Percentage change is the single most common calculation in business reporting, and it is also the one most often done wrong. The rule that trips people up is that the percentage is always measured against the starting value, never the ending one. This percentage change calculator takes the original and the new number and gives you the change in both absolute and percentage terms, along with the reverse calculation you need to undo it.
What Is the Percentage Change Calculator?
Percentage change describes how much a value moved relative to where it started. If a price rises from 100 dollars to 125 dollars the change is 25 dollars and the percentage change is 25 percent, because the original value is the denominator.
The calculator also returns the reverse move, which is the percentage decrease needed to get from the new figure back to the original. That number is always slightly larger in magnitude than the increase, and knowing why is the quickest way to catch a common mistake.
How the Percentage Change Formula Works
Percentage change = (New value − Original value) ÷ |Original value| × 100
Using the absolute value of the original figure keeps the sign of the change meaningful when the starting number is negative. So a move from minus 50 to minus 25 is a positive 50 percent change, because the position has genuinely improved even though the raw arithmetic gives a misleading answer.
The undo percentage is calculated against the new value rather than the original: (Original − New) divided by New. That is why a 50 percent rise needs a 33.33 percent fall to reverse it, not 50 percent.
Why the Reverse Percentage Is Not the Same
The percentages are not symmetrical because they are measured against different bases. Going from 100 to 120 is a 20 percent increase, and going from 120 back to 100 is a 16.67 percent decrease, because the second calculation divides by 120 while the first divided by 100.
This is why claims such as a 50 percent loss followed by a 50 percent gain do not cancel out. The starting value and ending value differ, and every subsequent percentage is measured against the most recent figure. Always work from the actual numbers rather than adding or subtracting percentages.
Common Uses
Percentage change is the standard way to report price movements, headcount growth, budget overruns and year-on-year results. In each case the comparison should be against the equivalent period in the previous year, not against the most recent period.
When you report it, also state the absolute change and the starting value. A 40 percent increase sounds dramatic until you learn it is a rise from 15 to 21, and the context determines whether the change matters.
Frequently Asked Questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. For example, a price rising from 80 dollars to 100 dollars gives (100 minus 80) divided by 80, which is 25 percent.
How do I calculate a percentage decrease?
Use the same formula, which will produce a negative number, and report it as a decrease. From 200 dollars down to 150 dollars is a change of negative 50 over 200, which is a 25 percent decrease.
Why is a 50 percent loss not recovered by a 50 percent gain?
Because the two percentages use different bases. Starting from 100 dollars, a 50 percent loss leaves 50 dollars, and a 50 percent gain on 50 dollars is only 25 dollars, giving 75 dollars rather than the original 100.
What happens if the original value is zero?
A percentage change from zero cannot be expressed as a finite number, because it would require dividing by zero. The calculator reports the change as not defined in that case and still shows the absolute difference.
Should I use the absolute value of the original value?
Yes when the starting figure is negative. A company moving from a loss of 50 million to a loss of 25 million has improved by 50 percent, and taking the absolute value of the base expresses that correctly.