Percentage Change vs Percentage Difference

Two percentages can describe the same pair of numbers and still not be interchangeable. Percentage change needs a starting point. Percentage difference treats the two values as peers. Percent Folio keeps them on separate calculators so the formula strip cannot quietly switch meaning.

What percentage change measures

Change = ((New − Original) / Original) × 100. It has a direction: INCREASE, DECREASE, or NO CHANGE. The change calculator on this site uses a positive original and a nonnegative new value. Original 80 to new 100 is a 25% increase. Original 100 to new 80 is a 20% decrease. Those two sentences are both true.

What percentage difference measures

Difference = |A − B| / ((|A| + |B|) / 2) × 100. The denominator is the average of the absolute magnitudes. The difference calculator allows negatives and zeros (with a documented 0% convention when both are zero). It never labels the output as an increase or decrease, because the measure has no preferred start.

Directional versus symmetric comparisons

Swap original and new, and change must move. Swap A and B, and difference must stay put. If a swapped pair changes the difference result, the implementation is wrong. If a swapped pair does not change a “percentage change” result, you are no longer measuring change from a start.

The role of the original value

Change divides by original. If original is 0, change is undefined here. Difference divides by average magnitude, so a zero paired with a nonzero value is defined: |0 − 10| / ((0 + 10) / 2) × 100 = 200%.

Average magnitude

For 40 and 60, average magnitude is (40 + 60) / 2 = 50. Absolute difference is 20. 20 / 50 × 100 = 40%. That 40% is example 10 on the examples list. It is not the 50% increase you get by treating 40 as original and 60 as new: ((60 − 40) / 40) × 100 = 50%.

Negative values

The change tool refuses a negative original and a negative new value, because this version is for nonnegative quantities. Difference takes signs into the absolute values. Opposite-sign values of equal magnitude, such as 10 and −10, have absolute difference 20 and average magnitude 10, so the difference is 200%.

Zero values

Both zero: difference reports 0% and explains that the ordinary ratio would have a zero denominator, so the tool uses an identical-zero convention. One zero: 200% difference. Change still will not use original 0.

Percentage points

A move from 20% to 25% is 5 percentage points and a 25% relative increase. Neither of those is a percentage difference between 20 and 25, which would be |20 − 25| / ((20 + 25) / 2) × 100 ≈ 22.22%. Three different sentences, three formulas. Name the one you need before you open a calculator.

Choosing the correct formula

Use change when you have a before and an after: enrollment this year versus last year, a price that used to be 80 and is now 100. Use difference when neither value is the baseline: two laboratory readings, two quoted quotes, two independent measurements. Use points when both numbers are already percents and you are subtracting them as percents. Use the percentage of a number tool when you are not comparing two observed values at all, but taking P% of N.

Side by side, 40 and 60:

Change, 40 → 60: 50% increase.
Change, 60 → 40: about 33.33% decrease.
Difference, either order: 40%.

Related: increase and decrease and the formula reference.

FAQ