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Percent Change

Also known as percent increase · percent decrease

c=xnew−xoldxoldc = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}

Worked example: 80 → 100 is a +25% change (c = 0.25) — press Try an example to run it live, then adjust anything.

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Percent Change explained

cxoldxnew

Percent change measures a difference relative to where you started: a price moving from $80 to $92 changed by (92 − 80)/80 = 0.15, a 15% rise; a fall from $80 to $68 gives −0.15. Pick the % display unit to see it as a percentage directly, and note that the old value is always the reference — which is why a 50% loss needs a 100% gain to break even.

The rearrangements handle both everyday directions: what a $60 jacket costs after a 30% markup (60 × 1.30 = $78), and the reverse — the pre-sale price of an item now $45 after a 25% discount, 45 / 0.75 = $60, not $56.25 as adding 25% back would wrongly suggest.

Percent Change formula

c=xnew−xoldxoldc = \frac{x_{\text{new}} - x_{\text{old}}}{x_{\text{old}}}
Where
  • cc= Relative change
  • xnewx_{\text{new}}= New value
  • xoldx_{\text{old}}= Old value

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