Percentage Change Calculator

Formula

Change = 100 × (New value - Original value) ÷ abs(Original value)

Worked example

With Original value: 100, New value: 120, change is 20 %.

Calculation method

The rule is Change = 100 × (New value - Original value) ÷ abs(Original value).

The difference between new and original values is divided by the absolute original value. A positive result indicates an increase and a negative result indicates a decrease.

For this percentage change example, changing original value from 100 to 101 while keeping the other inputs fixed changes change from 20 % to 18.81 %.

Reading change

The result represents a proportion or an adjusted value. A percent change is relative to the original value, while a percentage-point difference is the arithmetic difference between two percentages. In the worked values on this page, original value 100, new value 120 produce change 20 %.

Practical use

Use percentages to compare prices, scores, growth, discounts, and rates when the quantities share a meaningful reference base. The specific task here is to find change from original value, new value.

Limits and common mistakes

A change from 20% to 25% is 5 percentage points but a 25% relative increase. Mixing the two descriptions is a common source of error. Verify original value before interpreting change; a value measured on another basis would answer a different question.

Why the relationship works

A percent is a ratio expressed per hundred. Before calculating, identify the reference amount: the number of which a percentage is taken, the whole used to find a share, or the original amount used to measure change. Switching that reference changes the question even when the same two numbers appear. The percentage change rule uses original value, new value in Change = 100 × (New value - Original value) ÷ abs(Original value); read each symbol as the field named on this page.

Interpreting another set of values

For percentage change, the fields labeled original value, new value are the known quantities. The calculator solves for change in % using Change = 100 × (New value - Original value) ÷ abs(Original value). Say which quantity is the percentage base and whether the answer is a rate, a change, or a new total. Those are different outputs even when they use the same starting figures. When comparing two calculations, keep their units and input definitions identical.

For a second percentage change check, keep the other default inputs fixed and change original value from 100 to 102. Change changes from 20 % to 17.65 %. This is a comparison of two particular cases. Repeat it near the values relevant to your task; do not assume that every formula changes at a constant rate.

Checks and limits

Keep the percentage and percentage-point concepts separate. A 20% increase followed by a 20% decrease does not return to the starting value, because the second change uses a different base. Check whether you need the adjusted total, the size of the adjustment, or the rate itself before using the result. The reported change is 20 % in the worked example. Keep its stated unit or counting convention when checking it against another calculation.