Percentage Change Calculator

Compare an original and new value, including negative numbers, with an explicitly defined percentage-change convention.

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How to Use the Percentage Change Calculator

Enter the original and new values. Read the signed difference, absolute magnitude of the difference, increase/decrease classification and percentage relative to the magnitude of the original. Results update as you edit; reset restores the worked example.

Formula and Explanation

Signed difference = new value − original value
Absolute difference = |new value − original value|
Percentage change = ((new − original) / |original|) × 100

The denominator uses the absolute original value so the sign follows numerical movement: −100 to −80 is a 20% increase, while −100 to −120 is a 20% decrease. With a zero original, a percentage relative to that baseline is undefined, even when both values are zero. The difference and classification remain meaningful. Display formatting suppresses ordinary floating-point artifacts without changing the underlying formula.

This absolute-original-value convention should be stated when comparing negative baselines; other disciplines may use a different convention or avoid negative-base percentages. A percentage-point difference between rates is not the same as relative percentage change. This tool does not adjust for inflation, compounding or time periods. Very large or extremely differently scaled values may exceed representable precision.

Worked Example

From 80 to 100, the difference is +20 and the percentage change is 20 / 80 × 100 = 25%, an increase. From −100 to −80, the difference is also +20, but the denominator is |−100| = 100, giving a 20% increase. A rate moving from 4% to 5% rises by 1 percentage point and by 25% relative to its original rate.

Frequently Asked Questions

Why use the absolute original value?

It keeps the percentage sign consistent with whether the new number is greater or smaller. For example, a move from −100 to −80 is upward and returns +20% under this stated convention.

What happens when the original is zero?

The percentage is shown as undefined rather than a misleading finite number. Differences and increase/decrease/no-change classification still appear. Zero to zero also has no defined relative percentage baseline.

What is a percentage-point change?

It is the arithmetic difference between two percentages. Moving from 4% to 5% is +1 percentage point, whereas the relative increase is (5 − 4) / 4 × 100 = 25%.

Why are long decimal artifacts not shown?

Computer decimal arithmetic can produce tiny representation errors. Results are formatted to a practical number of significant digits; the calculation itself still uses the entered values without manually rounding intermediate differences.