\text{old},\ \text{new}
the reference value and the value compared with it

How it works

Percent change expresses the difference between two values as a fraction of the original. Fold change expresses the ratio: a value that goes from 12.5 to 31 has risen 148%, or 2.48-fold. Biologists often use the log₂ fold change, because it is symmetric about zero: a doubling is +1 and a halving is −1, where as a fold change a doubling is 2 and a halving 0.5.

When neither value is the reference, for example the same quantity measured by two methods, the symmetric percent difference divides the difference by the mean of the two, so it does not depend on which is called first. Changes do not add: a 50% increase followed by a 50% decrease leaves the value 25% below where it started.

Worked example

A measurement that goes from 12.5 to 31.0.

  1. Percent change = (31.0 − 12.5) / 12.5 × 100 = +148%.
  2. Fold change = 31.0 / 12.5 = 2.48; log₂ fold change = 1.310.

An increase of 148%, which is a 2.48-fold rise, or +1.31 on the log₂ scale.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Both values are positive quantities on a ratio scale.
  • The old value is not zero; a change from zero is undefined as a percentage.

Common mistakes

  • Adding or averaging percent changes instead of combining fold changes.
  • Reporting a percent change for values near zero, or across zero, where it is meaningless.
  • Mixing up a percent change with a change in percentage points.

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