Percent Change Calculation Equation and Examples

The percent change calculation equation is percent change = ((new value − original value) ÷ original value) × 100%. Enter the original and new values to calculate how much the value increased or decreased, expressed as a percentage of the original.

Formula

In symbols, the equation is Percent change = ((new value − original value) / original value) × 100%. The calculator reports the result as a number of percent, so its expression multiplies the ratio by 100.

• Original value: the starting or reference amount, in the unit used for the new value.
• New value: the later or comparison amount, in the same unit.
• Percent change: the signed change relative to the original, expressed in percent.
• Absolute change: new value minus original value, in the values’ original unit.

The original value must not be zero: division by zero is undefined, so a standard percent change from zero cannot be calculated. The values can have units such as dollars, kilograms, miles, or degrees, but the two inputs must use matching units. The units cancel in the division, leaving a percentage.

Worked Example

With the calculator’s default values, the original value is 100 and the new value is 125. First find the difference: 125 − 100 = 25. Then divide by the original value and multiply by 100:

((125 − 100) ÷ 100) × 100 = (25 ÷ 100) × 100 = 25%

The percent change is 25.00%, and the absolute change is 25 units. Because the result is positive, the value increased.

How to Interpret the Result

A positive result means the new value is greater than the original; a negative result means it is lower. A result of zero means both values are equal. For example, if a quantity falls from 80 to 60, the difference is −20, and (−20 ÷ 80) × 100 = −25%. It decreased by 25%.

The percentage is relative to the starting value, not a percentage of the ending value. A change of 25 units from 100 is 25%, while the same 25-unit change from 500 is 5%. Always identify which figure is the baseline before interpreting or comparing percentages.

Percent change is a relative measure, while absolute change is the simple subtraction of the two values. Both can be useful: “up 25%” describes the change in relation to the starting amount; “up 25 units” gives its size in the original measurement.

When to Use Percent Change

Use this calculation when comparing two measurements of the same kind across time or between comparable cases. Examples include a change in monthly visitors, the weight of an object, distance traveled, or the number of items produced. It is especially useful when the starting amounts differ, because it puts changes on a relative scale.

For a reliable comparison, check that:

• The values measure the same thing and use the same unit.
• The original value is a meaningful baseline and is not zero.
• The order is correct: the earlier or reference amount is original, and the comparison amount is new.
• The reported precision is appropriate for the data. A calculator can show decimal places, but extra digits do not make approximate inputs more precise.

If units differ, convert one value first. For example, do not compare a distance in miles directly with one in kilometers. Convert both to miles or both to kilometers, then calculate the percentage change. The final percentage is the same whichever consistent unit you use.

Common Mistakes and Important Limits

Using the wrong denominator: divide by the original value, not the new value. The denominator sets the reference point, so reversing it can produce a different answer. For a move from 100 to 125, the increase is 25% of 100. The reverse move, from 125 to 100, is a 20% decrease because the starting value is now 125.

Confusing percentage points with percent change: if a rate goes from 20% to 25%, it rises by 5 percentage points. Its relative percent change is ((25 − 20) ÷ 20) × 100 = 25%. These describe different things: the first subtracts the two percentage rates; the second compares their difference with the starting rate.

Assuming increases and decreases cancel: a 10% increase followed by a 10% decrease does not return a value to its starting point. Starting at 100, a 10% increase gives 110; a 10% decrease from 110 gives 99. Each step uses the value at the start of that step as its baseline.

Starting from zero: changing from zero to a positive number has no finite, standard percent change because the formula requires division by zero. Describe the absolute change or report that the baseline was zero instead. Likewise, percent change can be difficult to interpret when the original value is very close to zero, since a small absolute difference can create a very large percentage.

The equation describes the difference between two values; it does not explain why the difference occurred or establish whether it is important. When values are estimates, rounded, or subject to measurement variation, the result should be interpreted with that uncertainty in mind.

Frequently Asked Questions

How do you calculate percent change between two numbers?
Subtract the original number from the new number, divide by the original number, and multiply by 100. Keep the sign: positive indicates an increase and negative indicates a decrease.

What is the percent change from 50 to 75?
The difference is 25. Divide 25 by the original value, 50, and multiply by 100: (25 ÷ 50) × 100 = 50%. The value increased by 50%.

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

Can you calculate percent change when the original value is zero?
Not with the standard equation. Dividing by zero is undefined, so report the absolute difference or explain that the value changed from a zero baseline.

Is percent change the same as percentage-point change?
No. Percentage-point change is the subtraction of two percentages. Percent change divides their difference by the original percentage and multiplies by 100, so the two results can differ substantially.

Related

• Factor Calculation Methods and Examples
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• Percent Change: Formula, Examples, and How to Calculate It

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