Percent Change: Formula, Examples, and How to Calculate It

Percent change shows how much a value increased or decreased relative to its starting value. Enter the original value and the new value to calculate the percent change, along with the absolute difference; a positive result means an increase and a negative result means a decrease.

Formula

Percent change = (new value − original value) ÷ original value × 100. The calculator’s first result is the percent change, expressed as a percentage. The second result is the signed absolute difference in the same units as the values entered.

• Original value: the starting amount, before the change. It must be greater than zero for this formula.
• New value: the amount after the change, measured on the same scale and in the same units.
• Percent change: the difference divided by the original value, multiplied by 100.
• Absolute difference: new value minus original value. It is positive for an increase and negative for a decrease.

The formula is often written as ((new − original) / original) × 100%. The denominator is the original value because the question is how large the change is compared with where the quantity began.

Worked Example

Using the calculator’s default values, the original value is 100 and the new value is 125. The calculations are:

1. Subtract the original value: 125 − 100 = 25.
2. Divide by the original value: 25 ÷ 100 = 0.25.
3. Convert to a percentage: 0.25 × 100 = 25%.
4. Find the absolute difference: 125 − 100 = 25.

The result is a 25% increase, with an absolute difference of 25 units. The percentage is unitless: whether the values are dollars, kilograms, points, or something else, the calculation is the same as long as both values use the same unit.

How to Interpret the Result

A positive percent change means the new value is greater than the original; a negative percent change means it is smaller. A result of 0% means the two values are equal. For example, if a quantity changes from 80 to 60, the difference is −20, and −20 ÷ 80 × 100 = −25%. This is a 25% decrease.

Percent change describes relative movement, not the size of the change by itself. A rise of 10 units is a 10% increase when the original amount is 100, but only a 1% increase when the original is 1,000. For a useful comparison, consider both the percentage and the actual difference.

Keep the sign when it conveys direction. Saying “−25%” or “a 25% decrease” is clear; saying only “25%” leaves it uncertain whether the value went up or down. If you want the size of the change without direction, use the absolute value of the percentage, but label it as a magnitude rather than an increase or decrease.

When to Use Percent Change

Percent change is useful for comparing changes across quantities that start at different levels. It can describe changes in counts, measurements, scores, or other numerical values. It is especially informative when the starting amount matters: a difference of 5 has a different meaning if the original was 10 than if it was 1,000.

• Compare periods: compare a measurement this month with the same measurement last month, provided the definitions and units are consistent.
• Compare groups: compare relative changes for groups with different starting values, while also checking that each group’s baseline is meaningful.
• Describe a target: measure how far a new result is above or below a stated starting value.

Percent change is not always the best comparison. If the original value is close to zero, even a small absolute difference can create an unusually large percentage. In that situation, report the absolute difference too, and explain the scale and context.

Common Mistakes and Limits

• Using the wrong denominator: divide by the original value, not the new value. Reversing the denominator changes the answer.
• Mixing units: convert measurements to the same unit before subtracting. For example, do not directly compare 2 meters with 250 centimeters; first convert one value.
• Confusing percentage points with percent change: a rate moving from 10% to 15% rises by 5 percentage points. Its percent change is (15 − 10) ÷ 10 × 100 = 50%.
• Rounding too early: keep full precision during the calculation and round the final result to a sensible number of decimal places.
• Using a zero baseline: division by zero is undefined, so percent change from an original value of zero cannot be calculated with this formula. State the absolute change or choose a different comparison appropriate to the question.

The formula also assumes the values represent comparable things. A change in measurement method, category definition, or time period can make the result misleading even if the arithmetic is correct. Percent change is a description of two values; by itself, it does not explain why a change occurred.

Percent Change Versus Percent Difference

Percent change uses a designated starting value as its baseline. That makes it appropriate when values are ordered in time or one value is explicitly the original. Percent difference is used when comparing two values without treating either as the starting point; a common version divides the absolute difference by the average of the two values, then multiplies by 100.

These measures answer different questions and can produce different results. If one value is a before measurement and the other is an after measurement, use percent change. If neither is a baseline and you want a symmetric comparison, identify the percent-difference convention you are using rather than calling it percent change.

Frequently Asked Questions

How do I calculate percent change between two numbers?
Subtract the original number from the new number, divide by the original number, and multiply by 100. A positive answer indicates an increase; a negative answer indicates a decrease.

Can percent change be negative?
Yes. A negative result means the new value is lower than the original. For example, a result of −12% represents a 12% decrease.

What if the original value is zero?
The standard calculation is undefined because it requires division by zero. Report the absolute difference or use another clearly explained measure instead.

Is percent change the same as percentage-point change?
No. A move from 10% to 15% is a 5-percentage-point increase and a 50% percent change relative to the original 10%.

How do I calculate the original value if I know the new value and percent change?
For a percent change r expressed as a decimal, original value = new value ÷ (1 + r). For example, if a value after a 25% increase is 125, calculate 125 ÷ 1.25 = 100. The multiplier must not be zero.

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in old | Original value | - | 100 | 0
in new | New value | - | 125 | 0
out change | Percent change | % | (new - old) / old * 100 | 2
out difference | Absolute difference | - | new - old | 2