Percentage Change Calculator: Percent Increase & Decrease

Percentage Change Calculator

A percentage change calculator measures how much a value grew or shrank between two points, expressed as a percent of the starting value. It can also work in the other direction: given a starting value and a percent, it applies that change and returns the new value.

What the calculator does

The calculator has two modes.

Percent change from A to B. Enter an initial value (A) and a final value (B). The calculator returns three results: the percent change, a direction label (increase, decrease, or no change), and the raw difference B − A. A positive percent means the value went up. A negative percent means it went down. The initial value cannot be zero; the calculator shows an error message in that case, because a change from zero has no defined percent.

Apply a percent change to a value. Enter a starting value (A) and a signed percent (p). The calculator returns the new value (B) and the change amount, which is how much was added or subtracted. A percent of +25 grows the value; −25 shrinks it. Here the starting value may be zero, and the result is simply zero.

Results carry an explicit plus or minus sign, so +25% and −25% are never confused. Very large or very small results switch to scientific notation with six significant digits; ordinary results show up to six decimal places.

Percent change formula

$c = \frac{B - A}{|A|} \times 100$

where c is the percent change, A the initial value and B the final value. |A| is the absolute value of A: the value with any minus sign removed.

When A is positive, |A| equals A, and this is the familiar $\frac{B - A}{A} \times 100$. The absolute value only matters when A is negative, which the next section explains.

The apply mode uses the same rule in reverse:

$B = A + \frac{p}{100} \times |A|$

where p is the signed percent. The change amount is the $\frac{p}{100} \times |A|$ part on its own.

Example: percent change from A to B

A price rises from 100 to 125.

1. Difference: 125 − 100 = 25.
2. Divide by the initial value: 25 ÷ 100 = 0.25.
3. Multiply by 100: 0.25 × 100 = 25.

The calculator reports +25%, the label "Increase", and a difference of +25.

A second example, going down: a value falls from 80 to 60. The difference is 60 − 80 = −20, and −20 ÷ 80 × 100 = −25. The calculator reports −25%, "Decrease", and a difference of −20.

Example: applying a percent change

A bill of 60 gets a 15% discount. Enter a starting value of 60 and a percent of −15.

1. Change amount: (−15 ÷ 100) × 60 = −9.
2. New value: 60 + (−9) = 51.

The calculator reports a new value of 51 and a change amount of −9.

Why the calculator divides by |A|, not A

Different tools disagree about percent change when the initial value is negative. Some divide by A itself. This calculator divides by |A|, the absolute value, following the convention described in the Wikipedia article on relative change.

The reason is that the sign of the result should say whether the quantity went up or down. Take a temperature that rises from −10 to −5. That is a gain of 5 degrees. With the |A| convention the calculator computes ((−5 − (−10)) ÷ |−10|) × 100 = (5 ÷ 10) × 100 = +50%, an increase, which matches what happened. Dividing by A itself would give 5 ÷ (−10) × 100 = −50%, which reads as a decrease even though the value went up.

The apply mode mirrors the same convention. Applying +50% to a starting value of −10 gives a change amount of (50 ÷ 100) × |−10| = +5 and a new value of −5. Each mode exactly undoes the other, whatever the sign of A.

Percent change is not symmetric

The percent depends on which value comes first. Going from 100 to 125 is a +25% change, because the difference of 25 is compared against 100. Going back from 125 to 100 is a −20% change, because the same difference of 25 is now compared against 125. Swapping A and B does not just flip the sign.

For the same reason, an increase and a decrease of the same percent do not cancel. A value of 100 raised by 25% becomes 125, but 125 lowered by 25% becomes 93.75, not 100.

Frequently asked questions

How is percent change calculated? Subtract the initial value from the final value, divide by the absolute value of the initial value, and multiply by 100. From 40 to 46, that is (46 − 40) ÷ 40 × 100 = +15%.

Why can't the initial value be zero? The formula divides by the initial value, and division by zero has no answer. There is no meaningful percent for a change that starts at zero: going from 0 to 5 is not 5% or 500% of anything. The calculator shows an error instead of a number.

What happens when the initial value is negative? The calculator divides by the absolute value of the initial value, so the sign of the result still shows the direction of the change. From −10 to −5 it reports +50%, an increase, because the value moved up by half its starting size.

What is the difference between percent change and percentage points? Percent change compares the change to the starting value. Percentage points measure the plain difference between two percentages. If an interest rate moves from 4% to 5%, that is a rise of 1 percentage point, but a percent change of +25%, since 1 is a quarter of 4.

How is a percent decrease reversed? Not by applying the same percent as an increase. A 20% decrease from 100 gives 80, and a 20% increase from 80 gives 96. To get back to 100 from 80 requires a +25% change, which the percent-change mode finds directly from the two values.