Percentage Change from an Old Value to a New Value

Find relative increase or decrease from an initial value, with the signed difference, multiplier, and zero-baseline limit.

Percentage Change Calculator

What the change measures

This calculator compares a final value with an initial value. Enter the starting quantity in Initial Value and the later quantity in Final Value. The percentage describes the difference relative to the size of the start. Compare amounts expressed in the same unit and measured on a comparable basis; an increase of 20 dollars and an increase of 20 people are different quantities even if the arithmetic is similar.

Formula and units

Let I be the initial value and F the final value. The absolute change is F − I, retaining the input unit. The percentage change is ((F − I) ÷ |I|) × 100, where |I| is the magnitude of I. The multiplier is F ÷ I. For a positive starting value, a positive percentage is an increase and a negative one is a decrease. The absolute denominator preserves the direction of F − I even when I is negative. A starting value of zero is rejected because relative change cannot use a zero baseline.

Worked example: 80 to 100

Enter Initial Value = 80 and Final Value = 100. Absolute Change is 100 − 80 = 20, Percentage Change is (20 ÷ 80) × 100 = +25.00%, and Multiplier is 100 ÷ 80 = 1.25. The result card displays all three values with two decimal places. If the values are prices in dollars, the absolute change is $20, while +25% and 1.25 are unitless comparisons. A reverse move from 100 to 80 is −20%, because it uses 100 as the new baseline.

Limits and interpretation

The form treats equal values as no change and accepts negative values, but crossing zero or using negative baselines can make everyday labels such as growth misleading. State the starting value and sign when reporting those cases. Do not use this result for a difference between two rates already expressed as percentages: 10% to 9% is a decline of one percentage point, while the relative change in the rate is −10%. Display values are rounded to two decimal places, so keep the original inputs for decisions that need more precision.

Common questions

Why is an increase from 80 to 100 not reversed by a 25% decrease?

The return trip starts at 100, so a fall of 20 is 20% of that new baseline. A 25% decrease from 100 would end at 75.

What happens if Initial Value is zero?

The form rejects zero as an initial value because the relative-change formula would divide by zero. The absolute difference can still be found separately.

Sources

Last reviewed: 2026-09-28.