Math · 5 min read
How to Calculate Percentage Change
New minus old, divided by old — the sign is the story
Percentage change answers how far a number moved relative to where it started, not what share it is of a whole. This tutorial walks through (new − old) / old × 100, a 100 → 125 worked example (a 25% increase), and a signed bar that shows increase versus decrease. It is not the same question as “what is P% of X.”
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Percent change always uses the starting value in the denominator. A zero start is undefined. Percentage points (a rate moving from 10% to 12%) are a different measure.
1.Percentage change measures how far a value moved relative to where it started
You need two readings of the same quantity: an old (start) value and a new (end) value. The result is a signed percent of the start. Positive means increase; negative means decrease. “12 is what percent of 80” and “what is 15% of 80” are part–whole questions. Percent change is a movement question. A 15% rise followed by a 15% fall does not return to the start, because the second move uses a new base.
2.Calculate percentage change with (new − old) ÷ old × 100
Subtract the old value from the new value, divide by the old value, then multiply by 100. The old value must be nonzero. The units cancel, so the same identity works for prices, headcount, or scores. Using the new value (or an average of old and new) in the denominator answers a different question and will not match this formula.
\[ \%\Delta = \frac{\text{new} - \text{old}}{\text{old}} \times 100 \]
3.Worked example: 100 to 125 is a 25% increase
The Percentage Calculator’s percent-change fields default to 100 → 125. New minus old is 125 − 100 = 25. Divide by the start: 25 / 100 = 0.25. Times 100 is a 25% increase. From 100 down to 80: (80 − 100) / 100 × 100 = −20%, a 20% decrease. From 80 up to 100 is +25%, not +20% — the base changed.
\[ \frac{125-100}{100}\times 100=25\% \]
4.Signed percent bar: increase versus decrease
Move the old and new sliders. The bar grows right for an increase and left for a decrease, with 0% at the center. The caption substitutes your numbers into (new − old) / old × 100. This is a teaching widget — no part-of mode, no full calculator chrome. Open the Percentage Calculator when you want percent-of, reverse percent, and change on one page.
Inline playground
+25% increase
Percent change
25.00%
(125 − 100) / 100 × 100 = 25%
Teaching aid only — the denominator is always the old value. A zero start is undefined. This widget does not compute “P% of X.”
Open the full Percentage calculator →5.Open the Percentage Calculator for the other percent setups
The Percentage Calculator uses this same change identity, the same 100 → 125 example, and two other boxes: P% of X, and X as a percent of Y. Use those when the question is a share of a whole rather than a move from old to new.
Try it yourself
Open the related calculator and put these formulas to work.